%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG154+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Thu Jul 14 18:30:38 EDT 2022 % Result : Unsatisfiable 29.69s 29.89s % Output : Proof 30.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG154+1 : TPTP v8.1.0. Released v2.7.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Thu Jun 9 02:27:53 EDT 2022 % 0.12/0.33 % CPUTime : % 29.69/29.89 (* PROOF-FOUND *) % 29.69/29.89 % SZS status Unsatisfiable % 29.69/29.89 (* BEGIN-PROOF *) % 29.69/29.89 % SZS output start Proof % 29.69/29.89 Theorem zenon_thm : False. % 29.69/29.89 Proof. % 29.69/29.89 assert (zenon_L1_ : (~((e0) = (e0))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H1d. % 29.69/29.89 apply zenon_H1d. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L1_ *) % 29.69/29.89 assert (zenon_L2_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H1e zenon_H1f zenon_H20. % 29.69/29.89 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 29.69/29.89 cut (((e1) = (e1)) = ((e0) = (e1))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H20. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H21. % 29.69/29.89 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.89 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 29.69/29.89 congruence. % 29.69/29.89 cut (((op (e0) (e1)) = (e0)) = ((e1) = (e0))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H23. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H1e. % 29.69/29.89 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.89 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 29.69/29.89 congruence. % 29.69/29.89 exact (zenon_H24 zenon_H1f). % 29.69/29.89 apply zenon_H1d. apply refl_equal. % 29.69/29.89 apply zenon_H22. apply refl_equal. % 29.69/29.89 apply zenon_H22. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L2_ *) % 29.69/29.89 assert (zenon_L3_ : ((op (e2) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H25 zenon_H26 zenon_H27. % 29.69/29.89 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.89 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H27. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H28. % 29.69/29.89 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.89 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 29.69/29.89 congruence. % 29.69/29.89 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H2a. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H25. % 29.69/29.89 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 29.69/29.89 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.89 congruence. % 29.69/29.89 apply zenon_H29. apply refl_equal. % 29.69/29.89 apply zenon_H2b. apply sym_equal. exact zenon_H26. % 29.69/29.89 apply zenon_H29. apply refl_equal. % 29.69/29.89 apply zenon_H29. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L3_ *) % 29.69/29.89 assert (zenon_L4_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H1e zenon_H2c zenon_H2d. % 29.69/29.89 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.69/29.89 cut (((e3) = (e3)) = ((e0) = (e3))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H2d. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H2e. % 29.69/29.89 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.89 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 29.69/29.89 congruence. % 29.69/29.89 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H30. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H1e. % 29.69/29.89 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.89 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 29.69/29.89 congruence. % 29.69/29.89 exact (zenon_H31 zenon_H2c). % 29.69/29.89 apply zenon_H1d. apply refl_equal. % 29.69/29.89 apply zenon_H2f. apply refl_equal. % 29.69/29.89 apply zenon_H2f. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L4_ *) % 29.69/29.89 assert (zenon_L5_ : (~((op (e0) (e1)) = (op (e0) (op (e0) (e3))))) -> ((op (e0) (e3)) = (e1)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H32 zenon_H33. % 29.69/29.89 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 29.69/29.89 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.89 congruence. % 29.69/29.89 apply zenon_H1d. apply refl_equal. % 29.69/29.89 apply zenon_H34. apply sym_equal. exact zenon_H33. % 29.69/29.89 (* end of lemma zenon_L5_ *) % 29.69/29.89 assert (zenon_L6_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H35 zenon_H36 zenon_H33 zenon_H37. % 29.69/29.89 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H35. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H36. % 29.69/29.89 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 29.69/29.89 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 29.69/29.89 congruence. % 29.69/29.89 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e1)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H39. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H3a. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 29.69/29.89 congruence. % 29.69/29.89 apply (zenon_L5_); trivial. % 29.69/29.89 apply zenon_H3b. apply refl_equal. % 29.69/29.89 apply zenon_H3b. apply refl_equal. % 29.69/29.89 apply zenon_H38. apply sym_equal. exact zenon_H37. % 29.69/29.89 (* end of lemma zenon_L6_ *) % 29.69/29.89 assert (zenon_L7_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H3c zenon_H36 zenon_H33 zenon_H3d. % 29.69/29.89 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H3c. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H36. % 29.69/29.89 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 29.69/29.89 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 29.69/29.89 congruence. % 29.69/29.89 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e1)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H39. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H3a. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 29.69/29.89 congruence. % 29.69/29.89 apply (zenon_L5_); trivial. % 29.69/29.89 apply zenon_H3b. apply refl_equal. % 29.69/29.89 apply zenon_H3b. apply refl_equal. % 29.69/29.89 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 29.69/29.89 (* end of lemma zenon_L7_ *) % 29.69/29.89 assert (zenon_L8_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H3f zenon_H36 zenon_H33 zenon_H40. % 29.69/29.89 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H3f. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H36. % 29.69/29.89 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 29.69/29.89 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 29.69/29.89 congruence. % 29.69/29.89 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e1)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H39. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H3a. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 29.69/29.89 congruence. % 29.69/29.89 apply (zenon_L5_); trivial. % 29.69/29.89 apply zenon_H3b. apply refl_equal. % 29.69/29.89 apply zenon_H3b. apply refl_equal. % 29.69/29.89 apply zenon_H41. apply sym_equal. exact zenon_H40. % 29.69/29.89 (* end of lemma zenon_L8_ *) % 29.69/29.89 assert (zenon_L9_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e1)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H35 zenon_H3c zenon_H3f zenon_H36 zenon_H33. % 29.69/29.89 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.69/29.89 apply (zenon_L4_); trivial. % 29.69/29.89 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.69/29.89 apply (zenon_L6_); trivial. % 29.69/29.89 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.69/29.89 apply (zenon_L7_); trivial. % 29.69/29.89 apply (zenon_L8_); trivial. % 29.69/29.89 (* end of lemma zenon_L9_ *) % 29.69/29.89 assert (zenon_L10_ : (((op (e1) (op (e1) (e0))) = (e0))/\(((op (e1) (op (e1) (e1))) = (e1))/\(((op (e1) (op (e1) (e2))) = (e2))/\(((op (e1) (op (e1) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2)))/\((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3)))))))))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e2) (e2)) = (e1)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H45 zenon_H46 zenon_H25. % 29.69/29.89 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 29.69/29.89 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 29.69/29.89 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 29.69/29.89 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 29.69/29.89 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 29.69/29.89 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 29.69/29.89 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 29.69/29.89 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 29.69/29.89 exact (zenon_H56 zenon_H25). % 29.69/29.89 exact (zenon_H46 zenon_H55). % 29.69/29.89 (* end of lemma zenon_L10_ *) % 29.69/29.89 assert (zenon_L11_ : (~((e2) = (e2))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H57. % 29.69/29.89 apply zenon_H57. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L11_ *) % 29.69/29.89 assert (zenon_L12_ : (~((op (e2) (e1)) = (op (e2) (op (e2) (e2))))) -> ((op (e2) (e2)) = (e1)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H58 zenon_H25. % 29.69/29.89 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 29.69/29.89 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.89 congruence. % 29.69/29.89 apply zenon_H57. apply refl_equal. % 29.69/29.89 apply zenon_H59. apply sym_equal. exact zenon_H25. % 29.69/29.89 (* end of lemma zenon_L12_ *) % 29.69/29.89 assert (zenon_L13_ : (((op (e2) (op (e2) (e0))) = (e0))/\(((op (e2) (op (e2) (e1))) = (e1))/\(((op (e2) (op (e2) (e2))) = (e2))/\(((op (e2) (op (e2) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0)))/\(((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3)))))))))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e2) (e2)) = (e1)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H5a zenon_H46 zenon_H25. % 29.69/29.89 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 29.69/29.89 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 29.69/29.89 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 29.69/29.89 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e1)) = (e2))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H46. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H60. % 29.69/29.89 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.89 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 29.69/29.89 congruence. % 29.69/29.89 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.69/29.89 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e1)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H61. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H62. % 29.69/29.89 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.89 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 29.69/29.89 congruence. % 29.69/29.89 apply (zenon_L12_); trivial. % 29.69/29.89 apply zenon_H63. apply refl_equal. % 29.69/29.89 apply zenon_H63. apply refl_equal. % 29.69/29.89 apply zenon_H57. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L13_ *) % 29.69/29.89 assert (zenon_L14_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H1e zenon_H64 zenon_H65. % 29.69/29.89 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (e0)) = (op (e0) (e1)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H65. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H3a. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 29.69/29.89 congruence. % 29.69/29.89 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e0)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H66. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H1e. % 29.69/29.89 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.69/29.89 congruence. % 29.69/29.89 apply zenon_H3b. apply refl_equal. % 29.69/29.89 apply zenon_H67. apply sym_equal. exact zenon_H64. % 29.69/29.89 apply zenon_H3b. apply refl_equal. % 29.69/29.89 apply zenon_H3b. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L14_ *) % 29.69/29.89 assert (zenon_L15_ : (~((e1) = (e1))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H22. % 29.69/29.89 apply zenon_H22. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L15_ *) % 29.69/29.89 assert (zenon_L16_ : (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H20 zenon_H68 zenon_H69. % 29.69/29.89 cut (((op (e1) (e0)) = (e1)) = ((e0) = (e1))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H20. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H68. % 29.69/29.89 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.89 cut (((op (e1) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 29.69/29.89 congruence. % 29.69/29.89 exact (zenon_H6a zenon_H69). % 29.69/29.89 apply zenon_H22. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L16_ *) % 29.69/29.89 assert (zenon_L17_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H6b zenon_H6c zenon_H25. % 29.69/29.89 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H6b. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H6c. % 29.69/29.89 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 29.69/29.89 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.69/29.89 congruence. % 29.69/29.89 apply zenon_H6d. apply refl_equal. % 29.69/29.89 apply zenon_H59. apply sym_equal. exact zenon_H25. % 29.69/29.89 (* end of lemma zenon_L17_ *) % 29.69/29.89 assert (zenon_L18_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H68 zenon_H6e zenon_H6f. % 29.69/29.89 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.69/29.89 cut (((e3) = (e3)) = ((e1) = (e3))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H6f. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H2e. % 29.69/29.89 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.89 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 29.69/29.89 congruence. % 29.69/29.89 cut (((op (e1) (e0)) = (e1)) = ((e3) = (e1))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H70. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H68. % 29.69/29.89 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.89 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 29.69/29.89 congruence. % 29.69/29.89 exact (zenon_H71 zenon_H6e). % 29.69/29.89 apply zenon_H22. apply refl_equal. % 29.69/29.89 apply zenon_H2f. apply refl_equal. % 29.69/29.89 apply zenon_H2f. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L18_ *) % 29.69/29.89 assert (zenon_L19_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H72 zenon_H73. % 29.69/29.89 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 29.69/29.89 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 29.69/29.89 congruence. % 29.69/29.89 exact (zenon_H74 zenon_H73). % 29.69/29.89 exact (zenon_H74 zenon_H73). % 29.69/29.89 (* end of lemma zenon_L19_ *) % 29.69/29.89 assert (zenon_L20_ : (~((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H75 zenon_H73. % 29.69/29.89 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.89 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 29.69/29.89 congruence. % 29.69/29.89 exact (zenon_H74 zenon_H73). % 29.69/29.89 apply zenon_H1d. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L20_ *) % 29.69/29.89 assert (zenon_L21_ : (~((e3) = (e3))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H2f. % 29.69/29.89 apply zenon_H2f. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L21_ *) % 29.69/29.89 assert (zenon_L22_ : ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((e3) = (op (op (e0) (e0)) (e0)))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H76 zenon_H73 zenon_H77. % 29.69/29.89 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 29.69/29.89 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e3) = (op (op (e0) (e0)) (e0)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H77. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H78. % 29.69/29.89 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 29.69/29.89 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 29.69/29.89 congruence. % 29.69/29.89 cut (((op (e2) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H7a. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H76. % 29.69/29.89 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.89 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 29.69/29.89 congruence. % 29.69/29.89 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 29.69/29.89 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H7b. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H78. % 29.69/29.89 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 29.69/29.89 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 29.69/29.89 congruence. % 29.69/29.89 apply (zenon_L20_); trivial. % 29.69/29.89 apply zenon_H79. apply refl_equal. % 29.69/29.89 apply zenon_H79. apply refl_equal. % 29.69/29.89 apply zenon_H2f. apply refl_equal. % 29.69/29.89 apply zenon_H79. apply refl_equal. % 29.69/29.89 apply zenon_H79. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L22_ *) % 29.69/29.89 assert (zenon_L23_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H25 zenon_H76 zenon_H73. % 29.69/29.89 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 29.69/29.89 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 29.69/29.89 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H7d. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H7e. % 29.69/29.89 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 29.69/29.89 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 29.69/29.89 congruence. % 29.69/29.89 cut (((op (e2) (e2)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H80. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H25. % 29.69/29.89 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.89 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 29.69/29.89 congruence. % 29.69/29.89 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 29.69/29.89 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))))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H81. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H7e. % 29.69/29.89 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 29.69/29.89 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 29.69/29.89 congruence. % 29.69/29.89 apply (zenon_L19_); trivial. % 29.69/29.89 apply zenon_H7f. apply refl_equal. % 29.69/29.89 apply zenon_H7f. apply refl_equal. % 29.69/29.89 apply zenon_H22. apply refl_equal. % 29.69/29.89 apply zenon_H7f. apply refl_equal. % 29.69/29.89 apply zenon_H7f. apply refl_equal. % 29.69/29.89 apply (zenon_notand_s _ _ zenon_H7c); [ zenon_intro zenon_H77 | zenon_intro zenon_H82 ]. % 29.69/29.89 apply (zenon_L22_); trivial. % 29.69/29.89 apply zenon_H82. apply sym_equal. exact zenon_H73. % 29.69/29.89 (* end of lemma zenon_L23_ *) % 29.69/29.89 assert (zenon_L24_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H83 zenon_H65 zenon_H1e zenon_H84 zenon_H76 zenon_H25 zenon_H85. % 29.69/29.89 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 29.69/29.89 apply (zenon_L14_); trivial. % 29.69/29.89 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 29.69/29.89 exact (zenon_H84 zenon_H88). % 29.69/29.89 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 29.69/29.89 apply (zenon_L23_); trivial. % 29.69/29.89 exact (zenon_H85 zenon_H89). % 29.69/29.89 (* end of lemma zenon_L24_ *) % 29.69/29.89 assert (zenon_L25_ : (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H2d zenon_H8a zenon_H8b. % 29.69/29.89 cut (((op (e3) (e0)) = (e3)) = ((e0) = (e3))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H2d. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H8a. % 29.69/29.89 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.89 cut (((op (e3) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 29.69/29.89 congruence. % 29.69/29.89 exact (zenon_H8c zenon_H8b). % 29.69/29.89 apply zenon_H2f. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L25_ *) % 29.69/29.89 assert (zenon_L26_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H8d zenon_H6f zenon_H68 zenon_H85 zenon_H25 zenon_H84 zenon_H1e zenon_H65 zenon_H83 zenon_H2d zenon_H8b. % 29.69/29.89 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.69/29.89 exact (zenon_H85 zenon_H89). % 29.69/29.89 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.69/29.89 apply (zenon_L18_); trivial. % 29.69/29.89 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.69/29.89 apply (zenon_L24_); trivial. % 29.69/29.89 apply (zenon_L25_); trivial. % 29.69/29.89 (* end of lemma zenon_L26_ *) % 29.69/29.89 assert (zenon_L27_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H8b zenon_H90 zenon_H20. % 29.69/29.89 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 29.69/29.89 cut (((e1) = (e1)) = ((e0) = (e1))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H20. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H21. % 29.69/29.89 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.89 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 29.69/29.89 congruence. % 29.69/29.89 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H23. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H8b. % 29.69/29.89 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.89 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 29.69/29.89 congruence. % 29.69/29.89 exact (zenon_H91 zenon_H90). % 29.69/29.89 apply zenon_H1d. apply refl_equal. % 29.69/29.89 apply zenon_H22. apply refl_equal. % 29.69/29.89 apply zenon_H22. apply refl_equal. % 29.69/29.89 (* end of lemma zenon_L27_ *) % 29.69/29.89 assert (zenon_L28_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 29.69/29.89 do 0 intro. intros zenon_H92 zenon_H2d zenon_H83 zenon_H65 zenon_H1e zenon_H84 zenon_H85 zenon_H6f zenon_H8d zenon_H25 zenon_H6b zenon_H8b zenon_H20. % 29.69/29.89 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.69/29.89 exact (zenon_H84 zenon_H88). % 29.69/29.89 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.69/29.89 apply (zenon_L26_); trivial. % 29.69/29.89 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.69/29.89 apply (zenon_L17_); trivial. % 29.69/29.89 apply (zenon_L27_); trivial. % 29.69/29.89 (* end of lemma zenon_L28_ *) % 29.69/29.89 assert (zenon_L29_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H3f zenon_H1e zenon_H95. % 29.69/29.89 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H3f. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H1e. % 29.69/29.89 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 29.69/29.89 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.69/29.89 congruence. % 29.69/29.89 apply zenon_H3b. apply refl_equal. % 29.69/29.89 apply zenon_H96. apply sym_equal. exact zenon_H95. % 29.69/29.89 (* end of lemma zenon_L29_ *) % 29.69/29.89 assert (zenon_L30_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 29.69/29.89 do 0 intro. intros zenon_H97 zenon_H90 zenon_H98. % 29.69/29.89 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 29.69/29.89 intro zenon_D_pnotp. % 29.69/29.89 apply zenon_H97. % 29.69/29.89 rewrite <- zenon_D_pnotp. % 29.69/29.89 exact zenon_H90. % 29.69/29.89 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 29.69/29.89 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.89 congruence. % 29.69/29.89 apply zenon_H9a. apply refl_equal. % 29.69/29.89 apply zenon_H99. apply sym_equal. exact zenon_H98. % 29.69/29.89 (* end of lemma zenon_L30_ *) % 29.69/29.90 assert (zenon_L31_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e2)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H97 zenon_H9b zenon_H9c zenon_H9d. % 29.69/29.90 cut (((op (e3) (op (e3) (e2))) = (e2)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H97. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H9b. % 29.69/29.90 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 29.69/29.90 cut (((op (e3) (op (e3) (e2))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9a ]. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e3) (op (e3) (e2))) = (op (e3) (e0)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H9f. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Ha0. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 apply zenon_Ha2. apply sym_equal. exact zenon_H9c. % 29.69/29.90 apply zenon_H9a. apply refl_equal. % 29.69/29.90 apply zenon_H9a. apply refl_equal. % 29.69/29.90 apply zenon_H9e. apply sym_equal. exact zenon_H9d. % 29.69/29.90 (* end of lemma zenon_L31_ *) % 29.69/29.90 assert (zenon_L32_ : ((op (e3) (op (e3) (e1))) = (e1)) -> ((op (e3) (e1)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Ha3 zenon_H40 zenon_H33 zenon_Ha4. % 29.69/29.90 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Ha4. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Ha5. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e3) (op (e3) (e1))) = (e1)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Ha7. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Ha3. % 29.69/29.90 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 29.69/29.90 cut (((op (e3) (op (e3) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (op (e3) (e1))) = (op (e3) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Ha8. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Ha5. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 apply zenon_H41. apply sym_equal. exact zenon_H40. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 apply zenon_H34. apply sym_equal. exact zenon_H33. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L32_ *) % 29.69/29.90 assert (zenon_L33_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Haa zenon_H1e zenon_H3f zenon_H90 zenon_H9c zenon_H9b zenon_H97 zenon_Ha3 zenon_H33 zenon_Ha4. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H95 | zenon_intro zenon_Hab ]. % 29.69/29.90 apply (zenon_L29_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H98 | zenon_intro zenon_Hac ]. % 29.69/29.90 apply (zenon_L30_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9d | zenon_intro zenon_H40 ]. % 29.69/29.90 apply (zenon_L31_); trivial. % 29.69/29.90 apply (zenon_L32_); trivial. % 29.69/29.90 (* end of lemma zenon_L33_ *) % 29.69/29.90 assert (zenon_L34_ : ((op (e3) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H8a zenon_H6e zenon_Had. % 29.69/29.90 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9a ]. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e1) (e0)) = (op (e3) (e0)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Had. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Ha0. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e1) (e0)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hae. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H8a. % 29.69/29.90 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H9a. apply refl_equal. % 29.69/29.90 apply zenon_Haf. apply sym_equal. exact zenon_H6e. % 29.69/29.90 apply zenon_H9a. apply refl_equal. % 29.69/29.90 apply zenon_H9a. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L34_ *) % 29.69/29.90 assert (zenon_L35_ : (~((op (e3) (e0)) = (op (e3) (op (e3) (e3))))) -> ((op (e3) (e3)) = (e0)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hb0 zenon_Hb1. % 29.69/29.90 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 apply zenon_Hb2. apply sym_equal. exact zenon_Hb1. % 29.69/29.90 (* end of lemma zenon_L35_ *) % 29.69/29.90 assert (zenon_L36_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H97 zenon_Hb3 zenon_Hb1 zenon_H40. % 29.69/29.90 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H97. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hb3. % 29.69/29.90 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 29.69/29.90 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9a ]. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e0)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hb4. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Ha0. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 29.69/29.90 congruence. % 29.69/29.90 apply (zenon_L35_); trivial. % 29.69/29.90 apply zenon_H9a. apply refl_equal. % 29.69/29.90 apply zenon_H9a. apply refl_equal. % 29.69/29.90 apply zenon_H41. apply sym_equal. exact zenon_H40. % 29.69/29.90 (* end of lemma zenon_L36_ *) % 29.69/29.90 assert (zenon_L37_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hb5 zenon_Hb3 zenon_Hb1 zenon_Hb6. % 29.69/29.90 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hb5. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hb3. % 29.69/29.90 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 29.69/29.90 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9a ]. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e0)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hb4. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Ha0. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.90 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 29.69/29.90 congruence. % 29.69/29.90 apply (zenon_L35_); trivial. % 29.69/29.90 apply zenon_H9a. apply refl_equal. % 29.69/29.90 apply zenon_H9a. apply refl_equal. % 29.69/29.90 apply zenon_Hb7. apply sym_equal. exact zenon_Hb6. % 29.69/29.90 (* end of lemma zenon_L37_ *) % 29.69/29.90 assert (zenon_L38_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hb8 zenon_Had zenon_H6e zenon_H97 zenon_Hb1 zenon_Hb3 zenon_Hb5 zenon_Hb9. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 29.69/29.90 apply (zenon_L34_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 29.69/29.90 apply (zenon_L36_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 29.69/29.90 apply (zenon_L37_); trivial. % 29.69/29.90 exact (zenon_Hb9 zenon_Hbc). % 29.69/29.90 (* end of lemma zenon_L38_ *) % 29.69/29.90 assert (zenon_L39_ : (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H6f zenon_H8a zenon_H90. % 29.69/29.90 cut (((op (e3) (e0)) = (e3)) = ((e1) = (e3))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H6f. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H8a. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_H91 zenon_H90). % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L39_ *) % 29.69/29.90 assert (zenon_L40_ : (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (op (e3) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hb9 zenon_Hb5 zenon_Hb3 zenon_H97 zenon_Had zenon_Hb8 zenon_Haa zenon_H3f zenon_H9b zenon_Ha3 zenon_H33 zenon_Ha4 zenon_H92 zenon_H2d zenon_H8d zenon_H6b zenon_H20 zenon_Hbd zenon_H85 zenon_H25 zenon_H84 zenon_H1e zenon_H65 zenon_H83 zenon_H6f zenon_H90. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.69/29.90 exact (zenon_H85 zenon_H89). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.69/29.90 apply (zenon_L28_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.69/29.90 apply (zenon_L29_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.69/29.90 apply (zenon_L33_); trivial. % 29.69/29.90 apply (zenon_L38_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.69/29.90 apply (zenon_L24_); trivial. % 29.69/29.90 apply (zenon_L39_); trivial. % 29.69/29.90 (* end of lemma zenon_L40_ *) % 29.69/29.90 assert (zenon_L41_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (op (e3) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e1) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hc0 zenon_H27 zenon_H69 zenon_Hb9 zenon_Hb5 zenon_Hb3 zenon_H97 zenon_Had zenon_Hb8 zenon_Haa zenon_H3f zenon_H9b zenon_Ha3 zenon_Ha4 zenon_H92 zenon_H2d zenon_H8d zenon_H6b zenon_H20 zenon_Hbd zenon_H85 zenon_H25 zenon_H84 zenon_H1e zenon_H65 zenon_H83 zenon_H6f. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.69/29.90 exact (zenon_H84 zenon_H88). % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.69/29.90 apply (zenon_L2_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.69/29.90 apply (zenon_L3_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.69/29.90 exact (zenon_H84 zenon_H88). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.69/29.90 apply (zenon_L16_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.69/29.90 apply (zenon_L17_); trivial. % 29.69/29.90 apply (zenon_L40_); trivial. % 29.69/29.90 (* end of lemma zenon_L41_ *) % 29.69/29.90 assert (zenon_L42_ : ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hc3 zenon_H1e zenon_H35. % 29.69/29.90 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H35. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hc4. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hc6. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hc3. % 29.69/29.90 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hc5. apply refl_equal. % 29.69/29.90 apply zenon_Hc7. apply sym_equal. exact zenon_H1e. % 29.69/29.90 apply zenon_Hc5. apply refl_equal. % 29.69/29.90 apply zenon_Hc5. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L42_ *) % 29.69/29.90 assert (zenon_L43_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hc8 zenon_H73 zenon_Hc9. % 29.69/29.90 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hc8. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H73. % 29.69/29.90 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 29.69/29.90 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hcb. apply refl_equal. % 29.69/29.90 apply zenon_Hca. apply sym_equal. exact zenon_Hc9. % 29.69/29.90 (* end of lemma zenon_L43_ *) % 29.69/29.90 assert (zenon_L44_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H25 zenon_Hcc zenon_Hcd. % 29.69/29.90 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 29.69/29.90 cut (((e2) = (e2)) = ((e1) = (e2))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hcd. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hce. % 29.69/29.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.90 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e2) (e2)) = (e1)) = ((e2) = (e1))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hcf. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H25. % 29.69/29.90 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.90 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_Hd0 zenon_Hcc). % 29.69/29.90 apply zenon_H22. apply refl_equal. % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L44_ *) % 29.69/29.90 assert (zenon_L45_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hd1 zenon_H68 zenon_Hd2. % 29.69/29.90 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hd1. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H68. % 29.69/29.90 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 29.69/29.90 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hd4. apply refl_equal. % 29.69/29.90 apply zenon_Hd3. apply sym_equal. exact zenon_Hd2. % 29.69/29.90 (* end of lemma zenon_L45_ *) % 29.69/29.90 assert (zenon_L46_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H25 zenon_Hd5 zenon_Hd6. % 29.69/29.90 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.90 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hd6. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H28. % 29.69/29.90 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.90 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hd7. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H25. % 29.69/29.90 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 29.69/29.90 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H29. apply refl_equal. % 29.69/29.90 apply zenon_Hd8. apply sym_equal. exact zenon_Hd5. % 29.69/29.90 apply zenon_H29. apply refl_equal. % 29.69/29.90 apply zenon_H29. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L46_ *) % 29.69/29.90 assert (zenon_L47_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hd9 zenon_H73 zenon_Hda. % 29.69/29.90 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e0) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hd9. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H73. % 29.69/29.90 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 29.69/29.90 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hcb. apply refl_equal. % 29.69/29.90 apply zenon_Hdb. apply sym_equal. exact zenon_Hda. % 29.69/29.90 (* end of lemma zenon_L47_ *) % 29.69/29.90 assert (zenon_L48_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H68 zenon_Hdc zenon_Hcd. % 29.69/29.90 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 29.69/29.90 cut (((e2) = (e2)) = ((e1) = (e2))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hcd. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hce. % 29.69/29.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.90 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hcf. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H68. % 29.69/29.90 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.90 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_Hdd zenon_Hdc). % 29.69/29.90 apply zenon_H22. apply refl_equal. % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L48_ *) % 29.69/29.90 assert (zenon_L49_ : (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hde zenon_Hc9 zenon_Hdf. % 29.69/29.90 cut (((op (e2) (e0)) = (e2)) = ((e0) = (e2))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hde. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hc9. % 29.69/29.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.90 cut (((op (e2) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_He0 zenon_Hdf). % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L49_ *) % 29.69/29.90 assert (zenon_L50_ : (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_He1 zenon_H8a zenon_He2. % 29.69/29.90 cut (((op (e3) (e0)) = (e3)) = ((e2) = (e3))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_He1. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H8a. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_He3 zenon_He2). % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L50_ *) % 29.69/29.90 assert (zenon_L51_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 29.69/29.90 do 0 intro. intros zenon_He4 zenon_Hda zenon_Hd9 zenon_Hcd zenon_H68 zenon_Hdf zenon_Hde zenon_He1 zenon_H8a. % 29.69/29.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.69/29.90 apply (zenon_L47_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.69/29.90 apply (zenon_L48_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.69/29.90 apply (zenon_L49_); trivial. % 29.69/29.90 apply (zenon_L50_); trivial. % 29.69/29.90 (* end of lemma zenon_L51_ *) % 29.69/29.90 assert (zenon_L52_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_He7 zenon_H73 zenon_He2. % 29.69/29.90 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_He7. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H73. % 29.69/29.90 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 29.69/29.90 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hcb. apply refl_equal. % 29.69/29.90 apply zenon_He8. apply sym_equal. exact zenon_He2. % 29.69/29.90 (* end of lemma zenon_L52_ *) % 29.69/29.90 assert (zenon_L53_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H3f zenon_He9 zenon_H9d. % 29.69/29.90 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H3f. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_He9. % 29.69/29.90 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 29.69/29.90 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H3b. apply refl_equal. % 29.69/29.90 apply zenon_H9e. apply sym_equal. exact zenon_H9d. % 29.69/29.90 (* end of lemma zenon_L53_ *) % 29.69/29.90 assert (zenon_L54_ : (~((op (e3) (e2)) = (op (e3) (op (e3) (e2))))) -> ((op (e3) (e2)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hea zenon_Heb. % 29.69/29.90 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 apply zenon_Hec. apply sym_equal. exact zenon_Heb. % 29.69/29.90 (* end of lemma zenon_L54_ *) % 29.69/29.90 assert (zenon_L55_ : ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H9b zenon_Heb zenon_Hed zenon_Hee. % 29.69/29.90 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hee. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hef. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e3) (op (e3) (e2))) = (e2)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hf1. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H9b. % 29.69/29.90 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 29.69/29.90 cut (((op (e3) (op (e3) (e2))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (op (e3) (e2))) = (op (e3) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hf3. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hef. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 29.69/29.90 congruence. % 29.69/29.90 apply (zenon_L54_); trivial. % 29.69/29.90 apply zenon_Hf0. apply refl_equal. % 29.69/29.90 apply zenon_Hf0. apply refl_equal. % 29.69/29.90 apply zenon_Hf2. apply sym_equal. exact zenon_Hed. % 29.69/29.90 apply zenon_Hf0. apply refl_equal. % 29.69/29.90 apply zenon_Hf0. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L55_ *) % 29.69/29.90 assert (zenon_L56_ : ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hf4 zenon_Hf5 zenon_Hf6. % 29.69/29.90 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hf6. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Ha5. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hf7. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hf4. % 29.69/29.90 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 apply zenon_Hf8. apply sym_equal. exact zenon_Hf5. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L56_ *) % 29.69/29.90 assert (zenon_L57_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hf9 zenon_H73 zenon_He7 zenon_He9 zenon_H3f zenon_Hee zenon_Hed zenon_H9b zenon_Hf5 zenon_Hf6. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.69/29.90 apply (zenon_L52_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.69/29.90 apply (zenon_L53_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.69/29.90 apply (zenon_L55_); trivial. % 29.69/29.90 apply (zenon_L56_); trivial. % 29.69/29.90 (* end of lemma zenon_L57_ *) % 29.69/29.90 assert (zenon_L58_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hfc zenon_Hfd zenon_Hed. % 29.69/29.90 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hfc. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hfd. % 29.69/29.90 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hc5. apply refl_equal. % 29.69/29.90 apply zenon_Hf2. apply sym_equal. exact zenon_Hed. % 29.69/29.90 (* end of lemma zenon_L58_ *) % 29.69/29.90 assert (zenon_L59_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hfc zenon_Hc3 zenon_Hfe. % 29.69/29.90 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hfc. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hc3. % 29.69/29.90 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hc5. apply refl_equal. % 29.69/29.90 apply zenon_Hff. apply sym_equal. exact zenon_Hfe. % 29.69/29.90 (* end of lemma zenon_L59_ *) % 29.69/29.90 assert (zenon_L60_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H100 zenon_Hfd zenon_H9d. % 29.69/29.90 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H100. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hfd. % 29.69/29.90 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hc5. apply refl_equal. % 29.69/29.90 apply zenon_H9e. apply sym_equal. exact zenon_H9d. % 29.69/29.90 (* end of lemma zenon_L60_ *) % 29.69/29.90 assert (zenon_L61_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H101 zenon_Hf6 zenon_Hf5 zenon_H9b zenon_Hee zenon_H3f zenon_He7 zenon_H73 zenon_Hf9 zenon_Hed zenon_H46 zenon_H102 zenon_Hfe zenon_Hfc zenon_H68 zenon_Hd1 zenon_H100 zenon_H103. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.69/29.90 apply (zenon_L57_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.69/29.90 apply (zenon_L58_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.69/29.90 exact (zenon_H46 zenon_H55). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 29.69/29.90 apply (zenon_L59_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 29.69/29.90 apply (zenon_L45_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 29.69/29.90 apply (zenon_L60_); trivial. % 29.69/29.90 exact (zenon_H103 zenon_H37). % 29.69/29.90 (* end of lemma zenon_L61_ *) % 29.69/29.90 assert (zenon_L62_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hf5 zenon_Hcc zenon_H108. % 29.69/29.90 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.69/29.90 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e2)) = (op (e2) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H108. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H109. % 29.69/29.90 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.90 cut (((op (e2) (e3)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H10b. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hf5. % 29.69/29.90 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 29.69/29.90 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H10a. apply refl_equal. % 29.69/29.90 apply zenon_H10c. apply sym_equal. exact zenon_Hcc. % 29.69/29.90 apply zenon_H10a. apply refl_equal. % 29.69/29.90 apply zenon_H10a. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L62_ *) % 29.69/29.90 assert (zenon_L63_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H10d zenon_H10e zenon_H9c. % 29.69/29.90 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H10d. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H10e. % 29.69/29.90 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 29.69/29.90 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H10f. apply refl_equal. % 29.69/29.90 apply zenon_Ha2. apply sym_equal. exact zenon_H9c. % 29.69/29.90 (* end of lemma zenon_L63_ *) % 29.69/29.90 assert (zenon_L64_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H10d zenon_Hda zenon_Heb. % 29.69/29.90 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H10d. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hda. % 29.69/29.90 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 29.69/29.90 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H10f. apply refl_equal. % 29.69/29.90 apply zenon_Hec. apply sym_equal. exact zenon_Heb. % 29.69/29.90 (* end of lemma zenon_L64_ *) % 29.69/29.90 assert (zenon_L65_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hb1 zenon_H9c zenon_H110. % 29.69/29.90 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H110. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Ha5. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H111. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hb1. % 29.69/29.90 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 apply zenon_Ha2. apply sym_equal. exact zenon_H9c. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L65_ *) % 29.69/29.90 assert (zenon_L66_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H112 zenon_H98 zenon_H113. % 29.69/29.90 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H113. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Ha5. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H114. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H112. % 29.69/29.90 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 29.69/29.90 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 apply zenon_H99. apply sym_equal. exact zenon_H98. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 apply zenon_Ha6. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L66_ *) % 29.69/29.90 assert (zenon_L67_ : (~((op (e3) (e2)) = (op (e3) (op (e3) (e3))))) -> ((op (e3) (e3)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H115 zenon_Hf4. % 29.69/29.90 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 apply zenon_H116. apply sym_equal. exact zenon_Hf4. % 29.69/29.90 (* end of lemma zenon_L67_ *) % 29.69/29.90 assert (zenon_L68_ : ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hb3 zenon_Hf4 zenon_H117 zenon_H10d. % 29.69/29.90 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H10d. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hef. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H118. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hb3. % 29.69/29.90 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 29.69/29.90 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H11a]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H11a. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hef. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.69/29.90 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 29.69/29.90 congruence. % 29.69/29.90 apply (zenon_L67_); trivial. % 29.69/29.90 apply zenon_Hf0. apply refl_equal. % 29.69/29.90 apply zenon_Hf0. apply refl_equal. % 29.69/29.90 apply zenon_H119. apply sym_equal. exact zenon_H117. % 29.69/29.90 apply zenon_Hf0. apply refl_equal. % 29.69/29.90 apply zenon_Hf0. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L68_ *) % 29.69/29.90 assert (zenon_L69_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H11b zenon_H110 zenon_H9c zenon_H113 zenon_H98 zenon_H10d zenon_H117 zenon_Hb3 zenon_Hb9. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 29.69/29.90 apply (zenon_L65_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 29.69/29.90 apply (zenon_L66_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 29.69/29.90 apply (zenon_L68_); trivial. % 29.69/29.90 exact (zenon_Hb9 zenon_Hbc). % 29.69/29.90 (* end of lemma zenon_L69_ *) % 29.69/29.90 assert (zenon_L70_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H11e zenon_H27 zenon_H25 zenon_Heb zenon_H11b zenon_H110 zenon_H9c zenon_H113 zenon_H98 zenon_H10d zenon_Hb3 zenon_Hb9. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H10e | zenon_intro zenon_H11f ]. % 29.69/29.90 apply (zenon_L63_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H26 | zenon_intro zenon_H120 ]. % 29.69/29.90 apply (zenon_L3_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hda | zenon_intro zenon_H117 ]. % 29.69/29.90 apply (zenon_L64_); trivial. % 29.69/29.90 apply (zenon_L69_); trivial. % 29.69/29.90 (* end of lemma zenon_L70_ *) % 29.69/29.90 assert (zenon_L71_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))) -> ((op (e3) (e3)) = (e0)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H121 zenon_Hb1. % 29.69/29.90 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 29.69/29.90 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_H122 zenon_Hb1). % 29.69/29.90 exact (zenon_H122 zenon_Hb1). % 29.69/29.90 (* end of lemma zenon_L71_ *) % 29.69/29.90 assert (zenon_L72_ : (~((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H123 zenon_Hb1. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_H122 zenon_Hb1). % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L72_ *) % 29.69/29.90 assert (zenon_L73_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H124 zenon_H20 zenon_Hd6 zenon_H125 zenon_H8a zenon_He1 zenon_Hde zenon_Hdf zenon_Hcd zenon_Hd9 zenon_He4 zenon_H103 zenon_H100 zenon_Hd1 zenon_Hfc zenon_Hfe zenon_H102 zenon_H46 zenon_Hf9 zenon_He7 zenon_Hee zenon_H9b zenon_Hf6 zenon_H101 zenon_H108 zenon_Hf5 zenon_Hbd zenon_H2d zenon_H83 zenon_H65 zenon_H84 zenon_H85 zenon_H68 zenon_H6f zenon_H8d zenon_H1e zenon_H3f zenon_Hb9 zenon_Hb3 zenon_H10d zenon_H113 zenon_H110 zenon_H11b zenon_H25 zenon_H27 zenon_H11e zenon_H73 zenon_H33. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 29.69/29.90 apply (zenon_L2_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 29.69/29.90 apply (zenon_L45_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 29.69/29.90 apply (zenon_L46_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.69/29.90 apply (zenon_L51_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.69/29.90 apply (zenon_L61_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.69/29.90 apply (zenon_L62_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.69/29.90 apply (zenon_L26_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.69/29.90 apply (zenon_L29_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.69/29.90 apply (zenon_L70_); trivial. % 29.69/29.90 apply (zenon_notand_s _ _ ax29); [ zenon_intro zenon_H12b | zenon_intro zenon_H12a ]. % 29.69/29.90 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 29.69/29.90 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e2) = (op (op (e3) (e3)) (op (e3) (e3))))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H12b. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H12c. % 29.69/29.90 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 29.69/29.90 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e0) (e0)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H12e. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H73. % 29.69/29.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.90 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 29.69/29.90 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H12f. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H12c. % 29.69/29.90 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 29.69/29.90 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 29.69/29.90 congruence. % 29.69/29.90 apply (zenon_L71_); trivial. % 29.69/29.90 apply zenon_H12d. apply refl_equal. % 29.69/29.90 apply zenon_H12d. apply refl_equal. % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 apply zenon_H12d. apply refl_equal. % 29.69/29.90 apply zenon_H12d. apply refl_equal. % 29.69/29.90 apply (zenon_notand_s _ _ zenon_H12a); [ zenon_intro zenon_H130 | zenon_intro zenon_Hb2 ]. % 29.69/29.90 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 29.69/29.90 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e1) = (op (op (e3) (e3)) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H130. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H131. % 29.69/29.90 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 29.69/29.90 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e0) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H133. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H33. % 29.69/29.90 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.90 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 29.69/29.90 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H134. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H131. % 29.69/29.90 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 29.69/29.90 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 29.69/29.90 congruence. % 29.69/29.90 apply (zenon_L72_); trivial. % 29.69/29.90 apply zenon_H132. apply refl_equal. % 29.69/29.90 apply zenon_H132. apply refl_equal. % 29.69/29.90 apply zenon_H22. apply refl_equal. % 29.69/29.90 apply zenon_H132. apply refl_equal. % 29.69/29.90 apply zenon_H132. apply refl_equal. % 29.69/29.90 apply zenon_Hb2. apply sym_equal. exact zenon_Hb1. % 29.69/29.90 (* end of lemma zenon_L73_ *) % 29.69/29.90 assert (zenon_L74_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H135 zenon_Hc8 zenon_H124 zenon_H20 zenon_Hd6 zenon_H125 zenon_H8a zenon_He1 zenon_Hde zenon_Hdf zenon_Hcd zenon_Hd9 zenon_He4 zenon_H103 zenon_H100 zenon_Hd1 zenon_Hfc zenon_Hfe zenon_H102 zenon_H46 zenon_Hf9 zenon_He7 zenon_Hee zenon_H9b zenon_Hf6 zenon_H101 zenon_H108 zenon_Hbd zenon_H2d zenon_H83 zenon_H65 zenon_H84 zenon_H85 zenon_H68 zenon_H6f zenon_H8d zenon_H1e zenon_H3f zenon_Hb9 zenon_Hb3 zenon_H10d zenon_H113 zenon_H110 zenon_H11b zenon_H25 zenon_H27 zenon_H11e zenon_H73 zenon_H33. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.69/29.90 apply (zenon_L43_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.69/29.90 exact (zenon_H46 zenon_H55). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.69/29.90 apply (zenon_L44_); trivial. % 29.69/29.90 apply (zenon_L73_); trivial. % 29.69/29.90 (* end of lemma zenon_L74_ *) % 29.69/29.90 assert (zenon_L75_ : (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H138 zenon_H1e zenon_H10e. % 29.69/29.90 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H138. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H1e. % 29.69/29.90 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 29.69/29.90 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H3b. apply refl_equal. % 29.69/29.90 apply zenon_H139. apply sym_equal. exact zenon_H10e. % 29.69/29.90 (* end of lemma zenon_L75_ *) % 29.69/29.90 assert (zenon_L76_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H13a zenon_Hfd. % 29.69/29.90 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 29.69/29.90 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_H13b zenon_Hfd). % 29.69/29.90 exact (zenon_H13b zenon_Hfd). % 29.69/29.90 (* end of lemma zenon_L76_ *) % 29.69/29.90 assert (zenon_L77_ : (~((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H13c zenon_Hfd. % 29.69/29.90 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.90 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_H13b zenon_Hfd). % 29.69/29.90 apply zenon_H22. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L77_ *) % 29.69/29.90 assert (zenon_L78_ : ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e3) = (op (op (e1) (e1)) (e1)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H3d zenon_Hfd zenon_H13d. % 29.69/29.90 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 29.69/29.90 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e3) = (op (op (e1) (e1)) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H13d. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H13e. % 29.69/29.90 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 29.69/29.90 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e2) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H140. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H3d. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 29.69/29.90 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H141. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H13e. % 29.69/29.90 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 29.69/29.90 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 29.69/29.90 congruence. % 29.69/29.90 apply (zenon_L77_); trivial. % 29.69/29.90 apply zenon_H13f. apply refl_equal. % 29.69/29.90 apply zenon_H13f. apply refl_equal. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 apply zenon_H13f. apply refl_equal. % 29.69/29.90 apply zenon_H13f. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L78_ *) % 29.69/29.90 assert (zenon_L79_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H142 zenon_H3d zenon_Hfd. % 29.69/29.90 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H144 | zenon_intro zenon_H143 ]. % 29.69/29.90 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 29.69/29.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H144. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H145. % 29.69/29.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 29.69/29.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e2) (e2)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H147. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H142. % 29.69/29.90 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.90 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 29.69/29.90 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))))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H148. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H145. % 29.69/29.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 29.69/29.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 29.69/29.90 congruence. % 29.69/29.90 apply (zenon_L76_); trivial. % 29.69/29.90 apply zenon_H146. apply refl_equal. % 29.69/29.90 apply zenon_H146. apply refl_equal. % 29.69/29.90 apply zenon_H1d. apply refl_equal. % 29.69/29.90 apply zenon_H146. apply refl_equal. % 29.69/29.90 apply zenon_H146. apply refl_equal. % 29.69/29.90 apply (zenon_notand_s _ _ zenon_H143); [ zenon_intro zenon_H13d | zenon_intro zenon_H149 ]. % 29.69/29.90 apply (zenon_L78_); trivial. % 29.69/29.90 apply zenon_H149. apply sym_equal. exact zenon_Hfd. % 29.69/29.90 (* end of lemma zenon_L79_ *) % 29.69/29.90 assert (zenon_L80_ : (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H6f zenon_H40 zenon_H98. % 29.69/29.90 cut (((op (e3) (e1)) = (e3)) = ((e1) = (e3))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H6f. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H40. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_H14a zenon_H98). % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L80_ *) % 29.69/29.90 assert (zenon_L81_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_Hfd zenon_H142 zenon_H6f zenon_H98. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.69/29.90 apply (zenon_L4_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.69/29.90 exact (zenon_H103 zenon_H37). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.69/29.90 apply (zenon_L79_); trivial. % 29.69/29.90 apply (zenon_L80_); trivial. % 29.69/29.90 (* end of lemma zenon_L81_ *) % 29.69/29.90 assert (zenon_L82_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H125 zenon_H8a zenon_He1 zenon_Hde zenon_Hdf zenon_H68 zenon_Hcd zenon_Hd9 zenon_He4 zenon_Hfd zenon_Hfc zenon_H108 zenon_Hf5 zenon_H11e zenon_H27 zenon_H25 zenon_H11b zenon_H110 zenon_H9c zenon_H113 zenon_H98 zenon_H10d zenon_Hb3 zenon_Hb9. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.69/29.90 apply (zenon_L51_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.69/29.90 apply (zenon_L58_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.69/29.90 apply (zenon_L62_); trivial. % 29.69/29.90 apply (zenon_L70_); trivial. % 29.69/29.90 (* end of lemma zenon_L82_ *) % 29.69/29.90 assert (zenon_L83_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H14b zenon_H138 zenon_H33 zenon_H73 zenon_H3f zenon_H8d zenon_H85 zenon_H84 zenon_H65 zenon_H83 zenon_Hbd zenon_H101 zenon_Hf6 zenon_H9b zenon_Hee zenon_He7 zenon_Hf9 zenon_H102 zenon_Hd1 zenon_H100 zenon_Hd6 zenon_H20 zenon_H124 zenon_Hc8 zenon_H6f zenon_H103 zenon_H1e zenon_H2d zenon_H42 zenon_H135 zenon_H46 zenon_H125 zenon_H8a zenon_He1 zenon_Hde zenon_Hdf zenon_H68 zenon_Hcd zenon_Hd9 zenon_He4 zenon_Hfd zenon_Hfc zenon_H108 zenon_H11e zenon_H27 zenon_H25 zenon_H11b zenon_H110 zenon_H113 zenon_H98 zenon_H10d zenon_Hb3 zenon_Hb9. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.69/29.90 apply (zenon_L75_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.69/29.90 apply (zenon_L74_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.69/29.90 apply (zenon_L81_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.69/29.90 apply (zenon_L49_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.69/29.90 exact (zenon_H46 zenon_H55). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.69/29.90 apply (zenon_L44_); trivial. % 29.69/29.90 apply (zenon_L82_); trivial. % 29.69/29.90 (* end of lemma zenon_L83_ *) % 29.69/29.90 assert (zenon_L84_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H14e zenon_H14f zenon_Hb1. % 29.69/29.90 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H14e. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H14f. % 29.69/29.90 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 29.69/29.90 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H150. apply refl_equal. % 29.69/29.90 apply zenon_Hb2. apply sym_equal. exact zenon_Hb1. % 29.69/29.90 (* end of lemma zenon_L84_ *) % 29.69/29.90 assert (zenon_L85_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H6b zenon_H25 zenon_H8d zenon_H6f zenon_H85 zenon_H84 zenon_H65 zenon_H83 zenon_H2d zenon_H92 zenon_H1e zenon_H3f zenon_H9d zenon_H9b zenon_H97 zenon_H14e zenon_H14f. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.69/29.90 apply (zenon_L28_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.69/29.90 apply (zenon_L29_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.69/29.90 apply (zenon_L31_); trivial. % 29.69/29.90 apply (zenon_L84_); trivial. % 29.69/29.90 (* end of lemma zenon_L85_ *) % 29.69/29.90 assert (zenon_L86_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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 (e1) (e2)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hf9 zenon_H8a zenon_He1 zenon_H14f zenon_H14e zenon_H97 zenon_H3f zenon_H1e zenon_H92 zenon_H2d zenon_H83 zenon_H65 zenon_H84 zenon_H85 zenon_H6f zenon_H8d zenon_H25 zenon_H6b zenon_H20 zenon_Hbd zenon_Hee zenon_Hed zenon_H9b zenon_Hb3 zenon_H117 zenon_H10d. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.69/29.90 apply (zenon_L50_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.69/29.90 apply (zenon_L85_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.69/29.90 apply (zenon_L55_); trivial. % 29.69/29.90 apply (zenon_L68_); trivial. % 29.69/29.90 (* end of lemma zenon_L86_ *) % 29.69/29.90 assert (zenon_L87_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H10e zenon_H117 zenon_H2d. % 29.69/29.90 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.69/29.90 cut (((e3) = (e3)) = ((e0) = (e3))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H2d. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H2e. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H30. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H10e. % 29.69/29.90 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.90 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_H151 zenon_H117). % 29.69/29.90 apply zenon_H1d. apply refl_equal. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L87_ *) % 29.69/29.90 assert (zenon_L88_ : ((op (e2) (e1)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H55 zenon_He9 zenon_H3c. % 29.69/29.90 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.69/29.90 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e0) (e1)) = (op (e2) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H3c. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H62. % 29.69/29.90 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.90 cut (((op (e2) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e0) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H152. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H55. % 29.69/29.90 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 29.69/29.90 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H63. apply refl_equal. % 29.69/29.90 apply zenon_H153. apply sym_equal. exact zenon_He9. % 29.69/29.90 apply zenon_H63. apply refl_equal. % 29.69/29.90 apply zenon_H63. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L88_ *) % 29.69/29.90 assert (zenon_L89_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H142 zenon_Hcc zenon_Hde. % 29.69/29.90 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 29.69/29.90 cut (((e2) = (e2)) = ((e0) = (e2))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hde. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hce. % 29.69/29.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.90 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e2) (e2)) = (e0)) = ((e2) = (e0))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H154. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H142. % 29.69/29.90 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.90 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_Hd0 zenon_Hcc). % 29.69/29.90 apply zenon_H1d. apply refl_equal. % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L89_ *) % 29.69/29.90 assert (zenon_L90_ : ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hf5 zenon_H155 zenon_H156. % 29.69/29.90 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.69/29.90 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H156. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H109. % 29.69/29.90 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.90 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H157. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hf5. % 29.69/29.90 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 29.69/29.90 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H10a. apply refl_equal. % 29.69/29.90 apply zenon_H158. apply sym_equal. exact zenon_H155. % 29.69/29.90 apply zenon_H10a. apply refl_equal. % 29.69/29.90 apply zenon_H10a. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L90_ *) % 29.69/29.90 assert (zenon_L91_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H135 zenon_H73 zenon_Hc8 zenon_H3c zenon_He9 zenon_Hde zenon_H142 zenon_H155 zenon_H156. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.69/29.90 apply (zenon_L43_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.69/29.90 apply (zenon_L88_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.69/29.90 apply (zenon_L89_); trivial. % 29.69/29.90 apply (zenon_L90_); trivial. % 29.69/29.90 (* end of lemma zenon_L91_ *) % 29.69/29.90 assert (zenon_L92_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H14b zenon_H33 zenon_H11e zenon_H27 zenon_H25 zenon_H3f zenon_H1e zenon_H8d zenon_H6f zenon_H68 zenon_H85 zenon_H84 zenon_H65 zenon_H83 zenon_H2d zenon_Hbd zenon_H108 zenon_H101 zenon_Hf6 zenon_H9b zenon_Hee zenon_He7 zenon_Hf9 zenon_H46 zenon_H102 zenon_Hfc zenon_Hd1 zenon_H100 zenon_H103 zenon_He4 zenon_Hd9 zenon_Hcd zenon_Hdf zenon_He1 zenon_H8a zenon_H125 zenon_Hd6 zenon_H20 zenon_H124 zenon_H156 zenon_H155 zenon_Hde zenon_He9 zenon_H3c zenon_Hc8 zenon_H73 zenon_H135 zenon_H11b zenon_H110 zenon_H113 zenon_H98 zenon_H10d zenon_H117 zenon_Hb3 zenon_Hb9. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.69/29.90 apply (zenon_L87_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.69/29.90 apply (zenon_L74_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.69/29.90 apply (zenon_L91_); trivial. % 29.69/29.90 apply (zenon_L69_); trivial. % 29.69/29.90 (* end of lemma zenon_L92_ *) % 29.69/29.90 assert (zenon_L93_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H159 zenon_Hfd zenon_H155. % 29.69/29.90 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H159. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hfd. % 29.69/29.90 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hc5. apply refl_equal. % 29.69/29.90 apply zenon_H158. apply sym_equal. exact zenon_H155. % 29.69/29.90 (* end of lemma zenon_L93_ *) % 29.69/29.90 assert (zenon_L94_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H15a zenon_H73 zenon_Hdc. % 29.69/29.90 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H15a. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H73. % 29.69/29.90 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 29.69/29.90 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hcb. apply refl_equal. % 29.69/29.90 apply zenon_H15b. apply sym_equal. exact zenon_Hdc. % 29.69/29.90 (* end of lemma zenon_L94_ *) % 29.69/29.90 assert (zenon_L95_ : ((op (e1) (e1)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hfd zenon_He9 zenon_H35. % 29.69/29.90 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H35. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hc4. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hc6. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hfd. % 29.69/29.90 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_Hc5. apply refl_equal. % 29.69/29.90 apply zenon_H153. apply sym_equal. exact zenon_He9. % 29.69/29.90 apply zenon_Hc5. apply refl_equal. % 29.69/29.90 apply zenon_Hc5. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L95_ *) % 29.69/29.90 assert (zenon_L96_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))) -> ((op (e2) (e2)) = (e1)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H15c zenon_H25. % 29.69/29.90 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 29.69/29.90 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_H56 zenon_H25). % 29.69/29.90 exact (zenon_H56 zenon_H25). % 29.69/29.90 (* end of lemma zenon_L96_ *) % 29.69/29.90 assert (zenon_L97_ : (~((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e1)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H15d zenon_H25. % 29.69/29.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.90 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_H56 zenon_H25). % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L97_ *) % 29.69/29.90 assert (zenon_L98_ : ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> (~((e3) = (op (op (e2) (e2)) (e2)))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H15e zenon_H25 zenon_H15f. % 29.69/29.90 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 29.69/29.90 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e3) = (op (op (e2) (e2)) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H15f. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H160. % 29.69/29.90 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 29.69/29.90 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e1) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H162. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H15e. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 29.69/29.90 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H163. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H160. % 29.69/29.90 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 29.69/29.90 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 29.69/29.90 congruence. % 29.69/29.90 apply (zenon_L97_); trivial. % 29.69/29.90 apply zenon_H161. apply refl_equal. % 29.69/29.90 apply zenon_H161. apply refl_equal. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 apply zenon_H161. apply refl_equal. % 29.69/29.90 apply zenon_H161. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L98_ *) % 29.69/29.90 assert (zenon_L99_ : ((op (e1) (e1)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hc3 zenon_H15e zenon_H25. % 29.69/29.90 apply (zenon_notand_s _ _ ax19); [ zenon_intro zenon_H165 | zenon_intro zenon_H164 ]. % 29.69/29.90 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 29.69/29.90 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (e2) (e2))))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H165. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H166. % 29.69/29.90 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 29.69/29.90 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e1) (e1)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H168. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hc3. % 29.69/29.90 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.90 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 29.69/29.90 congruence. % 29.69/29.90 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 29.69/29.90 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))))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H169. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H166. % 29.69/29.90 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 29.69/29.90 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 29.69/29.90 congruence. % 29.69/29.90 apply (zenon_L96_); trivial. % 29.69/29.90 apply zenon_H167. apply refl_equal. % 29.69/29.90 apply zenon_H167. apply refl_equal. % 29.69/29.90 apply zenon_H1d. apply refl_equal. % 29.69/29.90 apply zenon_H167. apply refl_equal. % 29.69/29.90 apply zenon_H167. apply refl_equal. % 29.69/29.90 apply (zenon_notand_s _ _ zenon_H164); [ zenon_intro zenon_H15f | zenon_intro zenon_H59 ]. % 29.69/29.90 apply (zenon_L98_); trivial. % 29.69/29.90 apply zenon_H59. apply sym_equal. exact zenon_H25. % 29.69/29.90 (* end of lemma zenon_L99_ *) % 29.69/29.90 assert (zenon_L100_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H102 zenon_H25 zenon_H15e zenon_H68 zenon_Hd1 zenon_H35 zenon_He9 zenon_H103. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 29.69/29.90 apply (zenon_L99_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 29.69/29.90 apply (zenon_L45_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 29.69/29.90 apply (zenon_L95_); trivial. % 29.69/29.90 exact (zenon_H103 zenon_H37). % 29.69/29.90 (* end of lemma zenon_L100_ *) % 29.69/29.90 assert (zenon_L101_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H16a zenon_H16b zenon_H16c. % 29.69/29.90 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H16a. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H16b. % 29.69/29.90 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 29.69/29.90 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 29.69/29.90 congruence. % 29.69/29.90 apply zenon_H16e. apply refl_equal. % 29.69/29.90 apply zenon_H16d. apply sym_equal. exact zenon_H16c. % 29.69/29.90 (* end of lemma zenon_L101_ *) % 29.69/29.90 assert (zenon_L102_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H8d zenon_H85 zenon_H6f zenon_H73 zenon_H16f zenon_Had zenon_H103 zenon_He9 zenon_H35 zenon_Hd1 zenon_H68 zenon_H25 zenon_H102 zenon_H16a zenon_H16b. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.69/29.90 exact (zenon_H85 zenon_H89). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.69/29.90 apply (zenon_L18_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.69/29.90 apply (zenon_L23_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.69/29.90 apply (zenon_L34_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.69/29.90 exact (zenon_H103 zenon_H37). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.69/29.90 apply (zenon_L100_); trivial. % 29.69/29.90 apply (zenon_L101_); trivial. % 29.69/29.90 (* end of lemma zenon_L102_ *) % 29.69/29.90 assert (zenon_L103_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 29.69/29.90 do 0 intro. intros zenon_H8d zenon_H6f zenon_H68 zenon_H85 zenon_H25 zenon_H84 zenon_H1e zenon_H65 zenon_H83 zenon_He1 zenon_He2. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.69/29.90 exact (zenon_H85 zenon_H89). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.69/29.90 apply (zenon_L18_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.69/29.90 apply (zenon_L24_); trivial. % 29.69/29.90 apply (zenon_L50_); trivial. % 29.69/29.90 (* end of lemma zenon_L103_ *) % 29.69/29.90 assert (zenon_L104_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e2) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H16a zenon_H102 zenon_Hd1 zenon_H35 zenon_He9 zenon_H103 zenon_Had zenon_H16f zenon_H172 zenon_H173 zenon_H6b zenon_H92 zenon_H97 zenon_H14e zenon_H14b zenon_H33 zenon_H11e zenon_H27 zenon_H3f zenon_H2d zenon_Hbd zenon_H108 zenon_H101 zenon_Hf6 zenon_H9b zenon_Hee zenon_He7 zenon_Hf9 zenon_H46 zenon_Hfc zenon_H100 zenon_He4 zenon_Hd9 zenon_H125 zenon_Hd6 zenon_H20 zenon_H124 zenon_H156 zenon_H3c zenon_Hc8 zenon_H135 zenon_H11b zenon_H110 zenon_H113 zenon_H10d zenon_Hb3 zenon_Hb9 zenon_H174 zenon_Hcd zenon_Hdf zenon_Hde zenon_H8d zenon_H6f zenon_H68 zenon_H85 zenon_H25 zenon_H84 zenon_H1e zenon_H65 zenon_H83 zenon_He1. % 29.69/29.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.69/29.90 exact (zenon_H85 zenon_H89). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.69/29.90 apply (zenon_L4_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.69/29.90 exact (zenon_H85 zenon_H89). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.69/29.90 apply (zenon_L18_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.69/29.90 apply (zenon_L23_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.69/29.90 apply (zenon_L16_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.69/29.90 apply (zenon_L42_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.69/29.90 apply (zenon_L74_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 29.69/29.90 apply (zenon_L2_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 29.69/29.90 apply (zenon_L45_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 29.69/29.90 apply (zenon_L46_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.69/29.90 apply (zenon_L48_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.69/29.90 apply (zenon_L95_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.69/29.90 apply (zenon_L86_); trivial. % 29.69/29.90 apply (zenon_L92_); trivial. % 29.69/29.90 apply (zenon_L102_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.69/29.90 apply (zenon_L48_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.69/29.90 apply (zenon_L49_); trivial. % 29.69/29.90 apply (zenon_L103_); trivial. % 29.69/29.90 (* end of lemma zenon_L104_ *) % 29.69/29.90 assert (zenon_L105_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e2) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_He4 zenon_Hda zenon_Hd9 zenon_Hcd zenon_Hdf zenon_Hde zenon_H8d zenon_H6f zenon_H68 zenon_H85 zenon_H25 zenon_H84 zenon_H1e zenon_H65 zenon_H83 zenon_He1. % 29.69/29.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.69/29.90 apply (zenon_L47_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.69/29.90 apply (zenon_L48_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.69/29.90 apply (zenon_L49_); trivial. % 29.69/29.90 apply (zenon_L103_); trivial. % 29.69/29.90 (* end of lemma zenon_L105_ *) % 29.69/29.90 assert (zenon_L106_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 29.69/29.90 do 0 intro. intros zenon_H33 zenon_H17b zenon_Hcd. % 29.69/29.90 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 29.69/29.90 cut (((e2) = (e2)) = ((e1) = (e2))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hcd. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hce. % 29.69/29.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.90 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e0) (e3)) = (e1)) = ((e2) = (e1))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_Hcf. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H33. % 29.69/29.90 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.90 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_H17c zenon_H17b). % 29.69/29.90 apply zenon_H22. apply refl_equal. % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 apply zenon_H57. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L106_ *) % 29.69/29.90 assert (zenon_L107_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hb1 zenon_Hbc zenon_H2d. % 29.69/29.90 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.69/29.90 cut (((e3) = (e3)) = ((e0) = (e3))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H2d. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_H2e. % 29.69/29.90 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.90 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 29.69/29.90 congruence. % 29.69/29.90 cut (((op (e3) (e3)) = (e0)) = ((e3) = (e0))). % 29.69/29.90 intro zenon_D_pnotp. % 29.69/29.90 apply zenon_H30. % 29.69/29.90 rewrite <- zenon_D_pnotp. % 29.69/29.90 exact zenon_Hb1. % 29.69/29.90 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.90 cut (((op (e3) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 29.69/29.90 congruence. % 29.69/29.90 exact (zenon_Hb9 zenon_Hbc). % 29.69/29.90 apply zenon_H1d. apply refl_equal. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 apply zenon_H2f. apply refl_equal. % 29.69/29.90 (* end of lemma zenon_L107_ *) % 29.69/29.90 assert (zenon_L108_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (op (e3) (e1))) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hbd zenon_H20 zenon_Ha4 zenon_H33 zenon_Ha3 zenon_H97 zenon_H9b zenon_H90 zenon_H3f zenon_H1e zenon_Haa zenon_Hbc zenon_H2d. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.69/29.90 apply (zenon_L27_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.69/29.90 apply (zenon_L29_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.69/29.90 apply (zenon_L33_); trivial. % 29.69/29.90 apply (zenon_L107_); trivial. % 29.69/29.90 (* end of lemma zenon_L108_ *) % 29.69/29.90 assert (zenon_L109_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e1))) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 29.69/29.90 do 0 intro. intros zenon_Hc0 zenon_H27 zenon_H92 zenon_H84 zenon_H69 zenon_H25 zenon_H6b zenon_Hbd zenon_H20 zenon_Ha4 zenon_Ha3 zenon_H97 zenon_H9b zenon_H3f zenon_H1e zenon_Haa zenon_Hbc zenon_H2d. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.69/29.90 exact (zenon_H84 zenon_H88). % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.69/29.90 apply (zenon_L2_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.69/29.90 apply (zenon_L3_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.69/29.90 exact (zenon_H84 zenon_H88). % 29.69/29.90 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.69/29.90 apply (zenon_L16_); trivial. % 29.69/29.90 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.69/29.90 apply (zenon_L17_); trivial. % 29.69/29.90 apply (zenon_L108_); trivial. % 29.69/29.90 (* end of lemma zenon_L109_ *) % 29.69/29.91 assert (zenon_L110_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H17d zenon_H8a zenon_Hbc. % 29.69/29.91 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H17d. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H8a. % 29.69/29.91 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 29.69/29.91 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H9a. apply refl_equal. % 29.69/29.91 apply zenon_H17e. apply sym_equal. exact zenon_Hbc. % 29.69/29.91 (* end of lemma zenon_L110_ *) % 29.69/29.91 assert (zenon_L111_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H8d zenon_H85 zenon_H6f zenon_H68 zenon_H73 zenon_H25 zenon_H17d zenon_Hbc. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.69/29.91 exact (zenon_H85 zenon_H89). % 29.69/29.91 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.69/29.91 apply (zenon_L18_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.69/29.91 apply (zenon_L23_); trivial. % 29.69/29.91 apply (zenon_L110_); trivial. % 29.69/29.91 (* end of lemma zenon_L111_ *) % 29.69/29.91 assert (zenon_L112_ : (~((op (e3) (e3)) = (op (e3) (op (e3) (e3))))) -> ((op (e3) (e3)) = (e3)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H17f zenon_Hbc. % 29.69/29.91 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 29.69/29.91 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H2f. apply refl_equal. % 29.69/29.91 apply zenon_H17e. apply sym_equal. exact zenon_Hbc. % 29.69/29.91 (* end of lemma zenon_L112_ *) % 29.69/29.91 assert (zenon_L113_ : ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_Hb3 zenon_Hbc zenon_H16c zenon_H14e. % 29.69/29.91 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H14e. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_Ha5. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H180. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_Hb3. % 29.69/29.91 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 29.69/29.91 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 29.69/29.91 congruence. % 29.69/29.91 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H181. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_Ha5. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 29.69/29.91 congruence. % 29.69/29.91 apply (zenon_L112_); trivial. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 apply zenon_H16d. apply sym_equal. exact zenon_H16c. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L113_ *) % 29.69/29.91 assert (zenon_L114_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H16f zenon_H6f zenon_H103 zenon_He9 zenon_H35 zenon_Hd1 zenon_H68 zenon_H25 zenon_H102 zenon_Hb3 zenon_Hbc zenon_H14e. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.69/29.91 apply (zenon_L18_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.69/29.91 exact (zenon_H103 zenon_H37). % 29.69/29.91 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.69/29.91 apply (zenon_L100_); trivial. % 29.69/29.91 apply (zenon_L113_); trivial. % 29.69/29.91 (* end of lemma zenon_L114_ *) % 29.69/29.91 assert (zenon_L115_ : ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H182 zenon_H33 zenon_H16a. % 29.69/29.91 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 29.69/29.91 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H16a. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H183. % 29.69/29.91 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 29.69/29.91 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H184. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H182. % 29.69/29.91 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 29.69/29.91 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H150. apply refl_equal. % 29.69/29.91 apply zenon_H34. apply sym_equal. exact zenon_H33. % 29.69/29.91 apply zenon_H150. apply refl_equal. % 29.69/29.91 apply zenon_H150. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L115_ *) % 29.69/29.91 assert (zenon_L116_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_Hc0 zenon_H84 zenon_H20 zenon_H1e zenon_H27 zenon_H25 zenon_H182 zenon_H16a. % 29.69/29.91 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.69/29.91 exact (zenon_H84 zenon_H88). % 29.69/29.91 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.69/29.91 apply (zenon_L2_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.69/29.91 apply (zenon_L3_); trivial. % 29.69/29.91 apply (zenon_L115_); trivial. % 29.69/29.91 (* end of lemma zenon_L116_ *) % 29.69/29.91 assert (zenon_L117_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H185 zenon_H33 zenon_H20. % 29.69/29.91 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 29.69/29.91 cut (((e1) = (e1)) = ((e0) = (e1))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H20. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H21. % 29.69/29.91 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.91 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H23. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H185. % 29.69/29.91 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.91 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H186]. % 29.69/29.91 congruence. % 29.69/29.91 exact (zenon_H186 zenon_H33). % 29.69/29.91 apply zenon_H1d. apply refl_equal. % 29.69/29.91 apply zenon_H22. apply refl_equal. % 29.69/29.91 apply zenon_H22. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L117_ *) % 29.69/29.91 assert (zenon_L118_ : (~((op (e0) (e0)) = (op (e0) (op (e0) (e1))))) -> ((op (e0) (e1)) = (e0)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H187 zenon_H1e. % 29.69/29.91 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 29.69/29.91 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H1d. apply refl_equal. % 29.69/29.91 apply zenon_Hc7. apply sym_equal. exact zenon_H1e. % 29.69/29.91 (* end of lemma zenon_L118_ *) % 29.69/29.91 assert (zenon_L119_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H15a zenon_H188 zenon_H1e zenon_H68. % 29.69/29.91 cut (((op (e0) (op (e0) (e1))) = (e1)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H15a. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H188. % 29.69/29.91 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 29.69/29.91 cut (((op (e0) (op (e0) (e1))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 29.69/29.91 congruence. % 29.69/29.91 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H18b | zenon_intro zenon_Hcb ]. % 29.69/29.91 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (e0) (op (e0) (e1))) = (op (e0) (e0)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H18a. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H18b. % 29.69/29.91 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 29.69/29.91 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 29.69/29.91 congruence. % 29.69/29.91 apply (zenon_L118_); trivial. % 29.69/29.91 apply zenon_Hcb. apply refl_equal. % 29.69/29.91 apply zenon_Hcb. apply refl_equal. % 29.69/29.91 apply zenon_H189. apply sym_equal. exact zenon_H68. % 29.69/29.91 (* end of lemma zenon_L119_ *) % 29.69/29.91 assert (zenon_L120_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H18c zenon_H68 zenon_H6c. % 29.69/29.91 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e2) (e0)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H18c. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H68. % 29.69/29.91 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18d]. % 29.69/29.91 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_Hd4. apply refl_equal. % 29.69/29.91 apply zenon_H18d. apply sym_equal. exact zenon_H6c. % 29.69/29.91 (* end of lemma zenon_L120_ *) % 29.69/29.91 assert (zenon_L121_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.69/29.91 do 0 intro. intros zenon_Haa zenon_H1e zenon_H113 zenon_H112 zenon_He9 zenon_H3f zenon_H18e. % 29.69/29.91 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H95 | zenon_intro zenon_Hab ]. % 29.69/29.91 apply (zenon_L29_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H98 | zenon_intro zenon_Hac ]. % 29.69/29.91 apply (zenon_L66_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9d | zenon_intro zenon_H40 ]. % 29.69/29.91 apply (zenon_L53_); trivial. % 29.69/29.91 exact (zenon_H18e zenon_H40). % 29.69/29.91 (* end of lemma zenon_L121_ *) % 29.69/29.91 assert (zenon_L122_ : (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> False). % 29.69/29.91 do 0 intro. intros zenon_Hcd zenon_Hfd zenon_Hd2. % 29.69/29.91 cut (((op (e1) (e1)) = (e2)) = ((e1) = (e2))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_Hcd. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_Hfd. % 29.69/29.91 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.91 cut (((op (e1) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 29.69/29.91 congruence. % 29.69/29.91 exact (zenon_H18f zenon_Hd2). % 29.69/29.91 apply zenon_H57. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L122_ *) % 29.69/29.91 assert (zenon_L123_ : (~((op (e0) (e3)) = (op (e0) (op (e0) (e1))))) -> ((op (e0) (e1)) = (e3)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H190 zenon_H2c. % 29.69/29.91 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 29.69/29.91 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H1d. apply refl_equal. % 29.69/29.91 apply zenon_H191. apply sym_equal. exact zenon_H2c. % 29.69/29.91 (* end of lemma zenon_L123_ *) % 29.69/29.91 assert (zenon_L124_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> False). % 29.69/29.91 do 0 intro. intros zenon_Ha4 zenon_H188 zenon_H2c zenon_H112. % 29.69/29.91 cut (((op (e0) (op (e0) (e1))) = (e1)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_Ha4. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H188. % 29.69/29.91 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 29.69/29.91 cut (((op (e0) (op (e0) (e1))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 29.69/29.91 congruence. % 29.69/29.91 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H16e ]. % 29.69/29.91 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (op (e0) (e1))) = (op (e0) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H193. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H194. % 29.69/29.91 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 29.69/29.91 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 29.69/29.91 congruence. % 29.69/29.91 apply (zenon_L123_); trivial. % 29.69/29.91 apply zenon_H16e. apply refl_equal. % 29.69/29.91 apply zenon_H16e. apply refl_equal. % 29.69/29.91 apply zenon_H192. apply sym_equal. exact zenon_H112. % 29.69/29.91 (* end of lemma zenon_L124_ *) % 29.69/29.91 assert (zenon_L125_ : (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H6f zenon_H37 zenon_Hd2. % 29.69/29.91 cut (((op (e1) (e1)) = (e3)) = ((e1) = (e3))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H6f. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H37. % 29.69/29.91 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.91 cut (((op (e1) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 29.69/29.91 congruence. % 29.69/29.91 exact (zenon_H18f zenon_Hd2). % 29.69/29.91 apply zenon_H2f. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L125_ *) % 29.69/29.91 assert (zenon_L126_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H55 zenon_H3d zenon_He1. % 29.69/29.91 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.69/29.91 cut (((e3) = (e3)) = ((e2) = (e3))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_He1. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H2e. % 29.69/29.91 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.91 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H195. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H55. % 29.69/29.91 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.91 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 29.69/29.91 congruence. % 29.69/29.91 exact (zenon_H196 zenon_H3d). % 29.69/29.91 apply zenon_H57. apply refl_equal. % 29.69/29.91 apply zenon_H2f. apply refl_equal. % 29.69/29.91 apply zenon_H2f. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L126_ *) % 29.69/29.91 assert (zenon_L127_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H42 zenon_H112 zenon_H188 zenon_Ha4 zenon_Hd2 zenon_H6f zenon_He1 zenon_H55 zenon_H18e. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.69/29.91 apply (zenon_L124_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.69/29.91 apply (zenon_L125_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.69/29.91 apply (zenon_L126_); trivial. % 29.69/29.91 exact (zenon_H18e zenon_H40). % 29.69/29.91 (* end of lemma zenon_L127_ *) % 29.69/29.91 assert (zenon_L128_ : (~((op (e0) (e1)) = (op (e0) (op (e0) (e2))))) -> ((op (e0) (e2)) = (e1)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H197 zenon_H26. % 29.69/29.91 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 29.69/29.91 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H1d. apply refl_equal. % 29.69/29.91 apply zenon_H2b. apply sym_equal. exact zenon_H26. % 29.69/29.91 (* end of lemma zenon_L128_ *) % 29.69/29.91 assert (zenon_L129_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H3f zenon_H198 zenon_H26 zenon_H9d. % 29.69/29.91 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H3f. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H198. % 29.69/29.91 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 29.69/29.91 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 29.69/29.91 congruence. % 29.69/29.91 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 29.69/29.91 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e1)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H199. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H3a. % 29.69/29.91 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.69/29.91 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 29.69/29.91 congruence. % 29.69/29.91 apply (zenon_L128_); trivial. % 29.69/29.91 apply zenon_H3b. apply refl_equal. % 29.69/29.91 apply zenon_H3b. apply refl_equal. % 29.69/29.91 apply zenon_H9e. apply sym_equal. exact zenon_H9d. % 29.69/29.91 (* end of lemma zenon_L129_ *) % 29.69/29.91 assert (zenon_L130_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H19a zenon_Hd2 zenon_Hfc. % 29.69/29.91 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 29.69/29.91 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e1)) = (op (e1) (e2)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_Hfc. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H19b. % 29.69/29.91 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 29.69/29.91 cut (((op (e1) (e2)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19d]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e1)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H19d. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H19a. % 29.69/29.91 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 29.69/29.91 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H19c. apply refl_equal. % 29.69/29.91 apply zenon_Hd3. apply sym_equal. exact zenon_Hd2. % 29.69/29.91 apply zenon_H19c. apply refl_equal. % 29.69/29.91 apply zenon_H19c. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L130_ *) % 29.69/29.91 assert (zenon_L131_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H19e zenon_H37 zenon_H3d. % 29.69/29.91 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H19e. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H37. % 29.69/29.91 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 29.69/29.91 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_Hc5. apply refl_equal. % 29.69/29.91 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 29.69/29.91 (* end of lemma zenon_L131_ *) % 29.69/29.91 assert (zenon_L132_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H102 zenon_H19f zenon_Hfc zenon_H19a zenon_H9d zenon_H100 zenon_H19e zenon_H3d. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 29.69/29.91 exact (zenon_H19f zenon_Hc3). % 29.69/29.91 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 29.69/29.91 apply (zenon_L130_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 29.69/29.91 apply (zenon_L60_); trivial. % 29.69/29.91 apply (zenon_L131_); trivial. % 29.69/29.91 (* end of lemma zenon_L132_ *) % 29.69/29.91 assert (zenon_L133_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H112 zenon_H1a0 zenon_H110. % 29.69/29.91 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H110. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_Ha5. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H111. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H112. % 29.69/29.91 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 apply zenon_H1a1. apply sym_equal. exact zenon_H1a0. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L133_ *) % 29.69/29.91 assert (zenon_L134_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H1a2 zenon_H198 zenon_H3f zenon_H3d zenon_H19e zenon_H100 zenon_H9d zenon_Hfc zenon_H19f zenon_H102 zenon_H6c zenon_H6b zenon_H112 zenon_H110. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 29.69/29.91 apply (zenon_L129_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 29.69/29.91 apply (zenon_L132_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 29.69/29.91 apply (zenon_L17_); trivial. % 29.69/29.91 apply (zenon_L133_); trivial. % 29.69/29.91 (* end of lemma zenon_L134_ *) % 29.69/29.91 assert (zenon_L135_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_Hd2 zenon_H6f zenon_H110 zenon_H112 zenon_H6b zenon_H6c zenon_H102 zenon_H19f zenon_Hfc zenon_H9d zenon_H100 zenon_H19e zenon_H3f zenon_H198 zenon_H1a2 zenon_H18e. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.69/29.91 apply (zenon_L4_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.69/29.91 apply (zenon_L125_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.69/29.91 apply (zenon_L134_); trivial. % 29.69/29.91 exact (zenon_H18e zenon_H40). % 29.69/29.91 (* end of lemma zenon_L135_ *) % 29.69/29.91 assert (zenon_L136_ : ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H19a zenon_H26 zenon_H1a5. % 29.69/29.91 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 29.69/29.91 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H1a5. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H19b. % 29.69/29.91 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 29.69/29.91 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H1a6. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H19a. % 29.69/29.91 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 29.69/29.91 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H19c. apply refl_equal. % 29.69/29.91 apply zenon_H2b. apply sym_equal. exact zenon_H26. % 29.69/29.91 apply zenon_H19c. apply refl_equal. % 29.69/29.91 apply zenon_H19c. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L136_ *) % 29.69/29.91 assert (zenon_L137_ : ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H112 zenon_H182 zenon_H14e. % 29.69/29.91 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H14e. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_Ha5. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H180. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H112. % 29.69/29.91 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 apply zenon_H1a7. apply sym_equal. exact zenon_H182. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L137_ *) % 29.69/29.91 assert (zenon_L138_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H1a8 zenon_H18c zenon_H18e zenon_H1a2 zenon_H198 zenon_H3f zenon_H19e zenon_H100 zenon_Hfc zenon_H19f zenon_H102 zenon_H6c zenon_H6b zenon_H110 zenon_H6f zenon_H1e zenon_H2d zenon_H42 zenon_H188 zenon_Ha4 zenon_He1 zenon_Hcd zenon_Haa zenon_H113 zenon_H101 zenon_H1a5 zenon_H26 zenon_H112 zenon_H14e. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.69/29.91 apply (zenon_L120_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.69/29.91 apply (zenon_L121_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.69/29.91 apply (zenon_L122_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.69/29.91 apply (zenon_L127_); trivial. % 29.69/29.91 apply (zenon_L135_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.69/29.91 apply (zenon_L136_); trivial. % 29.69/29.91 apply (zenon_L137_); trivial. % 29.69/29.91 (* end of lemma zenon_L138_ *) % 29.69/29.91 assert (zenon_L139_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H17d zenon_H90 zenon_H112. % 29.69/29.91 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H17d. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H90. % 29.69/29.91 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 29.69/29.91 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H9a. apply refl_equal. % 29.69/29.91 apply zenon_H192. apply sym_equal. exact zenon_H112. % 29.69/29.91 (* end of lemma zenon_L139_ *) % 29.69/29.91 assert (zenon_L140_ : ((op (e3) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H112 zenon_H33 zenon_Ha4. % 29.69/29.91 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_Ha4. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_Ha5. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_Ha7. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H112. % 29.69/29.91 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 29.69/29.91 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 apply zenon_H34. apply sym_equal. exact zenon_H33. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 apply zenon_Ha6. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L140_ *) % 29.69/29.91 assert (zenon_L141_ : (((op (e1) (op (e1) (e0))) = (e0))/\(((op (e1) (op (e1) (e1))) = (e1))/\(((op (e1) (op (e1) (e2))) = (e2))/\(((op (e1) (op (e1) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2)))/\((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3)))))))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H45 zenon_H18e zenon_H112. % 29.69/29.91 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 29.69/29.91 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 29.69/29.91 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 29.69/29.91 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 29.69/29.91 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 29.69/29.91 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 29.69/29.91 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 29.69/29.91 exact (zenon_H1ab zenon_H112). % 29.69/29.91 exact (zenon_H18e zenon_H40). % 29.69/29.91 (* end of lemma zenon_L141_ *) % 29.69/29.91 assert (zenon_L142_ : ((op (e2) (e0)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_Hc9 zenon_Hdc zenon_H18c. % 29.69/29.91 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H6d ]. % 29.69/29.91 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e1) (e0)) = (op (e2) (e0)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H18c. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H1ac. % 29.69/29.91 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.69/29.91 cut (((op (e2) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ad]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e1) (e0)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H1ad. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_Hc9. % 29.69/29.91 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 29.69/29.91 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H6d. apply refl_equal. % 29.69/29.91 apply zenon_H15b. apply sym_equal. exact zenon_Hdc. % 29.69/29.91 apply zenon_H6d. apply refl_equal. % 29.69/29.91 apply zenon_H6d. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L142_ *) % 29.69/29.91 assert (zenon_L143_ : (~((op (e2) (e2)) = (op (e2) (op (e2) (e3))))) -> ((op (e2) (e3)) = (e2)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H1ae zenon_Hf5. % 29.69/29.91 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 29.69/29.91 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H57. apply refl_equal. % 29.69/29.91 apply zenon_Hf8. apply sym_equal. exact zenon_Hf5. % 29.69/29.91 (* end of lemma zenon_L143_ *) % 29.69/29.91 assert (zenon_L144_ : ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H1af zenon_Hf5 zenon_H3d zenon_Hd6. % 29.69/29.91 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.91 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_Hd6. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H28. % 29.69/29.91 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.91 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_Hd7. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H1af. % 29.69/29.91 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 29.69/29.91 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 29.69/29.91 congruence. % 29.69/29.91 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.91 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e2)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H1b0. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H28. % 29.69/29.91 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.91 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 29.69/29.91 congruence. % 29.69/29.91 apply (zenon_L143_); trivial. % 29.69/29.91 apply zenon_H29. apply refl_equal. % 29.69/29.91 apply zenon_H29. apply refl_equal. % 29.69/29.91 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 29.69/29.91 apply zenon_H29. apply refl_equal. % 29.69/29.91 apply zenon_H29. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L144_ *) % 29.69/29.91 assert (zenon_L145_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_He1 zenon_Hd0 zenon_H1af zenon_H3d zenon_Hd6. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.69/29.91 apply (zenon_L142_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.69/29.91 apply (zenon_L126_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.69/29.91 exact (zenon_Hd0 zenon_Hcc). % 29.69/29.91 apply (zenon_L144_); trivial. % 29.69/29.91 (* end of lemma zenon_L145_ *) % 29.69/29.91 assert (zenon_L146_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_Hd2 zenon_H6f zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.69/29.91 apply (zenon_L4_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.69/29.91 apply (zenon_L125_); trivial. % 29.69/29.91 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.69/29.91 apply (zenon_L145_); trivial. % 29.69/29.91 exact (zenon_H18e zenon_H40). % 29.69/29.91 (* end of lemma zenon_L146_ *) % 29.69/29.91 assert (zenon_L147_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H1b1 zenon_H68 zenon_H19a. % 29.69/29.91 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H1b1. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H68. % 29.69/29.91 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 29.69/29.91 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_Hd4. apply refl_equal. % 29.69/29.91 apply zenon_H1b2. apply sym_equal. exact zenon_H19a. % 29.69/29.91 (* end of lemma zenon_L147_ *) % 29.69/29.91 assert (zenon_L148_ : (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> False). % 29.69/29.91 do 0 intro. intros zenon_H2d zenon_H89 zenon_H64. % 29.69/29.91 cut (((op (e0) (e0)) = (e3)) = ((e0) = (e3))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H2d. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H89. % 29.69/29.91 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.91 cut (((op (e0) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1b3]. % 29.69/29.91 congruence. % 29.69/29.91 exact (zenon_H1b3 zenon_H64). % 29.69/29.91 apply zenon_H2f. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L148_ *) % 29.69/29.91 assert (zenon_L149_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> False). % 29.69/29.91 do 0 intro. intros zenon_Hd9 zenon_H89 zenon_H117. % 29.69/29.91 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e0) (e2)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_Hd9. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H89. % 29.69/29.91 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 29.69/29.91 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_Hcb. apply refl_equal. % 29.69/29.91 apply zenon_H119. apply sym_equal. exact zenon_H117. % 29.69/29.91 (* end of lemma zenon_L149_ *) % 29.69/29.91 assert (zenon_L150_ : ((op (e3) (e1)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H40 zenon_H37 zenon_H100. % 29.69/29.91 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 29.69/29.91 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e1) (e1)) = (op (e3) (e1)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H100. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H1b4. % 29.69/29.91 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 29.69/29.91 cut (((op (e3) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e1) (e1)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H1b6. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H40. % 29.69/29.91 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 29.69/29.91 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_H1b5. apply refl_equal. % 29.69/29.91 apply zenon_H38. apply sym_equal. exact zenon_H37. % 29.69/29.91 apply zenon_H1b5. apply refl_equal. % 29.69/29.91 apply zenon_H1b5. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L150_ *) % 29.69/29.91 assert (zenon_L151_ : ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 29.69/29.91 do 0 intro. intros zenon_Hb6 zenon_H117 zenon_H10d. % 29.69/29.91 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 29.69/29.91 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H10d. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_Hef. % 29.69/29.91 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.69/29.91 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H118. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_Hb6. % 29.69/29.91 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 29.69/29.91 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.69/29.91 congruence. % 29.69/29.91 apply zenon_Hf0. apply refl_equal. % 29.69/29.91 apply zenon_H119. apply sym_equal. exact zenon_H117. % 29.69/29.91 apply zenon_Hf0. apply refl_equal. % 29.69/29.91 apply zenon_Hf0. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L151_ *) % 29.69/29.91 assert (zenon_L152_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 29.69/29.91 do 0 intro. intros zenon_H112 zenon_Hbc zenon_H6f. % 29.69/29.91 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.69/29.91 cut (((e3) = (e3)) = ((e1) = (e3))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H6f. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H2e. % 29.69/29.91 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.91 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 29.69/29.91 congruence. % 29.69/29.91 cut (((op (e3) (e3)) = (e1)) = ((e3) = (e1))). % 29.69/29.91 intro zenon_D_pnotp. % 29.69/29.91 apply zenon_H70. % 29.69/29.91 rewrite <- zenon_D_pnotp. % 29.69/29.91 exact zenon_H112. % 29.69/29.91 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.91 cut (((op (e3) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 29.69/29.91 congruence. % 29.69/29.91 exact (zenon_Hb9 zenon_Hbc). % 29.69/29.91 apply zenon_H22. apply refl_equal. % 29.69/29.91 apply zenon_H2f. apply refl_equal. % 29.69/29.91 apply zenon_H2f. apply refl_equal. % 29.69/29.91 (* end of lemma zenon_L152_ *) % 29.69/29.91 assert (zenon_L153_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 29.69/29.91 do 0 intro. intros zenon_Hb8 zenon_Had zenon_H6e zenon_H100 zenon_H37 zenon_H10d zenon_H117 zenon_H112 zenon_H6f. % 29.69/29.92 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 29.69/29.92 apply (zenon_L34_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 29.69/29.92 apply (zenon_L150_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 29.69/29.92 apply (zenon_L151_); trivial. % 29.69/29.92 apply (zenon_L152_); trivial. % 29.69/29.92 (* end of lemma zenon_L153_ *) % 29.69/29.92 assert (zenon_L154_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> False). % 29.69/29.92 do 0 intro. intros zenon_Hd1 zenon_Hdc zenon_Hfd. % 29.69/29.92 cut (((op (e1) (e0)) = (e2)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_Hd1. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Hdc. % 29.69/29.92 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 29.69/29.92 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_Hd4. apply refl_equal. % 29.69/29.92 apply zenon_H149. apply sym_equal. exact zenon_Hfd. % 29.69/29.92 (* end of lemma zenon_L154_ *) % 29.69/29.92 assert (zenon_L155_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H102 zenon_H35 zenon_H1e zenon_Hfc zenon_H19a zenon_Hdc zenon_Hd1 zenon_H19e zenon_H3d. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 29.69/29.92 apply (zenon_L42_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 29.69/29.92 apply (zenon_L130_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 29.69/29.92 apply (zenon_L154_); trivial. % 29.69/29.92 apply (zenon_L131_); trivial. % 29.69/29.92 (* end of lemma zenon_L155_ *) % 29.69/29.92 assert (zenon_L156_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H42 zenon_H2d zenon_H6f zenon_H112 zenon_H117 zenon_H10d zenon_H100 zenon_H6e zenon_Had zenon_Hb8 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.69/29.92 apply (zenon_L4_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.69/29.92 apply (zenon_L153_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.69/29.92 apply (zenon_L155_); trivial. % 29.69/29.92 exact (zenon_H18e zenon_H40). % 29.69/29.92 (* end of lemma zenon_L156_ *) % 29.69/29.92 assert (zenon_L157_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H6c zenon_H76 zenon_H6f. % 29.69/29.92 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.69/29.92 cut (((e3) = (e3)) = ((e1) = (e3))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H6f. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H2e. % 29.69/29.92 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.92 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (e0)) = (e1)) = ((e3) = (e1))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H70. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H6c. % 29.69/29.92 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.92 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 29.69/29.92 congruence. % 29.69/29.92 exact (zenon_H1b7 zenon_H76). % 29.69/29.92 apply zenon_H22. apply refl_equal. % 29.69/29.92 apply zenon_H2f. apply refl_equal. % 29.69/29.92 apply zenon_H2f. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L157_ *) % 29.69/29.92 assert (zenon_L158_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_Hfd zenon_H37 zenon_He1. % 29.69/29.92 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.69/29.92 cut (((e3) = (e3)) = ((e2) = (e3))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_He1. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H2e. % 29.69/29.92 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.92 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e1) (e1)) = (e2)) = ((e3) = (e2))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H195. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Hfd. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 29.69/29.92 congruence. % 29.69/29.92 exact (zenon_H103 zenon_H37). % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_H2f. apply refl_equal. % 29.69/29.92 apply zenon_H2f. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L158_ *) % 29.69/29.92 assert (zenon_L159_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H19a zenon_Hed zenon_Hcd. % 29.69/29.92 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 29.69/29.92 cut (((e2) = (e2)) = ((e1) = (e2))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_Hcd. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Hce. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e1) (e2)) = (e1)) = ((e2) = (e1))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_Hcf. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H19a. % 29.69/29.92 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.92 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 29.69/29.92 congruence. % 29.69/29.92 exact (zenon_H1b8 zenon_Hed). % 29.69/29.92 apply zenon_H22. apply refl_equal. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L159_ *) % 29.69/29.92 assert (zenon_L160_ : ((op (e2) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1b9 zenon_H117 zenon_H27. % 29.69/29.92 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H27. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H28. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H2a. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1b9. % 29.69/29.92 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H119. apply sym_equal. exact zenon_H117. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L160_ *) % 29.69/29.92 assert (zenon_L161_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H142 zenon_H1ba zenon_Hd6. % 29.69/29.92 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_Hd6. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H28. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_Hd7. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H142. % 29.69/29.92 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H1bb. apply sym_equal. exact zenon_H1ba. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L161_ *) % 29.69/29.92 assert (zenon_L162_ : (~((op (e2) (e1)) = (op (e2) (op (e2) (e1))))) -> ((op (e2) (e1)) = (e1)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1bc zenon_Hd5. % 29.69/29.92 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_Hd8. apply sym_equal. exact zenon_Hd5. % 29.69/29.92 (* end of lemma zenon_L162_ *) % 29.69/29.92 assert (zenon_L163_ : ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H5e zenon_Hd5 zenon_H6c zenon_H1bd. % 29.69/29.92 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (e0)) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1bd. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H62. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (op (e2) (e1))) = (e1)) = ((op (e2) (e1)) = (op (e2) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1be. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H5e. % 29.69/29.92 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18d]. % 29.69/29.92 cut (((op (e2) (op (e2) (e1))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1bf]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (op (e2) (e1))) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1bf. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H62. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L162_); trivial. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H18d. apply sym_equal. exact zenon_H6c. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L163_ *) % 29.69/29.92 assert (zenon_L164_ : (~((op (e2) (e0)) = (op (e2) (op (e2) (e2))))) -> ((op (e2) (e2)) = (e0)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1c0 zenon_H142. % 29.69/29.92 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_H1c1. apply sym_equal. exact zenon_H142. % 29.69/29.92 (* end of lemma zenon_L164_ *) % 29.69/29.92 assert (zenon_L165_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1bd zenon_H60 zenon_H142 zenon_H55. % 29.69/29.92 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1bd. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H60. % 29.69/29.92 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 29.69/29.92 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H6d ]. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1c3. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1ac. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L164_); trivial. % 29.69/29.92 apply zenon_H6d. apply refl_equal. % 29.69/29.92 apply zenon_H6d. apply refl_equal. % 29.69/29.92 apply zenon_H1c2. apply sym_equal. exact zenon_H55. % 29.69/29.92 (* end of lemma zenon_L165_ *) % 29.69/29.92 assert (zenon_L166_ : (~((op (e2) (e3)) = (op (e2) (op (e2) (e3))))) -> ((op (e2) (e3)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1c4 zenon_H1c5. % 29.69/29.92 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_H1c6. apply sym_equal. exact zenon_H1c5. % 29.69/29.92 (* end of lemma zenon_L166_ *) % 29.69/29.92 assert (zenon_L167_ : ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1af zenon_H1c5 zenon_H3d zenon_H1c7. % 29.69/29.92 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1c7. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H109. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1c8. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1af. % 29.69/29.92 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e3)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1c9. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H109. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L166_); trivial. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L167_ *) % 29.69/29.92 assert (zenon_L168_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H142 zenon_H60 zenon_H1bd zenon_H1af zenon_H1c5 zenon_H1c7. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1cb ]. % 29.69/29.92 apply (zenon_L161_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H1cc ]. % 29.69/29.92 apply (zenon_L163_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H55 | zenon_intro zenon_H3d ]. % 29.69/29.92 apply (zenon_L165_); trivial. % 29.69/29.92 apply (zenon_L167_); trivial. % 29.69/29.92 (* end of lemma zenon_L168_ *) % 29.69/29.92 assert (zenon_L169_ : ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (op (op (e2) (e2)) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_Hfe zenon_H25 zenon_H1cd. % 29.69/29.92 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e0) = (op (op (e2) (e2)) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1cd. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H160. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e1) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1ce. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Hfe. % 29.69/29.92 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.92 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H163. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H160. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L97_); trivial. % 29.69/29.92 apply zenon_H161. apply refl_equal. % 29.69/29.92 apply zenon_H161. apply refl_equal. % 29.69/29.92 apply zenon_H1d. apply refl_equal. % 29.69/29.92 apply zenon_H161. apply refl_equal. % 29.69/29.92 apply zenon_H161. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L169_ *) % 29.69/29.92 assert (zenon_L170_ : ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H37 zenon_Hfe zenon_H25. % 29.69/29.92 apply (zenon_notand_s _ _ ax22); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H1cf ]. % 29.69/29.92 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 29.69/29.92 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e3) = (op (op (e2) (e2)) (op (e2) (e2))))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1d0. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H166. % 29.69/29.92 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 29.69/29.92 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e1) (e1)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1d1. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H37. % 29.69/29.92 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.92 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 29.69/29.92 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))))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H169. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H166. % 29.69/29.92 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 29.69/29.92 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L96_); trivial. % 29.69/29.92 apply zenon_H167. apply refl_equal. % 29.69/29.92 apply zenon_H167. apply refl_equal. % 29.69/29.92 apply zenon_H2f. apply refl_equal. % 29.69/29.92 apply zenon_H167. apply refl_equal. % 29.69/29.92 apply zenon_H167. apply refl_equal. % 29.69/29.92 apply (zenon_notand_s _ _ zenon_H1cf); [ zenon_intro zenon_H1cd | zenon_intro zenon_H59 ]. % 29.69/29.92 apply (zenon_L169_); trivial. % 29.69/29.92 apply zenon_H59. apply sym_equal. exact zenon_H25. % 29.69/29.92 (* end of lemma zenon_L170_ *) % 29.69/29.92 assert (zenon_L171_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H108 zenon_H1b9 zenon_H1c5. % 29.69/29.92 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H108. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1b9. % 29.69/29.92 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H1c6. apply sym_equal. exact zenon_H1c5. % 29.69/29.92 (* end of lemma zenon_L171_ *) % 29.69/29.92 assert (zenon_L172_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_Hfe zenon_H37 zenon_Hd0 zenon_H108 zenon_H1c5. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 29.69/29.92 apply (zenon_L168_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 29.69/29.92 apply (zenon_L170_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 29.69/29.92 exact (zenon_Hd0 zenon_Hcc). % 29.69/29.92 apply (zenon_L171_); trivial. % 29.69/29.92 (* end of lemma zenon_L172_ *) % 29.69/29.92 assert (zenon_L173_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1d5 zenon_H6f zenon_H19e zenon_H27 zenon_H117 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_Hfe zenon_H37 zenon_Hd0 zenon_H108. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.69/29.92 apply (zenon_L157_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.69/29.92 apply (zenon_L131_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.69/29.92 apply (zenon_L160_); trivial. % 29.69/29.92 apply (zenon_L172_); trivial. % 29.69/29.92 (* end of lemma zenon_L173_ *) % 29.69/29.92 assert (zenon_L174_ : ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H8a zenon_H76 zenon_H1d8. % 29.69/29.92 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9a ]. % 29.69/29.92 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1d8. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Ha0. % 29.69/29.92 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.92 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d9]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1d9. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H8a. % 29.69/29.92 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 29.69/29.92 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H9a. apply refl_equal. % 29.69/29.92 apply zenon_H1da. apply sym_equal. exact zenon_H76. % 29.69/29.92 apply zenon_H9a. apply refl_equal. % 29.69/29.92 apply zenon_H9a. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L174_ *) % 29.69/29.92 assert (zenon_L175_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H142 zenon_H1b9 zenon_H2d. % 29.69/29.92 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.69/29.92 cut (((e3) = (e3)) = ((e0) = (e3))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H2d. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H2e. % 29.69/29.92 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.92 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (e2)) = (e0)) = ((e3) = (e0))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H30. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H142. % 29.69/29.92 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.92 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 29.69/29.92 congruence. % 29.69/29.92 exact (zenon_H1db zenon_H1b9). % 29.69/29.92 apply zenon_H1d. apply refl_equal. % 29.69/29.92 apply zenon_H2f. apply refl_equal. % 29.69/29.92 apply zenon_H2f. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L175_ *) % 29.69/29.92 assert (zenon_L176_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H2d zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H142 zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.69/29.92 apply (zenon_L174_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.69/29.92 apply (zenon_L131_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.69/29.92 apply (zenon_L175_); trivial. % 29.69/29.92 apply (zenon_L168_); trivial. % 29.69/29.92 (* end of lemma zenon_L176_ *) % 29.69/29.92 assert (zenon_L177_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1dc zenon_H142 zenon_H9c. % 29.69/29.92 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1dc. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H142. % 29.69/29.92 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_Ha2. apply sym_equal. exact zenon_H9c. % 29.69/29.92 (* end of lemma zenon_L177_ *) % 29.69/29.92 assert (zenon_L178_ : (~((op (e2) (e3)) = (op (e2) (op (e2) (e2))))) -> ((op (e2) (e2)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1dd zenon_H1b9. % 29.69/29.92 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_H1de. apply sym_equal. exact zenon_H1b9. % 29.69/29.92 (* end of lemma zenon_L178_ *) % 29.69/29.92 assert (zenon_L179_ : ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H60 zenon_H1b9 zenon_H155 zenon_H156. % 29.69/29.92 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H156. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H109. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H157. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H60. % 29.69/29.92 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 29.69/29.92 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e3)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1df. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H109. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1dd]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L178_); trivial. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 apply zenon_H158. apply sym_equal. exact zenon_H155. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L179_ *) % 29.69/29.92 assert (zenon_L180_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1d2 zenon_H9c zenon_H1dc zenon_H6c zenon_H6b zenon_Hd0 zenon_H60 zenon_H155 zenon_H156. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 29.69/29.92 apply (zenon_L177_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 29.69/29.92 apply (zenon_L17_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 29.69/29.92 exact (zenon_Hd0 zenon_Hcc). % 29.69/29.92 apply (zenon_L179_); trivial. % 29.69/29.92 (* end of lemma zenon_L180_ *) % 29.69/29.92 assert (zenon_L181_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H14b zenon_H108 zenon_H117 zenon_H27 zenon_H6f zenon_H1c7 zenon_H1af zenon_H1bd zenon_H5e zenon_Hd6 zenon_H1ca zenon_H2d zenon_H19e zenon_H37 zenon_H8a zenon_H1d8 zenon_H1d5 zenon_H1d2 zenon_H1dc zenon_H6c zenon_H6b zenon_Hd0 zenon_H60 zenon_H155 zenon_H156. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.69/29.92 apply (zenon_L87_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.69/29.92 apply (zenon_L173_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.69/29.92 apply (zenon_L176_); trivial. % 29.69/29.92 apply (zenon_L180_); trivial. % 29.69/29.92 (* end of lemma zenon_L181_ *) % 29.69/29.92 assert (zenon_L182_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hc9 zenon_He1 zenon_Hcd zenon_H19a zenon_H14b zenon_H108 zenon_H117 zenon_H27 zenon_H6f zenon_H1c7 zenon_H1af zenon_H1bd zenon_H5e zenon_Hd6 zenon_H1ca zenon_H2d zenon_H19e zenon_H37 zenon_H8a zenon_H1d8 zenon_H1d5 zenon_H1d2 zenon_H1dc zenon_H6c zenon_H6b zenon_Hd0 zenon_H60 zenon_H156. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.69/29.92 apply (zenon_L142_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.69/29.92 apply (zenon_L158_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.69/29.92 apply (zenon_L159_); trivial. % 29.69/29.92 apply (zenon_L181_); trivial. % 29.69/29.92 (* end of lemma zenon_L182_ *) % 29.69/29.92 assert (zenon_L183_ : ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1af zenon_Hf5 zenon_H117 zenon_H27. % 29.69/29.92 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H27. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H28. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H2a. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1af. % 29.69/29.92 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1b0. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H28. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L143_); trivial. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H119. apply sym_equal. exact zenon_H117. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L183_ *) % 29.69/29.92 assert (zenon_L184_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H135 zenon_H156 zenon_H60 zenon_H6b zenon_H6c zenon_H1dc zenon_H1d2 zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H2d zenon_H1ca zenon_Hd6 zenon_H5e zenon_H1bd zenon_H1c7 zenon_H6f zenon_H108 zenon_H14b zenon_H19a zenon_Hcd zenon_He1 zenon_H18c zenon_H173 zenon_H3c zenon_He9 zenon_Hd0 zenon_H1af zenon_H117 zenon_H27. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.69/29.92 apply (zenon_L182_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.69/29.92 apply (zenon_L88_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.69/29.92 exact (zenon_Hd0 zenon_Hcc). % 29.69/29.92 apply (zenon_L183_); trivial. % 29.69/29.92 (* end of lemma zenon_L184_ *) % 29.69/29.92 assert (zenon_L185_ : (~((op (e2) (e0)) = (op (e2) (op (e2) (e3))))) -> ((op (e2) (e3)) = (e0)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1e0 zenon_H1e1. % 29.69/29.92 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_H1e2. apply sym_equal. exact zenon_H1e1. % 29.69/29.92 (* end of lemma zenon_L185_ *) % 29.69/29.92 assert (zenon_L186_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1d8 zenon_H1af zenon_H1e1 zenon_H8a. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e0)) = (op (e3) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1d8. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1af. % 29.69/29.92 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H6d ]. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1e4. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1ac. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L185_); trivial. % 29.69/29.92 apply zenon_H6d. apply refl_equal. % 29.69/29.92 apply zenon_H6d. apply refl_equal. % 29.69/29.92 apply zenon_H1e3. apply sym_equal. exact zenon_H8a. % 29.69/29.92 (* end of lemma zenon_L186_ *) % 29.69/29.92 assert (zenon_L187_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 29.69/29.92 do 0 intro. intros zenon_Hf6 zenon_H1e5 zenon_H112. % 29.69/29.92 cut (((op (e2) (e3)) = (e1)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_Hf6. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1e5. % 29.69/29.92 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 apply zenon_H192. apply sym_equal. exact zenon_H112. % 29.69/29.92 (* end of lemma zenon_L187_ *) % 29.69/29.92 assert (zenon_L188_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1e6 zenon_H8a zenon_H1d8 zenon_H112 zenon_Hf6 zenon_H27 zenon_H117 zenon_H1af zenon_H3d zenon_H1c7. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 29.69/29.92 apply (zenon_L186_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 29.69/29.92 apply (zenon_L187_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 29.69/29.92 apply (zenon_L183_); trivial. % 29.69/29.92 apply (zenon_L167_); trivial. % 29.69/29.92 (* end of lemma zenon_L188_ *) % 29.69/29.92 assert (zenon_L189_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H42 zenon_H1e zenon_Hd0 zenon_He9 zenon_H3c zenon_H173 zenon_H18c zenon_He1 zenon_Hcd zenon_H19a zenon_H14b zenon_H108 zenon_H6f zenon_H1bd zenon_H5e zenon_Hd6 zenon_H1ca zenon_H2d zenon_H19e zenon_H1d5 zenon_H1d2 zenon_H1dc zenon_H6c zenon_H6b zenon_H60 zenon_H156 zenon_H135 zenon_H1c7 zenon_H1af zenon_H117 zenon_H27 zenon_Hf6 zenon_H112 zenon_H1d8 zenon_H8a zenon_H1e6 zenon_H18e. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.69/29.92 apply (zenon_L4_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.69/29.92 apply (zenon_L184_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.69/29.92 apply (zenon_L188_); trivial. % 29.69/29.92 exact (zenon_H18e zenon_H40). % 29.69/29.92 (* end of lemma zenon_L189_ *) % 29.69/29.92 assert (zenon_L190_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H8d zenon_Hd9 zenon_H102 zenon_H35 zenon_Hfc zenon_Hdc zenon_Hd1 zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H42 zenon_H1e zenon_Hd0 zenon_He9 zenon_H3c zenon_H173 zenon_H18c zenon_He1 zenon_Hcd zenon_H19a zenon_H14b zenon_H108 zenon_H6f zenon_H1bd zenon_H5e zenon_Hd6 zenon_H1ca zenon_H2d zenon_H19e zenon_H1d5 zenon_H1d2 zenon_H1dc zenon_H6c zenon_H6b zenon_H60 zenon_H156 zenon_H135 zenon_H1c7 zenon_H1af zenon_H117 zenon_H27 zenon_Hf6 zenon_H112 zenon_H1d8 zenon_H1e6 zenon_H18e. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.69/29.92 apply (zenon_L149_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.69/29.92 apply (zenon_L156_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.69/29.92 apply (zenon_L157_); trivial. % 29.69/29.92 apply (zenon_L189_); trivial. % 29.69/29.92 (* end of lemma zenon_L190_ *) % 29.69/29.92 assert (zenon_L191_ : ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H5c zenon_Hc9 zenon_H10e zenon_H27. % 29.69/29.92 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H27. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H28. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (op (e2) (e0))) = (e0)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H2a. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H5c. % 29.69/29.92 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 29.69/29.92 cut (((op (e2) (op (e2) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (op (e2) (e0))) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1e9. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H28. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1ea]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_Hca. apply sym_equal. exact zenon_Hc9. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H139. apply sym_equal. exact zenon_H10e. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L191_ *) % 29.69/29.92 assert (zenon_L192_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H10e zenon_Hda zenon_Hde. % 29.69/29.92 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 29.69/29.92 cut (((e2) = (e2)) = ((e0) = (e2))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_Hde. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Hce. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e0) (e2)) = (e0)) = ((e2) = (e0))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H154. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H10e. % 29.69/29.92 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.92 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 29.69/29.92 congruence. % 29.69/29.92 exact (zenon_H1eb zenon_Hda). % 29.69/29.92 apply zenon_H1d. apply refl_equal. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L192_ *) % 29.69/29.92 assert (zenon_L193_ : ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1af zenon_Hf5 zenon_H76 zenon_H6b. % 29.69/29.92 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H6b. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H28. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1ec. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1af. % 29.69/29.92 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1b0. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H28. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L143_); trivial. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H1da. apply sym_equal. exact zenon_H76. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L193_ *) % 29.69/29.92 assert (zenon_L194_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1d8 zenon_H5c zenon_Hdf zenon_H8b. % 29.69/29.92 cut (((op (e2) (op (e2) (e0))) = (e0)) = ((op (e2) (e0)) = (op (e3) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1d8. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H5c. % 29.69/29.92 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 29.69/29.92 cut (((op (e2) (op (e2) (e0))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H6d ]. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (op (e2) (e0))) = (op (e2) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1ee. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1ac. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f0]. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_H1f0. apply sym_equal. exact zenon_Hdf. % 29.69/29.92 apply zenon_H6d. apply refl_equal. % 29.69/29.92 apply zenon_H6d. apply refl_equal. % 29.69/29.92 apply zenon_H1ed. apply sym_equal. exact zenon_H8b. % 29.69/29.92 (* end of lemma zenon_L194_ *) % 29.69/29.92 assert (zenon_L195_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1f1 zenon_H1b9. % 29.69/29.92 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 29.69/29.92 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 29.69/29.92 congruence. % 29.69/29.92 exact (zenon_H1db zenon_H1b9). % 29.69/29.92 exact (zenon_H1db zenon_H1b9). % 29.69/29.92 (* end of lemma zenon_L195_ *) % 29.69/29.92 assert (zenon_L196_ : (~((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1f2 zenon_H1b9. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 29.69/29.92 congruence. % 29.69/29.92 exact (zenon_H1db zenon_H1b9). % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L196_ *) % 29.69/29.92 assert (zenon_L197_ : ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (op (op (e2) (e2)) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H9c zenon_H1b9 zenon_H1cd. % 29.69/29.92 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e0) = (op (op (e2) (e2)) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1cd. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H160. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e3) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1ce. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H9c. % 29.69/29.92 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.69/29.92 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1f3. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H160. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 29.69/29.92 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L196_); trivial. % 29.69/29.92 apply zenon_H161. apply refl_equal. % 29.69/29.92 apply zenon_H161. apply refl_equal. % 29.69/29.92 apply zenon_H1d. apply refl_equal. % 29.69/29.92 apply zenon_H161. apply refl_equal. % 29.69/29.92 apply zenon_H161. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L197_ *) % 29.69/29.92 assert (zenon_L198_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H112 zenon_H9c zenon_H1b9. % 29.69/29.92 apply (zenon_notand_s _ _ ax20); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H1f4 ]. % 29.69/29.92 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 29.69/29.92 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e1) = (op (op (e2) (e2)) (op (e2) (e2))))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1f5. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H166. % 29.69/29.92 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 29.69/29.92 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e3) (e3)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1f6. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H112. % 29.69/29.92 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.69/29.92 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 29.69/29.92 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))))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1f7. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H166. % 29.69/29.92 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 29.69/29.92 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L195_); trivial. % 29.69/29.92 apply zenon_H167. apply refl_equal. % 29.69/29.92 apply zenon_H167. apply refl_equal. % 29.69/29.92 apply zenon_H22. apply refl_equal. % 29.69/29.92 apply zenon_H167. apply refl_equal. % 29.69/29.92 apply zenon_H167. apply refl_equal. % 29.69/29.92 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1cd | zenon_intro zenon_H1de ]. % 29.69/29.92 apply (zenon_L197_); trivial. % 29.69/29.92 apply zenon_H1de. apply sym_equal. exact zenon_H1b9. % 29.69/29.92 (* end of lemma zenon_L198_ *) % 29.69/29.92 assert (zenon_L199_ : ((op (e3) (e0)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H8a zenon_H89 zenon_He7. % 29.69/29.92 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9a ]. % 29.69/29.92 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e0) (e0)) = (op (e3) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_He7. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Ha0. % 29.69/29.92 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.92 cut (((op (e3) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e0) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1f8. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H8a. % 29.69/29.92 cut (((e3) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 29.69/29.92 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H9a. apply refl_equal. % 29.69/29.92 apply zenon_H1f9. apply sym_equal. exact zenon_H89. % 29.69/29.92 apply zenon_H9a. apply refl_equal. % 29.69/29.92 apply zenon_H9a. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L199_ *) % 29.69/29.92 assert (zenon_L200_ : ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_Hb6 zenon_H1b9 zenon_H1dc. % 29.69/29.92 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 29.69/29.92 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e2) (e2)) = (op (e3) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1dc. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Hef. % 29.69/29.92 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.69/29.92 cut (((op (e3) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1fa. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Hb6. % 29.69/29.92 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 29.69/29.92 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_Hf0. apply refl_equal. % 29.69/29.92 apply zenon_H1de. apply sym_equal. exact zenon_H1b9. % 29.69/29.92 apply zenon_Hf0. apply refl_equal. % 29.69/29.92 apply zenon_Hf0. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L200_ *) % 29.69/29.92 assert (zenon_L201_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_Hb8 zenon_He7 zenon_H89 zenon_H18e zenon_H1dc zenon_H1b9 zenon_Hb1 zenon_H2d. % 29.69/29.92 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 29.69/29.92 apply (zenon_L199_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 29.69/29.92 exact (zenon_H18e zenon_H40). % 29.69/29.92 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 29.69/29.92 apply (zenon_L200_); trivial. % 29.69/29.92 apply (zenon_L107_); trivial. % 29.69/29.92 (* end of lemma zenon_L201_ *) % 29.69/29.92 assert (zenon_L202_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_Hbd zenon_Hdf zenon_H5c zenon_H1d8 zenon_H1e zenon_H3f zenon_H112 zenon_Hb8 zenon_He7 zenon_H89 zenon_H18e zenon_H1dc zenon_H1b9 zenon_H2d. % 29.69/29.92 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.69/29.92 apply (zenon_L194_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.69/29.92 apply (zenon_L29_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.69/29.92 apply (zenon_L198_); trivial. % 29.69/29.92 apply (zenon_L201_); trivial. % 29.69/29.92 (* end of lemma zenon_L202_ *) % 29.69/29.92 assert (zenon_L203_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_Hfc zenon_H37 zenon_H15e. % 29.69/29.92 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_Hfc. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H37. % 29.69/29.92 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 29.69/29.92 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_Hc5. apply refl_equal. % 29.69/29.92 apply zenon_H1fb. apply sym_equal. exact zenon_H15e. % 29.69/29.92 (* end of lemma zenon_L203_ *) % 29.69/29.92 assert (zenon_L204_ : (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> False). % 29.69/29.92 do 0 intro. intros zenon_He1 zenon_Hb6 zenon_Heb. % 29.69/29.92 cut (((op (e3) (e2)) = (e3)) = ((e2) = (e3))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_He1. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Hb6. % 29.69/29.92 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.92 cut (((op (e3) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 29.69/29.92 congruence. % 29.69/29.92 exact (zenon_H1fc zenon_Heb). % 29.69/29.92 apply zenon_H2f. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L204_ *) % 29.69/29.92 assert (zenon_L205_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e2)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1fd zenon_H89 zenon_Hd9 zenon_H37 zenon_Hfc zenon_H1c5 zenon_H108 zenon_He1 zenon_Heb. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 29.69/29.92 apply (zenon_L149_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 29.69/29.92 apply (zenon_L203_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 29.69/29.92 apply (zenon_L171_); trivial. % 29.69/29.92 apply (zenon_L204_); trivial. % 29.69/29.92 (* end of lemma zenon_L205_ *) % 29.69/29.92 assert (zenon_L206_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H135 zenon_H27 zenon_H3c zenon_He9 zenon_H125 zenon_Hde zenon_H10e zenon_Hcd zenon_H19a zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1af zenon_H2d zenon_H1dc zenon_H18e zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1e zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1fd zenon_H89 zenon_Hd9 zenon_H37 zenon_Hfc zenon_H108 zenon_He1. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.69/29.92 apply (zenon_L191_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.69/29.92 apply (zenon_L88_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.69/29.92 exact (zenon_Hd0 zenon_Hcc). % 29.69/29.92 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.69/29.92 apply (zenon_L192_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.69/29.92 apply (zenon_L159_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.69/29.92 exact (zenon_Hd0 zenon_Hcc). % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.69/29.92 apply (zenon_L193_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.69/29.92 apply (zenon_L144_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.69/29.92 apply (zenon_L202_); trivial. % 29.69/29.92 apply (zenon_L205_); trivial. % 29.69/29.92 (* end of lemma zenon_L206_ *) % 29.69/29.92 assert (zenon_L207_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H3c zenon_H1e zenon_H1ba. % 29.69/29.92 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H3c. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1e. % 29.69/29.92 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 29.69/29.92 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H3b. apply refl_equal. % 29.69/29.92 apply zenon_H1bb. apply sym_equal. exact zenon_H1ba. % 29.69/29.92 (* end of lemma zenon_L207_ *) % 29.69/29.92 assert (zenon_L208_ : ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H142 zenon_H10e zenon_H27. % 29.69/29.92 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H27. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H28. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H2a. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H142. % 29.69/29.92 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H139. apply sym_equal. exact zenon_H10e. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L208_ *) % 29.69/29.92 assert (zenon_L209_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1bd zenon_H1af zenon_H1e1 zenon_H3d. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1bd. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1af. % 29.69/29.92 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H6d ]. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1e4. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1ac. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L185_); trivial. % 29.69/29.92 apply zenon_H6d. apply refl_equal. % 29.69/29.92 apply zenon_H6d. apply refl_equal. % 29.69/29.92 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 29.69/29.92 (* end of lemma zenon_L209_ *) % 29.69/29.92 assert (zenon_L210_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e0)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af zenon_H1e1. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1cb ]. % 29.69/29.92 apply (zenon_L207_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H1cc ]. % 29.69/29.92 apply (zenon_L163_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H55 | zenon_intro zenon_H3d ]. % 29.69/29.92 apply (zenon_L88_); trivial. % 29.69/29.92 apply (zenon_L209_); trivial. % 29.69/29.92 (* end of lemma zenon_L210_ *) % 29.69/29.92 assert (zenon_L211_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H200 zenon_He1 zenon_H108 zenon_Hfc zenon_H37 zenon_Hd9 zenon_H89 zenon_H1fd zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_H112 zenon_Hb8 zenon_He7 zenon_H18e zenon_H1dc zenon_H2d zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H19a zenon_Hcd zenon_Hde zenon_H125 zenon_H135 zenon_H27 zenon_H10e zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.69/29.92 apply (zenon_L206_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.69/29.92 apply (zenon_L207_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.69/29.92 apply (zenon_L208_); trivial. % 29.69/29.92 apply (zenon_L210_); trivial. % 29.69/29.92 (* end of lemma zenon_L211_ *) % 29.69/29.92 assert (zenon_L212_ : (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> False). % 29.69/29.92 do 0 intro. intros zenon_Hcd zenon_H55 zenon_Hd5. % 29.69/29.92 cut (((op (e2) (e1)) = (e2)) = ((e1) = (e2))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_Hcd. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H55. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 cut (((op (e2) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 29.69/29.92 congruence. % 29.69/29.92 exact (zenon_H203 zenon_Hd5). % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L212_ *) % 29.69/29.92 assert (zenon_L213_ : (~((op (e2) (e1)) = (op (e2) (op (e2) (e3))))) -> ((op (e2) (e3)) = (e1)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H204 zenon_H1e5. % 29.69/29.92 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_H205. apply sym_equal. exact zenon_H1e5. % 29.69/29.92 (* end of lemma zenon_L213_ *) % 29.69/29.92 assert (zenon_L214_ : ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1af zenon_H1e5 zenon_H37 zenon_H19e. % 29.69/29.92 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e1) (e1)) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H19e. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H62. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e1)) = (op (e1) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H206. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1af. % 29.69/29.92 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 29.69/29.92 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H207. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H62. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H204]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L213_); trivial. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H38. apply sym_equal. exact zenon_H37. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L214_ *) % 29.69/29.92 assert (zenon_L215_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H55 zenon_Hcd zenon_Hfe zenon_H1af zenon_H37 zenon_H19e. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.69/29.92 apply (zenon_L157_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.69/29.92 apply (zenon_L212_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.69/29.92 apply (zenon_L170_); trivial. % 29.69/29.92 apply (zenon_L214_); trivial. % 29.69/29.92 (* end of lemma zenon_L215_ *) % 29.69/29.92 assert (zenon_L216_ : ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H60 zenon_H1b9 zenon_H55 zenon_H1c7. % 29.69/29.92 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1c7. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H109. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1c8. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H60. % 29.69/29.92 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 29.69/29.92 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e3)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1df. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H109. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.69/29.92 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1dd]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L178_); trivial. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 apply zenon_H1c2. apply sym_equal. exact zenon_H55. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 apply zenon_H10a. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L216_ *) % 29.69/29.92 assert (zenon_L217_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H55 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_Hfe zenon_H37 zenon_Hd0 zenon_H108. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.69/29.92 apply (zenon_L215_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.69/29.92 apply (zenon_L126_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.69/29.92 apply (zenon_L216_); trivial. % 29.69/29.92 apply (zenon_L172_); trivial. % 29.69/29.92 (* end of lemma zenon_L217_ *) % 29.69/29.92 assert (zenon_L218_ : ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H5e zenon_Hd5 zenon_H1f zenon_H3c. % 29.69/29.92 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e0) (e1)) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H3c. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H62. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (op (e2) (e1))) = (e1)) = ((op (e2) (e1)) = (op (e0) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H152. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H5e. % 29.69/29.92 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 29.69/29.92 cut (((op (e2) (op (e2) (e1))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1bf]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (op (e2) (e1))) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1bf. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H62. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L162_); trivial. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H20b. apply sym_equal. exact zenon_H1f. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L218_ *) % 29.69/29.92 assert (zenon_L219_ : ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H60 zenon_H25 zenon_He9 zenon_H3c. % 29.69/29.92 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e0) (e1)) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H3c. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H62. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e1)) = (op (e0) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H152. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H60. % 29.69/29.92 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 29.69/29.92 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e1)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H61. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H62. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.69/29.92 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L12_); trivial. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H153. apply sym_equal. exact zenon_He9. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 apply zenon_H63. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L219_ *) % 29.69/29.92 assert (zenon_L220_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H1f zenon_H5e zenon_H3c zenon_He9 zenon_H60 zenon_H1af zenon_H37 zenon_H19e. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.69/29.92 apply (zenon_L157_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.69/29.92 apply (zenon_L218_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.69/29.92 apply (zenon_L219_); trivial. % 29.69/29.92 apply (zenon_L214_); trivial. % 29.69/29.92 (* end of lemma zenon_L220_ *) % 29.69/29.92 assert (zenon_L221_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_Hf5 zenon_H1c5 zenon_He1. % 29.69/29.92 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.69/29.92 cut (((e3) = (e3)) = ((e2) = (e3))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_He1. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H2e. % 29.69/29.92 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.69/29.92 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (e3)) = (e2)) = ((e3) = (e2))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H195. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_Hf5. % 29.69/29.92 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.69/29.92 cut (((op (e2) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 29.69/29.92 congruence. % 29.69/29.92 exact (zenon_H20c zenon_H1c5). % 29.69/29.92 apply zenon_H57. apply refl_equal. % 29.69/29.92 apply zenon_H2f. apply refl_equal. % 29.69/29.92 apply zenon_H2f. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L221_ *) % 29.69/29.92 assert (zenon_L222_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H135 zenon_Hde zenon_H108 zenon_Hfe zenon_H1ca zenon_H6c zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_Hcd zenon_Hd0 zenon_H1d5 zenon_H19e zenon_H37 zenon_H60 zenon_He9 zenon_H3c zenon_H5e zenon_H1f zenon_H6f zenon_H208 zenon_Hd6 zenon_H1af zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1e zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_He1. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.69/29.92 apply (zenon_L49_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.69/29.92 apply (zenon_L217_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.69/29.92 exact (zenon_Hd0 zenon_Hcc). % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.69/29.92 apply (zenon_L220_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.69/29.92 apply (zenon_L144_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.69/29.92 apply (zenon_L202_); trivial. % 29.69/29.92 apply (zenon_L221_); trivial. % 29.69/29.92 (* end of lemma zenon_L222_ *) % 29.69/29.92 assert (zenon_L223_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H20d zenon_H60 zenon_H142 zenon_Hf5. % 29.69/29.92 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H20d. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H60. % 29.69/29.92 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 29.69/29.92 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 29.69/29.92 congruence. % 29.69/29.92 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H6d ]. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e0)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H1c3. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H1ac. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.69/29.92 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 29.69/29.92 congruence. % 29.69/29.92 apply (zenon_L164_); trivial. % 29.69/29.92 apply zenon_H6d. apply refl_equal. % 29.69/29.92 apply zenon_H6d. apply refl_equal. % 29.69/29.92 apply zenon_Hf8. apply sym_equal. exact zenon_Hf5. % 29.69/29.92 (* end of lemma zenon_L223_ *) % 29.69/29.92 assert (zenon_L224_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> False). % 29.69/29.92 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_H3c zenon_He9 zenon_Hd0 zenon_H20d zenon_H60 zenon_H142. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.69/29.92 apply (zenon_L142_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.69/29.92 apply (zenon_L88_); trivial. % 29.69/29.92 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.69/29.92 exact (zenon_Hd0 zenon_Hcc). % 29.69/29.92 apply (zenon_L223_); trivial. % 29.69/29.92 (* end of lemma zenon_L224_ *) % 29.69/29.92 assert (zenon_L225_ : ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 29.69/29.92 do 0 intro. intros zenon_H25 zenon_H19a zenon_H20e. % 29.69/29.92 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H20e. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H28. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 29.69/29.92 congruence. % 29.69/29.92 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 29.69/29.92 intro zenon_D_pnotp. % 29.69/29.92 apply zenon_H20f. % 29.69/29.92 rewrite <- zenon_D_pnotp. % 29.69/29.92 exact zenon_H25. % 29.69/29.92 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 29.69/29.92 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.69/29.92 congruence. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H1b2. apply sym_equal. exact zenon_H19a. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 apply zenon_H29. apply refl_equal. % 29.69/29.92 (* end of lemma zenon_L225_ *) % 29.69/29.92 assert (zenon_L226_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H1d2 zenon_H1c7 zenon_H1c5 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H20e zenon_H19a zenon_Hd0 zenon_H112 zenon_H9c. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 29.77/29.93 apply (zenon_L168_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 29.77/29.93 apply (zenon_L225_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 29.77/29.93 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.93 apply (zenon_L198_); trivial. % 29.77/29.93 (* end of lemma zenon_L226_ *) % 29.77/29.93 assert (zenon_L227_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H1d5 zenon_H19e zenon_H37 zenon_He9 zenon_H3c zenon_H1f zenon_H6f zenon_H208 zenon_Hf5 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H20e zenon_H19a zenon_Hd0 zenon_H112 zenon_H9c. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.93 apply (zenon_L220_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.93 apply (zenon_L144_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.93 apply (zenon_L198_); trivial. % 29.77/29.93 apply (zenon_L226_); trivial. % 29.77/29.93 (* end of lemma zenon_L227_ *) % 29.77/29.93 assert (zenon_L228_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_H1d5 zenon_H19e zenon_H37 zenon_He9 zenon_H3c zenon_H1f zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H20e zenon_H19a zenon_Hd0 zenon_H112 zenon_H9c. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.93 apply (zenon_L142_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.93 apply (zenon_L88_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.93 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.93 apply (zenon_L227_); trivial. % 29.77/29.93 (* end of lemma zenon_L228_ *) % 29.77/29.93 assert (zenon_L229_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H14b zenon_H27 zenon_H125 zenon_H6b zenon_H1fd zenon_Hd9 zenon_Hfc zenon_H200 zenon_He1 zenon_Hbd zenon_Hdf zenon_H5c zenon_H1d8 zenon_H1e zenon_H3f zenon_Hb8 zenon_He7 zenon_H89 zenon_H18e zenon_H1dc zenon_H2d zenon_Hcd zenon_H108 zenon_Hde zenon_H20d zenon_H135 zenon_H18c zenon_Hdc zenon_H1d5 zenon_H19e zenon_H37 zenon_He9 zenon_H3c zenon_H1f zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H20e zenon_H19a zenon_Hd0 zenon_H112. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.77/29.93 apply (zenon_L211_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.77/29.93 apply (zenon_L222_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.77/29.93 apply (zenon_L224_); trivial. % 29.77/29.93 apply (zenon_L228_); trivial. % 29.77/29.93 (* end of lemma zenon_L229_ *) % 29.77/29.93 assert (zenon_L230_ : ((op (e3) (e3)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H112 zenon_H19a zenon_H20e zenon_Hd6 zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_H1f zenon_H37 zenon_H19e zenon_H1d5 zenon_Hde zenon_H108 zenon_Hcd zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_He1 zenon_H200 zenon_Hfc zenon_Hd9 zenon_H1fd zenon_H6b zenon_H125 zenon_H27 zenon_H14b zenon_H60 zenon_H20d zenon_Hd0 zenon_Hdc zenon_H18c zenon_H135 zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.93 apply (zenon_L229_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.93 apply (zenon_L207_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.93 apply (zenon_L224_); trivial. % 29.77/29.93 apply (zenon_L210_); trivial. % 29.77/29.93 (* end of lemma zenon_L230_ *) % 29.77/29.93 assert (zenon_L231_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H42 zenon_H1af zenon_H1bd zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1ca zenon_H135 zenon_H18c zenon_Hd0 zenon_H20d zenon_H60 zenon_H14b zenon_H27 zenon_H125 zenon_H6b zenon_H1fd zenon_Hd9 zenon_H200 zenon_He1 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H89 zenon_H1dc zenon_H2d zenon_Hcd zenon_H108 zenon_Hde zenon_H1d5 zenon_H1f zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_Hd6 zenon_H20e zenon_H112 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.93 apply (zenon_L4_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.93 apply (zenon_L230_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.93 apply (zenon_L155_); trivial. % 29.77/29.93 exact (zenon_H18e zenon_H40). % 29.77/29.93 (* end of lemma zenon_L231_ *) % 29.77/29.93 assert (zenon_L232_ : ((op (e0) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H73 zenon_H89 zenon_He1. % 29.77/29.93 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.77/29.93 cut (((e3) = (e3)) = ((e2) = (e3))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_He1. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H2e. % 29.77/29.93 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.77/29.93 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 29.77/29.93 congruence. % 29.77/29.93 cut (((op (e0) (e0)) = (e2)) = ((e3) = (e2))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H195. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H73. % 29.77/29.93 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.77/29.93 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 29.77/29.93 congruence. % 29.77/29.93 exact (zenon_H85 zenon_H89). % 29.77/29.93 apply zenon_H57. apply refl_equal. % 29.77/29.93 apply zenon_H2f. apply refl_equal. % 29.77/29.93 apply zenon_H2f. apply refl_equal. % 29.77/29.93 (* end of lemma zenon_L232_ *) % 29.77/29.93 assert (zenon_L233_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 29.77/29.93 do 0 intro. intros zenon_Hb8 zenon_Had zenon_H6e zenon_H18e zenon_Heb zenon_He1 zenon_H112 zenon_H6f. % 29.77/29.93 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 29.77/29.93 apply (zenon_L34_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 29.77/29.93 exact (zenon_H18e zenon_H40). % 29.77/29.93 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 29.77/29.93 apply (zenon_L204_); trivial. % 29.77/29.93 apply (zenon_L152_); trivial. % 29.77/29.93 (* end of lemma zenon_L233_ *) % 29.77/29.93 assert (zenon_L234_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H125 zenon_Hde zenon_H10e zenon_Hcd zenon_H19a zenon_Hd0 zenon_Hb8 zenon_Had zenon_H6e zenon_H18e zenon_He1 zenon_H112 zenon_H6f. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.77/29.93 apply (zenon_L192_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.77/29.93 apply (zenon_L159_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.77/29.93 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.93 apply (zenon_L233_); trivial. % 29.77/29.93 (* end of lemma zenon_L234_ *) % 29.77/29.93 assert (zenon_L235_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H19a zenon_H15e zenon_H6f. % 29.77/29.93 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.77/29.93 cut (((e3) = (e3)) = ((e1) = (e3))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H6f. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H2e. % 29.77/29.93 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.77/29.93 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 29.77/29.93 congruence. % 29.77/29.93 cut (((op (e1) (e2)) = (e1)) = ((e3) = (e1))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H70. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H19a. % 29.77/29.93 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.77/29.93 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 29.77/29.93 congruence. % 29.77/29.93 exact (zenon_H210 zenon_H15e). % 29.77/29.93 apply zenon_H22. apply refl_equal. % 29.77/29.93 apply zenon_H2f. apply refl_equal. % 29.77/29.93 apply zenon_H2f. apply refl_equal. % 29.77/29.93 (* end of lemma zenon_L235_ *) % 29.77/29.93 assert (zenon_L236_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H16f zenon_Had zenon_H8a zenon_He1 zenon_Hfd zenon_H6f zenon_H19a zenon_H16a zenon_H16b. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.77/29.93 apply (zenon_L34_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.77/29.93 apply (zenon_L158_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.77/29.93 apply (zenon_L235_); trivial. % 29.77/29.93 apply (zenon_L101_); trivial. % 29.77/29.93 (* end of lemma zenon_L236_ *) % 29.77/29.93 assert (zenon_L237_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e2)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_H156 zenon_H155 zenon_H60 zenon_He1 zenon_Heb. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 29.77/29.93 apply (zenon_L87_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 29.77/29.93 apply (zenon_L235_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 29.77/29.93 apply (zenon_L179_); trivial. % 29.77/29.93 apply (zenon_L204_); trivial. % 29.77/29.93 (* end of lemma zenon_L237_ *) % 29.77/29.93 assert (zenon_L238_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e2) = (e3))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H125 zenon_H73 zenon_Hd9 zenon_Hcd zenon_Hd0 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_H156 zenon_H155 zenon_H60 zenon_He1. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.77/29.93 apply (zenon_L47_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.77/29.93 apply (zenon_L159_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.77/29.93 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.93 apply (zenon_L237_); trivial. % 29.77/29.93 (* end of lemma zenon_L238_ *) % 29.77/29.93 assert (zenon_L239_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e2) = (e3))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H174 zenon_H1e zenon_H8d zenon_H112 zenon_H18e zenon_Hb8 zenon_Hde zenon_H6c zenon_H173 zenon_H15a zenon_H16a zenon_Had zenon_H16f zenon_H125 zenon_H73 zenon_Hd9 zenon_Hcd zenon_Hd0 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_H156 zenon_H60 zenon_He1. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.77/29.93 apply (zenon_L232_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.77/29.93 apply (zenon_L4_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.77/29.93 apply (zenon_L87_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.77/29.93 apply (zenon_L232_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.77/29.93 apply (zenon_L234_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.77/29.93 apply (zenon_L157_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.77/29.93 apply (zenon_L94_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.77/29.93 apply (zenon_L236_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.77/29.93 apply (zenon_L159_); trivial. % 29.77/29.93 apply (zenon_L238_); trivial. % 29.77/29.93 (* end of lemma zenon_L239_ *) % 29.77/29.93 assert (zenon_L240_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H42 zenon_H1af zenon_H1bd zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1ca zenon_H10e zenon_H27 zenon_H135 zenon_H125 zenon_Hde zenon_Hcd zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H2d zenon_H1dc zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H1fd zenon_H89 zenon_Hd9 zenon_H108 zenon_He1 zenon_H200 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.93 apply (zenon_L4_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.93 apply (zenon_L211_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.93 apply (zenon_L155_); trivial. % 29.77/29.93 exact (zenon_H18e zenon_H40). % 29.77/29.93 (* end of lemma zenon_L240_ *) % 29.77/29.93 assert (zenon_L241_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H15a zenon_H89 zenon_H6e. % 29.77/29.93 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H15a. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H89. % 29.77/29.93 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 29.77/29.93 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 29.77/29.93 congruence. % 29.77/29.93 apply zenon_Hcb. apply refl_equal. % 29.77/29.93 apply zenon_Haf. apply sym_equal. exact zenon_H6e. % 29.77/29.93 (* end of lemma zenon_L241_ *) % 29.77/29.93 assert (zenon_L242_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H10e zenon_H64 zenon_Hd9. % 29.77/29.93 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H10f ]. % 29.77/29.93 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_Hd9. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H211. % 29.77/29.93 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 29.77/29.93 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 29.77/29.93 congruence. % 29.77/29.93 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H212. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H10e. % 29.77/29.93 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 29.77/29.93 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 29.77/29.93 congruence. % 29.77/29.93 apply zenon_H10f. apply refl_equal. % 29.77/29.93 apply zenon_H67. apply sym_equal. exact zenon_H64. % 29.77/29.93 apply zenon_H10f. apply refl_equal. % 29.77/29.93 apply zenon_H10f. apply refl_equal. % 29.77/29.93 (* end of lemma zenon_L242_ *) % 29.77/29.93 assert (zenon_L243_ : ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (op (op (e0) (e0)) (e0)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H6c zenon_H73 zenon_H213. % 29.77/29.93 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e1) = (op (op (e0) (e0)) (e0)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H213. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H78. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 29.77/29.93 congruence. % 29.77/29.93 cut (((op (e2) (e0)) = (e1)) = ((op (op (e0) (e0)) (e0)) = (e1))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H214. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H6c. % 29.77/29.93 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.77/29.93 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 29.77/29.93 congruence. % 29.77/29.93 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H7b. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H78. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 29.77/29.93 congruence. % 29.77/29.93 apply (zenon_L20_); trivial. % 29.77/29.93 apply zenon_H79. apply refl_equal. % 29.77/29.93 apply zenon_H79. apply refl_equal. % 29.77/29.93 apply zenon_H22. apply refl_equal. % 29.77/29.93 apply zenon_H79. apply refl_equal. % 29.77/29.93 apply zenon_H79. apply refl_equal. % 29.77/29.93 (* end of lemma zenon_L243_ *) % 29.77/29.93 assert (zenon_L244_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H1b9 zenon_H6c zenon_H73. % 29.77/29.93 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_H216 | zenon_intro zenon_H215 ]. % 29.77/29.93 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 29.77/29.93 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e3) = (op (op (e0) (e0)) (op (e0) (e0))))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H216. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H7e. % 29.77/29.93 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 29.77/29.93 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H217]. % 29.77/29.93 congruence. % 29.77/29.93 cut (((op (e2) (e2)) = (e3)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e3))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H217. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H1b9. % 29.77/29.93 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.77/29.93 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 29.77/29.93 congruence. % 29.77/29.93 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 29.77/29.93 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))))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H81. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H7e. % 29.77/29.93 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 29.77/29.93 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 29.77/29.93 congruence. % 29.77/29.93 apply (zenon_L19_); trivial. % 29.77/29.93 apply zenon_H7f. apply refl_equal. % 29.77/29.93 apply zenon_H7f. apply refl_equal. % 29.77/29.93 apply zenon_H2f. apply refl_equal. % 29.77/29.93 apply zenon_H7f. apply refl_equal. % 29.77/29.93 apply zenon_H7f. apply refl_equal. % 29.77/29.93 apply (zenon_notand_s _ _ zenon_H215); [ zenon_intro zenon_H213 | zenon_intro zenon_H82 ]. % 29.77/29.93 apply (zenon_L243_); trivial. % 29.77/29.93 apply zenon_H82. apply sym_equal. exact zenon_H73. % 29.77/29.93 (* end of lemma zenon_L244_ *) % 29.77/29.93 assert (zenon_L245_ : ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H1af zenon_H1c5 zenon_H16b zenon_H218. % 29.77/29.93 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H218. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H109. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 29.77/29.93 congruence. % 29.77/29.93 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H219. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H1af. % 29.77/29.93 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 29.77/29.93 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 29.77/29.93 congruence. % 29.77/29.93 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e3)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H1c9. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H109. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 29.77/29.93 congruence. % 29.77/29.93 apply (zenon_L166_); trivial. % 29.77/29.93 apply zenon_H10a. apply refl_equal. % 29.77/29.93 apply zenon_H10a. apply refl_equal. % 29.77/29.93 apply zenon_H21a. apply sym_equal. exact zenon_H16b. % 29.77/29.93 apply zenon_H10a. apply refl_equal. % 29.77/29.93 apply zenon_H10a. apply refl_equal. % 29.77/29.93 (* end of lemma zenon_L245_ *) % 29.77/29.93 assert (zenon_L246_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H135 zenon_H27 zenon_H5c zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_He7 zenon_H8a zenon_H6c zenon_H84 zenon_H10e zenon_Hd9 zenon_H83 zenon_H1af zenon_H16b zenon_H218. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.93 apply (zenon_L191_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.93 apply (zenon_L88_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.93 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.93 apply (zenon_L193_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.93 apply (zenon_L144_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 29.77/29.93 apply (zenon_L242_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 29.77/29.93 exact (zenon_H84 zenon_H88). % 29.77/29.93 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 29.77/29.93 apply (zenon_L244_); trivial. % 29.77/29.93 apply (zenon_L199_); trivial. % 29.77/29.93 apply (zenon_L245_); trivial. % 29.77/29.93 (* end of lemma zenon_L246_ *) % 29.77/29.93 assert (zenon_L247_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H8d zenon_H16a zenon_H200 zenon_H108 zenon_Hfc zenon_H1fd zenon_Hbd zenon_H1d8 zenon_H3f zenon_H1dc zenon_H2d zenon_H1ca zenon_H1e zenon_H5e zenon_H1bd zenon_H15a zenon_H16f zenon_H112 zenon_He1 zenon_H18e zenon_Had zenon_Hb8 zenon_H19a zenon_Hcd zenon_Hde zenon_H125 zenon_H6f zenon_H135 zenon_H27 zenon_H5c zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_He7 zenon_H6c zenon_H84 zenon_H10e zenon_Hd9 zenon_H83 zenon_H1af zenon_H16b zenon_H218. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.77/29.93 apply (zenon_L241_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.77/29.93 apply (zenon_L211_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.77/29.93 apply (zenon_L235_); trivial. % 29.77/29.93 apply (zenon_L101_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.77/29.93 apply (zenon_L234_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.77/29.93 apply (zenon_L157_); trivial. % 29.77/29.93 apply (zenon_L246_); trivial. % 29.77/29.93 (* end of lemma zenon_L247_ *) % 29.77/29.93 assert (zenon_L248_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H174 zenon_H102 zenon_H35 zenon_Hdc zenon_Hd1 zenon_H19e zenon_H42 zenon_H8d zenon_H16a zenon_H200 zenon_H108 zenon_Hfc zenon_H1fd zenon_Hbd zenon_H1d8 zenon_H3f zenon_H1dc zenon_H2d zenon_H1ca zenon_H1e zenon_H5e zenon_H1bd zenon_H15a zenon_H16f zenon_H112 zenon_He1 zenon_H18e zenon_Had zenon_Hb8 zenon_H19a zenon_Hcd zenon_Hde zenon_H125 zenon_H6f zenon_H135 zenon_H27 zenon_H5c zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_He7 zenon_H6c zenon_H84 zenon_H10e zenon_Hd9 zenon_H83 zenon_H1af zenon_H218. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.77/29.93 apply (zenon_L240_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.77/29.93 apply (zenon_L4_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.77/29.93 apply (zenon_L87_); trivial. % 29.77/29.93 apply (zenon_L247_); trivial. % 29.77/29.93 (* end of lemma zenon_L248_ *) % 29.77/29.93 assert (zenon_L249_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H21b zenon_H89. % 29.77/29.93 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 29.77/29.93 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 29.77/29.93 congruence. % 29.77/29.93 exact (zenon_H85 zenon_H89). % 29.77/29.93 exact (zenon_H85 zenon_H89). % 29.77/29.93 (* end of lemma zenon_L249_ *) % 29.77/29.93 assert (zenon_L250_ : (~((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H21c zenon_H89. % 29.77/29.93 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.77/29.93 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 29.77/29.93 congruence. % 29.77/29.93 exact (zenon_H85 zenon_H89). % 29.77/29.93 apply zenon_H1d. apply refl_equal. % 29.77/29.93 (* end of lemma zenon_L250_ *) % 29.77/29.93 assert (zenon_L251_ : ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (op (op (e0) (e0)) (e0)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_He2 zenon_H89 zenon_H21d. % 29.77/29.93 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e2) = (op (op (e0) (e0)) (e0)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H21d. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H78. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 29.77/29.93 congruence. % 29.77/29.93 cut (((op (e3) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H21e. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_He2. % 29.77/29.93 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.77/29.93 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 29.77/29.93 congruence. % 29.77/29.93 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H21f. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H78. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 29.77/29.93 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 29.77/29.93 congruence. % 29.77/29.93 apply (zenon_L250_); trivial. % 29.77/29.93 apply zenon_H79. apply refl_equal. % 29.77/29.93 apply zenon_H79. apply refl_equal. % 29.77/29.93 apply zenon_H57. apply refl_equal. % 29.77/29.93 apply zenon_H79. apply refl_equal. % 29.77/29.93 apply zenon_H79. apply refl_equal. % 29.77/29.93 (* end of lemma zenon_L251_ *) % 29.77/29.93 assert (zenon_L252_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H112 zenon_He2 zenon_H89. % 29.77/29.93 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H7d | zenon_intro zenon_H220 ]. % 29.77/29.93 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 29.77/29.93 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H7d. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H7e. % 29.77/29.93 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 29.77/29.93 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 29.77/29.93 congruence. % 29.77/29.93 cut (((op (e3) (e3)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H80. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H112. % 29.77/29.93 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.77/29.93 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 29.77/29.93 congruence. % 29.77/29.93 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 29.77/29.93 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))))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H221. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H7e. % 29.77/29.93 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 29.77/29.93 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 29.77/29.93 congruence. % 29.77/29.93 apply (zenon_L249_); trivial. % 29.77/29.93 apply zenon_H7f. apply refl_equal. % 29.77/29.93 apply zenon_H7f. apply refl_equal. % 29.77/29.93 apply zenon_H22. apply refl_equal. % 29.77/29.93 apply zenon_H7f. apply refl_equal. % 29.77/29.93 apply zenon_H7f. apply refl_equal. % 29.77/29.93 apply (zenon_notand_s _ _ zenon_H220); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f9 ]. % 29.77/29.93 apply (zenon_L251_); trivial. % 29.77/29.93 apply zenon_H1f9. apply sym_equal. exact zenon_H89. % 29.77/29.93 (* end of lemma zenon_L252_ *) % 29.77/29.93 assert (zenon_L253_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H8d zenon_H112 zenon_H18e zenon_Had zenon_Hb8 zenon_Hd0 zenon_H19a zenon_Hcd zenon_H10e zenon_Hde zenon_H125 zenon_H6f zenon_H6c zenon_He1 zenon_He2. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.77/29.93 apply (zenon_L252_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.77/29.93 apply (zenon_L234_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.77/29.93 apply (zenon_L157_); trivial. % 29.77/29.93 apply (zenon_L50_); trivial. % 29.77/29.93 (* end of lemma zenon_L253_ *) % 29.77/29.93 assert (zenon_L254_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> False). % 29.77/29.93 do 0 intro. intros zenon_He4 zenon_H60 zenon_H156 zenon_H173 zenon_H218 zenon_H1af zenon_H83 zenon_Hd9 zenon_H84 zenon_He7 zenon_Hd6 zenon_H6b zenon_H1d5 zenon_He9 zenon_H3c zenon_H135 zenon_H16f zenon_H15a zenon_H1bd zenon_H5e zenon_H1e zenon_H1ca zenon_H2d zenon_H1dc zenon_H3f zenon_H1d8 zenon_Hbd zenon_H1fd zenon_Hfc zenon_H108 zenon_H200 zenon_H16a zenon_H42 zenon_H19e zenon_Hd1 zenon_H35 zenon_H102 zenon_H174 zenon_H27 zenon_H5c zenon_H8d zenon_H112 zenon_H18e zenon_Had zenon_Hb8 zenon_Hd0 zenon_H19a zenon_Hcd zenon_H10e zenon_Hde zenon_H125 zenon_H6f zenon_H6c zenon_He1. % 29.77/29.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.77/29.93 apply (zenon_L239_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.77/29.93 apply (zenon_L248_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.77/29.93 apply (zenon_L191_); trivial. % 29.77/29.93 apply (zenon_L253_); trivial. % 29.77/29.93 (* end of lemma zenon_L254_ *) % 29.77/29.93 assert (zenon_L255_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H55 zenon_Hcd zenon_H20e zenon_H19a zenon_H1af zenon_H37 zenon_H19e. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.77/29.93 apply (zenon_L157_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.77/29.93 apply (zenon_L212_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.77/29.93 apply (zenon_L225_); trivial. % 29.77/29.93 apply (zenon_L214_); trivial. % 29.77/29.93 (* end of lemma zenon_L255_ *) % 29.77/29.93 assert (zenon_L256_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H222 zenon_H60 zenon_H25 zenon_H9d. % 29.77/29.93 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H222. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H60. % 29.77/29.93 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 29.77/29.93 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 29.77/29.93 congruence. % 29.77/29.93 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.77/29.93 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e1)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H61. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H62. % 29.77/29.93 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.77/29.93 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 29.77/29.93 congruence. % 29.77/29.93 apply (zenon_L12_); trivial. % 29.77/29.93 apply zenon_H63. apply refl_equal. % 29.77/29.93 apply zenon_H63. apply refl_equal. % 29.77/29.93 apply zenon_H9e. apply sym_equal. exact zenon_H9d. % 29.77/29.93 (* end of lemma zenon_L256_ *) % 29.77/29.93 assert (zenon_L257_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.77/29.93 apply (zenon_L157_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.77/29.93 apply (zenon_L218_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.77/29.93 apply (zenon_L256_); trivial. % 29.77/29.93 apply (zenon_L214_); trivial. % 29.77/29.93 (* end of lemma zenon_L257_ *) % 29.77/29.93 assert (zenon_L258_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H101 zenon_Hdc zenon_Hd1 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H76 zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.77/29.93 apply (zenon_L220_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.77/29.93 apply (zenon_L154_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.77/29.93 apply (zenon_L255_); trivial. % 29.77/29.93 apply (zenon_L257_); trivial. % 29.77/29.93 (* end of lemma zenon_L258_ *) % 29.77/29.93 assert (zenon_L259_ : ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H60 zenon_H1b9 zenon_H17b zenon_H218. % 29.77/29.93 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H218. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H109. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 29.77/29.93 congruence. % 29.77/29.93 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H219. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H60. % 29.77/29.93 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 29.77/29.93 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 29.77/29.93 congruence. % 29.77/29.93 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e3)))). % 29.77/29.93 intro zenon_D_pnotp. % 29.77/29.93 apply zenon_H1df. % 29.77/29.93 rewrite <- zenon_D_pnotp. % 29.77/29.93 exact zenon_H109. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.77/29.93 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1dd]. % 29.77/29.93 congruence. % 29.77/29.93 apply (zenon_L178_); trivial. % 29.77/29.93 apply zenon_H10a. apply refl_equal. % 29.77/29.93 apply zenon_H10a. apply refl_equal. % 29.77/29.93 apply zenon_H223. apply sym_equal. exact zenon_H17b. % 29.77/29.93 apply zenon_H10a. apply refl_equal. % 29.77/29.93 apply zenon_H10a. apply refl_equal. % 29.77/29.93 (* end of lemma zenon_L259_ *) % 29.77/29.93 assert (zenon_L260_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e2)) -> False). % 29.77/29.93 do 0 intro. intros zenon_H1d5 zenon_H19e zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H19a zenon_Hd1 zenon_H101 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_Hdc zenon_H18c zenon_H135 zenon_H218 zenon_H17b zenon_H60 zenon_H1fd zenon_H89 zenon_Hd9 zenon_H37 zenon_Hfc zenon_H108 zenon_He1 zenon_Heb. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.93 apply (zenon_L258_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.93 apply (zenon_L145_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.93 apply (zenon_L259_); trivial. % 29.77/29.93 apply (zenon_L205_); trivial. % 29.77/29.93 (* end of lemma zenon_L260_ *) % 29.77/29.93 assert (zenon_L261_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.93 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H108 zenon_Hfc zenon_Hd9 zenon_H89 zenon_H1fd zenon_H60 zenon_H17b zenon_H218 zenon_H135 zenon_H18c zenon_Hdc zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H101 zenon_Hd1 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H19e zenon_H1d5 zenon_H10e zenon_Hde zenon_H125 zenon_He1 zenon_H55 zenon_H18e. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.93 apply (zenon_L4_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.77/29.93 apply (zenon_L192_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.77/29.93 apply (zenon_L159_); trivial. % 29.77/29.93 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.77/29.93 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.94 apply (zenon_L260_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.94 apply (zenon_L126_); trivial. % 29.77/29.94 exact (zenon_H18e zenon_H40). % 29.77/29.94 (* end of lemma zenon_L261_ *) % 29.77/29.94 assert (zenon_L262_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H101 zenon_H155 zenon_H159 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H76 zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.77/29.94 apply (zenon_L220_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.77/29.94 apply (zenon_L93_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.77/29.94 apply (zenon_L255_); trivial. % 29.77/29.94 apply (zenon_L257_); trivial. % 29.77/29.94 (* end of lemma zenon_L262_ *) % 29.77/29.94 assert (zenon_L263_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H173 zenon_Hd1 zenon_He1 zenon_H101 zenon_H159 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H76 zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.77/29.94 apply (zenon_L258_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.77/29.94 apply (zenon_L158_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.77/29.94 apply (zenon_L159_); trivial. % 29.77/29.94 apply (zenon_L262_); trivial. % 29.77/29.94 (* end of lemma zenon_L263_ *) % 29.77/29.94 assert (zenon_L264_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 29.77/29.94 do 0 intro. intros zenon_H222 zenon_H55 zenon_H9d. % 29.77/29.94 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H222. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H55. % 29.77/29.94 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 29.77/29.94 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.77/29.94 congruence. % 29.77/29.94 apply zenon_H63. apply refl_equal. % 29.77/29.94 apply zenon_H9e. apply sym_equal. exact zenon_H9d. % 29.77/29.94 (* end of lemma zenon_L264_ *) % 29.77/29.94 assert (zenon_L265_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H1ca zenon_H1e zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H222 zenon_H1af zenon_H1c5 zenon_H1c7. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1cb ]. % 29.77/29.94 apply (zenon_L207_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H1cc ]. % 29.77/29.94 apply (zenon_L218_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H55 | zenon_intro zenon_H3d ]. % 29.77/29.94 apply (zenon_L264_); trivial. % 29.77/29.94 apply (zenon_L167_); trivial. % 29.77/29.94 (* end of lemma zenon_L265_ *) % 29.77/29.94 assert (zenon_L266_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1c7 zenon_H1af zenon_H222 zenon_H9d zenon_H5e zenon_H1f zenon_H3c zenon_H1ca zenon_H60 zenon_H17b zenon_H218 zenon_H173 zenon_He1 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.94 apply (zenon_L4_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.94 apply (zenon_L263_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.94 apply (zenon_L155_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.94 apply (zenon_L259_); trivial. % 29.77/29.94 apply (zenon_L265_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.94 apply (zenon_L155_); trivial. % 29.77/29.94 exact (zenon_H18e zenon_H40). % 29.77/29.94 (* end of lemma zenon_L266_ *) % 29.77/29.94 assert (zenon_L267_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H17b zenon_H16b zenon_He1. % 29.77/29.94 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.77/29.94 cut (((e3) = (e3)) = ((e2) = (e3))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_He1. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H2e. % 29.77/29.94 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.77/29.94 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 29.77/29.94 congruence. % 29.77/29.94 cut (((op (e0) (e3)) = (e2)) = ((e3) = (e2))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H195. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H17b. % 29.77/29.94 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.77/29.94 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H224]. % 29.77/29.94 congruence. % 29.77/29.94 exact (zenon_H224 zenon_H16b). % 29.77/29.94 apply zenon_H57. apply refl_equal. % 29.77/29.94 apply zenon_H2f. apply refl_equal. % 29.77/29.94 apply zenon_H2f. apply refl_equal. % 29.77/29.94 (* end of lemma zenon_L267_ *) % 29.77/29.94 assert (zenon_L268_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H174 zenon_H18e zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hdc zenon_Hd1 zenon_H19e zenon_H1d5 zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H60 zenon_H1ca zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H42 zenon_H108 zenon_Hd9 zenon_H1fd zenon_H135 zenon_H18c zenon_Hd0 zenon_Hd6 zenon_Hde zenon_H125 zenon_H1bd zenon_H6c zenon_H27 zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H200 zenon_H1e zenon_H2d zenon_H10e zenon_H17b zenon_He1. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.77/29.94 apply (zenon_L240_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.77/29.94 apply (zenon_L154_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.77/29.94 apply (zenon_L261_); trivial. % 29.77/29.94 apply (zenon_L266_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.77/29.94 apply (zenon_L4_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.77/29.94 apply (zenon_L87_); trivial. % 29.77/29.94 apply (zenon_L267_); trivial. % 29.77/29.94 (* end of lemma zenon_L268_ *) % 29.77/29.94 assert (zenon_L269_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H174 zenon_He2 zenon_H112 zenon_H1e zenon_H2d zenon_H10e zenon_H17b zenon_He1. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.77/29.94 apply (zenon_L252_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.77/29.94 apply (zenon_L4_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.77/29.94 apply (zenon_L87_); trivial. % 29.77/29.94 apply (zenon_L267_); trivial. % 29.77/29.94 (* end of lemma zenon_L269_ *) % 29.77/29.94 assert (zenon_L270_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H225 zenon_H84 zenon_H83 zenon_He4 zenon_H156 zenon_H16f zenon_Had zenon_H16a zenon_H15a zenon_H8d zenon_H200 zenon_Hbd zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_H6c zenon_H1bd zenon_H125 zenon_Hde zenon_Hd6 zenon_Hd0 zenon_H18c zenon_H135 zenon_H1fd zenon_Hd9 zenon_H108 zenon_H42 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_H1ca zenon_H60 zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1d5 zenon_H19e zenon_Hd1 zenon_H19a zenon_Hfc zenon_H35 zenon_H102 zenon_H18e zenon_H27 zenon_H5c zenon_H174 zenon_H112 zenon_H1e zenon_H2d zenon_H10e zenon_He1. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.77/29.94 apply (zenon_L239_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.77/29.94 apply (zenon_L254_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.77/29.94 apply (zenon_L192_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.77/29.94 apply (zenon_L239_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.77/29.94 apply (zenon_L268_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.77/29.94 apply (zenon_L191_); trivial. % 29.77/29.94 apply (zenon_L269_); trivial. % 29.77/29.94 (* end of lemma zenon_L270_ *) % 29.77/29.94 assert (zenon_L271_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.77/29.94 do 0 intro. intros zenon_H92 zenon_H69 zenon_H20 zenon_He1 zenon_H10e zenon_H2d zenon_H1e zenon_H174 zenon_H5c zenon_H27 zenon_H18e zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hd1 zenon_H19e zenon_H1d5 zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H60 zenon_H1ca zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H42 zenon_H108 zenon_Hd9 zenon_H1fd zenon_H135 zenon_H18c zenon_Hd0 zenon_Hd6 zenon_Hde zenon_H125 zenon_H1bd zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_Hbd zenon_H200 zenon_H8d zenon_H15a zenon_H16a zenon_Had zenon_H16f zenon_H156 zenon_He4 zenon_H83 zenon_H84 zenon_H225 zenon_H17d zenon_H112. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.77/29.94 exact (zenon_H84 zenon_H88). % 29.77/29.94 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.77/29.94 apply (zenon_L16_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.77/29.94 apply (zenon_L270_); trivial. % 29.77/29.94 apply (zenon_L139_); trivial. % 29.77/29.94 (* end of lemma zenon_L271_ *) % 29.77/29.94 assert (zenon_L272_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H42 zenon_H2d zenon_He1 zenon_H1af zenon_H1bd zenon_Hfd zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.94 apply (zenon_L4_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.94 apply (zenon_L158_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.94 apply (zenon_L194_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.94 apply (zenon_L207_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.94 apply (zenon_L79_); trivial. % 29.77/29.94 apply (zenon_L209_); trivial. % 29.77/29.94 exact (zenon_H18e zenon_H40). % 29.77/29.94 (* end of lemma zenon_L272_ *) % 29.77/29.94 assert (zenon_L273_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_Hc9 zenon_H76 zenon_He1. % 29.77/29.94 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.77/29.94 cut (((e3) = (e3)) = ((e2) = (e3))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_He1. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H2e. % 29.77/29.94 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.77/29.94 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 29.77/29.94 congruence. % 29.77/29.94 cut (((op (e2) (e0)) = (e2)) = ((e3) = (e2))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H195. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_Hc9. % 29.77/29.94 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.77/29.94 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 29.77/29.94 congruence. % 29.77/29.94 exact (zenon_H1b7 zenon_H76). % 29.77/29.94 apply zenon_H57. apply refl_equal. % 29.77/29.94 apply zenon_H2f. apply refl_equal. % 29.77/29.94 apply zenon_H2f. apply refl_equal. % 29.77/29.94 (* end of lemma zenon_L273_ *) % 29.77/29.94 assert (zenon_L274_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H37 zenon_H19e zenon_H156 zenon_H155 zenon_H60 zenon_H1af zenon_H16b zenon_H218. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.94 apply (zenon_L273_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.94 apply (zenon_L131_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.94 apply (zenon_L179_); trivial. % 29.77/29.94 apply (zenon_L245_); trivial. % 29.77/29.94 (* end of lemma zenon_L274_ *) % 29.77/29.94 assert (zenon_L275_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H135 zenon_H218 zenon_H16b zenon_H1af zenon_H60 zenon_H19e zenon_H37 zenon_He1 zenon_H1d5 zenon_H3c zenon_He9 zenon_Hd0 zenon_H155 zenon_H156. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.94 apply (zenon_L274_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.94 apply (zenon_L88_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.94 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.94 apply (zenon_L90_); trivial. % 29.77/29.94 (* end of lemma zenon_L275_ *) % 29.77/29.94 assert (zenon_L276_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.77/29.94 do 0 intro. intros zenon_H228 zenon_H112. % 29.77/29.94 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 29.77/29.94 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 29.77/29.94 congruence. % 29.77/29.94 exact (zenon_H1ab zenon_H112). % 29.77/29.94 exact (zenon_H1ab zenon_H112). % 29.77/29.94 (* end of lemma zenon_L276_ *) % 29.77/29.94 assert (zenon_L277_ : (~((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.77/29.94 do 0 intro. intros zenon_H229 zenon_H112. % 29.77/29.94 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.77/29.94 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 29.77/29.94 congruence. % 29.77/29.94 exact (zenon_H1ab zenon_H112). % 29.77/29.94 apply zenon_H2f. apply refl_equal. % 29.77/29.94 (* end of lemma zenon_L277_ *) % 29.77/29.94 assert (zenon_L278_ : ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((e2) = (op (op (e3) (e3)) (e3)))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H155 zenon_H112 zenon_H22a. % 29.77/29.94 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 29.77/29.94 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e2) = (op (op (e3) (e3)) (e3)))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H22a. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H131. % 29.77/29.94 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 29.77/29.94 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22b]. % 29.77/29.94 congruence. % 29.77/29.94 cut (((op (e1) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H22b. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H155. % 29.77/29.94 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.77/29.94 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H22c]. % 29.77/29.94 congruence. % 29.77/29.94 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 29.77/29.94 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H22c. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H131. % 29.77/29.94 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 29.77/29.94 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H229]. % 29.77/29.94 congruence. % 29.77/29.94 apply (zenon_L277_); trivial. % 29.77/29.94 apply zenon_H132. apply refl_equal. % 29.77/29.94 apply zenon_H132. apply refl_equal. % 29.77/29.94 apply zenon_H57. apply refl_equal. % 29.77/29.94 apply zenon_H132. apply refl_equal. % 29.77/29.94 apply zenon_H132. apply refl_equal. % 29.77/29.94 (* end of lemma zenon_L278_ *) % 29.77/29.94 assert (zenon_L279_ : ((op (e1) (e1)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 29.77/29.94 do 0 intro. intros zenon_Hc3 zenon_H155 zenon_H112. % 29.77/29.94 apply (zenon_notand_s _ _ ax25); [ zenon_intro zenon_H22e | zenon_intro zenon_H22d ]. % 29.77/29.94 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 29.77/29.94 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H22e. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H12c. % 29.77/29.94 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 29.77/29.94 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 29.77/29.94 congruence. % 29.77/29.94 cut (((op (e1) (e1)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H22f. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_Hc3. % 29.77/29.94 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.77/29.94 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H230]. % 29.77/29.94 congruence. % 29.77/29.94 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 29.77/29.94 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))))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H230. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H12c. % 29.77/29.94 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 29.77/29.94 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 29.77/29.94 congruence. % 29.77/29.94 apply (zenon_L276_); trivial. % 29.77/29.94 apply zenon_H12d. apply refl_equal. % 29.77/29.94 apply zenon_H12d. apply refl_equal. % 29.77/29.94 apply zenon_H1d. apply refl_equal. % 29.77/29.94 apply zenon_H12d. apply refl_equal. % 29.77/29.94 apply zenon_H12d. apply refl_equal. % 29.77/29.94 apply (zenon_notand_s _ _ zenon_H22d); [ zenon_intro zenon_H22a | zenon_intro zenon_H192 ]. % 29.77/29.94 apply (zenon_L278_); trivial. % 29.77/29.94 apply zenon_H192. apply sym_equal. exact zenon_H112. % 29.77/29.94 (* end of lemma zenon_L279_ *) % 29.77/29.94 assert (zenon_L280_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 29.77/29.94 do 0 intro. intros zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H142 zenon_H19e zenon_H3d. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 29.77/29.94 apply (zenon_L279_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 29.77/29.94 apply (zenon_L130_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 29.77/29.94 apply (zenon_L79_); trivial. % 29.77/29.94 apply (zenon_L131_); trivial. % 29.77/29.94 (* end of lemma zenon_L280_ *) % 29.77/29.94 assert (zenon_L281_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 29.77/29.94 do 0 intro. intros zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_H19e zenon_H19a zenon_Hfc zenon_H155 zenon_H112 zenon_H102 zenon_H1bd zenon_H1af zenon_H3d. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.94 apply (zenon_L194_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.94 apply (zenon_L207_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.94 apply (zenon_L280_); trivial. % 29.77/29.94 apply (zenon_L209_); trivial. % 29.77/29.94 (* end of lemma zenon_L281_ *) % 29.77/29.94 assert (zenon_L282_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H55 zenon_Hc9 zenon_H1bd. % 29.77/29.94 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.77/29.94 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (e0)) = (op (e2) (e1)))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H1bd. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H62. % 29.77/29.94 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.77/29.94 cut (((op (e2) (e1)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 29.77/29.94 congruence. % 29.77/29.94 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e0)))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H1be. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H55. % 29.77/29.94 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 29.77/29.94 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.77/29.94 congruence. % 29.77/29.94 apply zenon_H63. apply refl_equal. % 29.77/29.94 apply zenon_Hca. apply sym_equal. exact zenon_Hc9. % 29.77/29.94 apply zenon_H63. apply refl_equal. % 29.77/29.94 apply zenon_H63. apply refl_equal. % 29.77/29.94 (* end of lemma zenon_L282_ *) % 29.77/29.94 assert (zenon_L283_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H135 zenon_H218 zenon_H16b zenon_H1af zenon_H60 zenon_H19e zenon_H37 zenon_He1 zenon_H1d5 zenon_H9d zenon_H222 zenon_Hd0 zenon_H155 zenon_H156. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.94 apply (zenon_L274_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.94 apply (zenon_L264_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.94 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.94 apply (zenon_L90_); trivial. % 29.77/29.94 (* end of lemma zenon_L283_ *) % 29.77/29.94 assert (zenon_L284_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H42 zenon_H2d zenon_H156 zenon_Hd0 zenon_H222 zenon_H9d zenon_H1d5 zenon_He1 zenon_H60 zenon_H16b zenon_H218 zenon_H135 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.94 apply (zenon_L4_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.94 apply (zenon_L283_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.94 apply (zenon_L281_); trivial. % 29.77/29.94 exact (zenon_H18e zenon_H40). % 29.77/29.94 (* end of lemma zenon_L284_ *) % 29.77/29.94 assert (zenon_L285_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hcd zenon_H101 zenon_H159 zenon_Hc9 zenon_H42 zenon_H2d zenon_H156 zenon_Hd0 zenon_H222 zenon_H1d5 zenon_He1 zenon_H60 zenon_H16b zenon_H218 zenon_H135 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.77/29.94 apply (zenon_L142_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.77/29.94 apply (zenon_L272_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.77/29.94 apply (zenon_L159_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.94 apply (zenon_L4_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.94 apply (zenon_L275_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.94 apply (zenon_L281_); trivial. % 29.77/29.94 exact (zenon_H18e zenon_H40). % 29.77/29.94 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.77/29.94 apply (zenon_L93_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.77/29.94 apply (zenon_L282_); trivial. % 29.77/29.94 apply (zenon_L284_); trivial. % 29.77/29.94 (* end of lemma zenon_L285_ *) % 29.77/29.94 assert (zenon_L286_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e2) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H173 zenon_H15a zenon_H18e zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_H1bd zenon_H1af zenon_H42 zenon_H125 zenon_H73 zenon_Hd9 zenon_Hcd zenon_Hd0 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_H156 zenon_H60 zenon_He1. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.77/29.94 apply (zenon_L94_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.77/29.94 apply (zenon_L272_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.77/29.94 apply (zenon_L159_); trivial. % 29.77/29.94 apply (zenon_L238_); trivial. % 29.77/29.94 (* end of lemma zenon_L286_ *) % 29.77/29.94 assert (zenon_L287_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.77/29.94 do 0 intro. intros zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H27 zenon_H10e zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.94 apply (zenon_L194_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.94 apply (zenon_L207_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.94 apply (zenon_L208_); trivial. % 29.77/29.94 apply (zenon_L210_); trivial. % 29.77/29.94 (* end of lemma zenon_L287_ *) % 29.77/29.94 assert (zenon_L288_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H8b zenon_He2 zenon_Hde. % 29.77/29.94 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 29.77/29.94 cut (((e2) = (e2)) = ((e0) = (e2))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_Hde. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_Hce. % 29.77/29.94 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.77/29.94 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 29.77/29.94 congruence. % 29.77/29.94 cut (((op (e3) (e0)) = (e0)) = ((e2) = (e0))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H154. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H8b. % 29.77/29.94 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.77/29.94 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 29.77/29.94 congruence. % 29.77/29.94 exact (zenon_He3 zenon_He2). % 29.77/29.94 apply zenon_H1d. apply refl_equal. % 29.77/29.94 apply zenon_H57. apply refl_equal. % 29.77/29.94 apply zenon_H57. apply refl_equal. % 29.77/29.94 (* end of lemma zenon_L288_ *) % 29.77/29.94 assert (zenon_L289_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 29.77/29.94 do 0 intro. intros zenon_Hf9 zenon_Hde zenon_H8b zenon_H55 zenon_H222 zenon_Hda zenon_H10d zenon_H231. % 29.77/29.94 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.77/29.94 apply (zenon_L288_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.77/29.94 apply (zenon_L264_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.77/29.94 apply (zenon_L64_); trivial. % 29.77/29.94 exact (zenon_H231 zenon_Hf4). % 29.77/29.94 (* end of lemma zenon_L289_ *) % 29.77/29.94 assert (zenon_L290_ : ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H1af zenon_H1c5 zenon_H16c zenon_H156. % 29.77/29.94 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.77/29.94 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H156. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H109. % 29.77/29.94 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.77/29.94 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 29.77/29.94 congruence. % 29.77/29.94 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H157. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H1af. % 29.77/29.94 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 29.77/29.94 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 29.77/29.94 congruence. % 29.77/29.94 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.77/29.94 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e3)))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_H1c9. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_H109. % 29.77/29.94 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.77/29.94 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 29.77/29.94 congruence. % 29.77/29.94 apply (zenon_L166_); trivial. % 29.77/29.94 apply zenon_H10a. apply refl_equal. % 29.77/29.94 apply zenon_H10a. apply refl_equal. % 29.77/29.94 apply zenon_H16d. apply sym_equal. exact zenon_H16c. % 29.77/29.94 apply zenon_H10a. apply refl_equal. % 29.77/29.94 apply zenon_H10a. apply refl_equal. % 29.77/29.94 (* end of lemma zenon_L290_ *) % 29.77/29.94 assert (zenon_L291_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H42 zenon_H2d zenon_H156 zenon_H16c zenon_H1af zenon_H60 zenon_H1c7 zenon_H1bd zenon_H101 zenon_Hdc zenon_Hd1 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H19e zenon_H1d5 zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_He1 zenon_H55 zenon_H18e. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.94 apply (zenon_L4_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.94 apply (zenon_L194_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.94 apply (zenon_L207_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.94 apply (zenon_L165_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.94 apply (zenon_L258_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.94 apply (zenon_L209_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.94 apply (zenon_L216_); trivial. % 29.77/29.94 apply (zenon_L290_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.94 apply (zenon_L126_); trivial. % 29.77/29.94 exact (zenon_H18e zenon_H40). % 29.77/29.94 (* end of lemma zenon_L291_ *) % 29.77/29.94 assert (zenon_L292_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H16f zenon_H15a zenon_H108 zenon_Hfc zenon_Hd9 zenon_H89 zenon_H1fd zenon_H17b zenon_H218 zenon_H6c zenon_Hd0 zenon_Hf9 zenon_Hde zenon_H10d zenon_H231 zenon_H125 zenon_H10e zenon_H27 zenon_H42 zenon_H2d zenon_H156 zenon_H1af zenon_H60 zenon_H1c7 zenon_H1bd zenon_H101 zenon_Hdc zenon_Hd1 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H19e zenon_H1d5 zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_He1 zenon_H55 zenon_H18e. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.77/29.94 apply (zenon_L241_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.94 apply (zenon_L194_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.94 apply (zenon_L207_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.94 apply (zenon_L208_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.77/29.94 apply (zenon_L289_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.77/29.94 apply (zenon_L159_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.77/29.94 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.94 apply (zenon_L157_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.94 apply (zenon_L209_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.94 apply (zenon_L259_); trivial. % 29.77/29.94 apply (zenon_L205_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.77/29.94 apply (zenon_L235_); trivial. % 29.77/29.94 apply (zenon_L291_); trivial. % 29.77/29.94 (* end of lemma zenon_L292_ *) % 29.77/29.94 assert (zenon_L293_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 29.77/29.94 do 0 intro. intros zenon_H225 zenon_He4 zenon_He1 zenon_H2d zenon_H1e zenon_H200 zenon_H1d8 zenon_H1bd zenon_H156 zenon_H125 zenon_H231 zenon_H10d zenon_Hf9 zenon_Hd0 zenon_H6c zenon_H1fd zenon_Hd9 zenon_H108 zenon_H15a zenon_H16f zenon_H42 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_H1ca zenon_H60 zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1d5 zenon_H19e zenon_Hd1 zenon_H19a zenon_Hfc zenon_H35 zenon_H102 zenon_H18e zenon_H174 zenon_H27 zenon_H10e zenon_H5c zenon_H8b zenon_Hde. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.77/29.94 apply (zenon_L286_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.77/29.94 apply (zenon_L287_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.77/29.94 apply (zenon_L192_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.77/29.94 apply (zenon_L286_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.77/29.94 apply (zenon_L287_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.77/29.94 apply (zenon_L154_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.77/29.94 apply (zenon_L292_); trivial. % 29.77/29.94 apply (zenon_L266_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.77/29.94 apply (zenon_L4_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.77/29.94 apply (zenon_L87_); trivial. % 29.77/29.94 apply (zenon_L267_); trivial. % 29.77/29.94 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.77/29.94 apply (zenon_L191_); trivial. % 29.77/29.94 apply (zenon_L288_); trivial. % 29.77/29.94 (* end of lemma zenon_L293_ *) % 29.77/29.94 assert (zenon_L294_ : (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> False). % 29.77/29.94 do 0 intro. intros zenon_Hde zenon_Hf5 zenon_H1e1. % 29.77/29.94 cut (((op (e2) (e3)) = (e2)) = ((e0) = (e2))). % 29.77/29.94 intro zenon_D_pnotp. % 29.77/29.94 apply zenon_Hde. % 29.77/29.94 rewrite <- zenon_D_pnotp. % 29.77/29.94 exact zenon_Hf5. % 29.77/29.94 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.77/29.94 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H232]. % 29.77/29.94 congruence. % 29.77/29.94 exact (zenon_H232 zenon_H1e1). % 29.77/29.94 apply zenon_H57. apply refl_equal. % 29.77/29.94 (* end of lemma zenon_L294_ *) % 29.77/29.94 assert (zenon_L295_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_H108 zenon_H37 zenon_Hfe zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_He1 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_Hd0 zenon_Hde zenon_H1e1. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.95 apply (zenon_L142_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.95 apply (zenon_L217_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.95 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.95 apply (zenon_L294_); trivial. % 29.77/29.95 (* end of lemma zenon_L295_ *) % 29.77/29.95 assert (zenon_L296_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H108 zenon_H142 zenon_H1e1. % 29.77/29.95 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H108. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_H142. % 29.77/29.95 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 29.77/29.95 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.77/29.95 congruence. % 29.77/29.95 apply zenon_H29. apply refl_equal. % 29.77/29.95 apply zenon_H1e2. apply sym_equal. exact zenon_H1e1. % 29.77/29.95 (* end of lemma zenon_L296_ *) % 29.77/29.95 assert (zenon_L297_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 29.77/29.95 do 0 intro. intros zenon_Hb5 zenon_H8b zenon_H9c. % 29.77/29.95 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_Hb5. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_H8b. % 29.77/29.95 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 29.77/29.95 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 29.77/29.95 congruence. % 29.77/29.95 apply zenon_H9a. apply refl_equal. % 29.77/29.95 apply zenon_Ha2. apply sym_equal. exact zenon_H9c. % 29.77/29.95 (* end of lemma zenon_L297_ *) % 29.77/29.95 assert (zenon_L298_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H18e zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hd1 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H1e zenon_H2d zenon_He4 zenon_H225 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H37 zenon_Hdc zenon_H18c zenon_H135 zenon_H1e1 zenon_H108 zenon_Hb5 zenon_H8b. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.77/29.95 apply (zenon_L293_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.77/29.95 apply (zenon_L295_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.77/29.95 apply (zenon_L296_); trivial. % 29.77/29.95 apply (zenon_L297_); trivial. % 29.77/29.95 (* end of lemma zenon_L298_ *) % 29.77/29.95 assert (zenon_L299_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H20d zenon_H16b zenon_H112 zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H18e zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hd1 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H1e zenon_H2d zenon_He4 zenon_H225 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H37 zenon_Hdc zenon_H18c zenon_H135 zenon_H108 zenon_Hb5 zenon_H8b. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.95 apply (zenon_L194_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.95 apply (zenon_L207_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.95 apply (zenon_L285_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.95 apply (zenon_L165_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.95 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.95 apply (zenon_L223_); trivial. % 29.77/29.95 apply (zenon_L298_); trivial. % 29.77/29.95 (* end of lemma zenon_L299_ *) % 29.77/29.95 assert (zenon_L300_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 29.77/29.95 do 0 intro. intros zenon_Hf9 zenon_H8a zenon_He1 zenon_He9 zenon_H3f zenon_Hda zenon_H10d zenon_H231. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.77/29.95 apply (zenon_L50_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.77/29.95 apply (zenon_L53_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.77/29.95 apply (zenon_L64_); trivial. % 29.77/29.95 exact (zenon_H231 zenon_Hf4). % 29.77/29.95 (* end of lemma zenon_L300_ *) % 29.77/29.95 assert (zenon_L301_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1af zenon_H1dc zenon_Hb6 zenon_Hf5 zenon_He1. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.95 apply (zenon_L193_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.95 apply (zenon_L144_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.95 apply (zenon_L200_); trivial. % 29.77/29.95 apply (zenon_L221_); trivial. % 29.77/29.95 (* end of lemma zenon_L301_ *) % 29.77/29.95 assert (zenon_L302_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H108 zenon_H37 zenon_Hfe zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1af zenon_H1dc zenon_Hb6 zenon_He1. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.95 apply (zenon_L49_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.95 apply (zenon_L217_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.95 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.95 apply (zenon_L301_); trivial. % 29.77/29.95 (* end of lemma zenon_L302_ *) % 29.77/29.95 assert (zenon_L303_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H142 zenon_Hdf zenon_H6b. % 29.77/29.95 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.77/29.95 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H6b. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_H28. % 29.77/29.95 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.77/29.95 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 29.77/29.95 congruence. % 29.77/29.95 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H1ec. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_H142. % 29.77/29.95 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f0]. % 29.77/29.95 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.77/29.95 congruence. % 29.77/29.95 apply zenon_H29. apply refl_equal. % 29.77/29.95 apply zenon_H1f0. apply sym_equal. exact zenon_Hdf. % 29.77/29.95 apply zenon_H29. apply refl_equal. % 29.77/29.95 apply zenon_H29. apply refl_equal. % 29.77/29.95 (* end of lemma zenon_L303_ *) % 29.77/29.95 assert (zenon_L304_ : (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H2d zenon_Hb6 zenon_H9c. % 29.77/29.95 cut (((op (e3) (e2)) = (e3)) = ((e0) = (e3))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H2d. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_Hb6. % 29.77/29.95 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.77/29.95 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H233]. % 29.77/29.95 congruence. % 29.77/29.95 exact (zenon_H233 zenon_H9c). % 29.77/29.95 apply zenon_H2f. apply refl_equal. % 29.77/29.95 (* end of lemma zenon_L304_ *) % 29.77/29.95 assert (zenon_L305_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H14b zenon_Hda zenon_He1 zenon_H1dc zenon_H1af zenon_Hd6 zenon_H1d5 zenon_Hd0 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_H1ca zenon_H37 zenon_H108 zenon_Hde zenon_H135 zenon_H6b zenon_Hdf zenon_H2d zenon_Hb6. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.77/29.95 apply (zenon_L192_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.77/29.95 apply (zenon_L302_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.77/29.95 apply (zenon_L303_); trivial. % 29.77/29.95 apply (zenon_L304_); trivial. % 29.77/29.95 (* end of lemma zenon_L305_ *) % 29.77/29.95 assert (zenon_L306_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H200 zenon_Hb6 zenon_H2d zenon_H6b zenon_Hde zenon_H108 zenon_H37 zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_Hd6 zenon_H1dc zenon_He1 zenon_Hda zenon_H14b zenon_H60 zenon_H20d zenon_Hd0 zenon_Hdc zenon_H18c zenon_H135 zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.95 apply (zenon_L305_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.95 apply (zenon_L207_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.95 apply (zenon_L224_); trivial. % 29.77/29.95 apply (zenon_L210_); trivial. % 29.77/29.95 (* end of lemma zenon_L306_ *) % 29.77/29.95 assert (zenon_L307_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H1d8 zenon_Hc9 zenon_He2. % 29.77/29.95 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e3) (e0)))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H1d8. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_Hc9. % 29.77/29.95 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 29.77/29.95 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.77/29.95 congruence. % 29.77/29.95 apply zenon_H6d. apply refl_equal. % 29.77/29.95 apply zenon_He8. apply sym_equal. exact zenon_He2. % 29.77/29.95 (* end of lemma zenon_L307_ *) % 29.77/29.95 assert (zenon_L308_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H135 zenon_He2 zenon_H1d8 zenon_He1 zenon_Hd0 zenon_H1af zenon_H3d zenon_Hd6. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.95 apply (zenon_L307_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.95 apply (zenon_L126_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.95 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.95 apply (zenon_L144_); trivial. % 29.77/29.95 (* end of lemma zenon_L308_ *) % 29.77/29.95 assert (zenon_L309_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H108 zenon_Hd0 zenon_Hfe zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_He1 zenon_H55 zenon_H18e. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.95 apply (zenon_L4_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.95 apply (zenon_L217_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.95 apply (zenon_L126_); trivial. % 29.77/29.95 exact (zenon_H18e zenon_H40). % 29.77/29.95 (* end of lemma zenon_L309_ *) % 29.77/29.95 assert (zenon_L310_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H135 zenon_He2 zenon_H1d8 zenon_H9d zenon_H222 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1af zenon_H1dc zenon_Hb6 zenon_He1. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.95 apply (zenon_L307_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.95 apply (zenon_L264_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.95 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.95 apply (zenon_L301_); trivial. % 29.77/29.95 (* end of lemma zenon_L310_ *) % 29.77/29.95 assert (zenon_L311_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_Hfd zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.95 apply (zenon_L4_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.95 apply (zenon_L158_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.95 apply (zenon_L308_); trivial. % 29.77/29.95 exact (zenon_H18e zenon_H40). % 29.77/29.95 (* end of lemma zenon_L311_ *) % 29.77/29.95 assert (zenon_L312_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_H155 zenon_He9 zenon_H3c zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.95 apply (zenon_L4_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.95 apply (zenon_L275_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.95 apply (zenon_L308_); trivial. % 29.77/29.95 exact (zenon_H18e zenon_H40). % 29.77/29.95 (* end of lemma zenon_L312_ *) % 29.77/29.95 assert (zenon_L313_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_H155 zenon_H222 zenon_H9d zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.95 apply (zenon_L4_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.95 apply (zenon_L283_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.95 apply (zenon_L308_); trivial. % 29.77/29.95 exact (zenon_H18e zenon_H40). % 29.77/29.95 (* end of lemma zenon_L313_ *) % 29.77/29.95 assert (zenon_L314_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H101 zenon_H3c zenon_H159 zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H5e zenon_H6c zenon_H1ca zenon_Hfe zenon_H108 zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_H155 zenon_H222 zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.77/29.95 apply (zenon_L312_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.77/29.95 apply (zenon_L93_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.77/29.95 apply (zenon_L309_); trivial. % 29.77/29.95 apply (zenon_L313_); trivial. % 29.77/29.95 (* end of lemma zenon_L314_ *) % 29.77/29.95 assert (zenon_L315_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H173 zenon_Hb6 zenon_H1dc zenon_H6b zenon_Hd1 zenon_H18c zenon_H20d zenon_H14b zenon_Hda zenon_Hde zenon_H200 zenon_H19a zenon_H101 zenon_H3c zenon_H159 zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H5e zenon_H6c zenon_H1ca zenon_Hfe zenon_H108 zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_H222 zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.95 apply (zenon_L4_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.95 apply (zenon_L306_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.95 apply (zenon_L308_); trivial. % 29.77/29.95 exact (zenon_H18e zenon_H40). % 29.77/29.95 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.77/29.95 apply (zenon_L154_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.77/29.95 apply (zenon_L309_); trivial. % 29.77/29.95 apply (zenon_L310_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.77/29.95 apply (zenon_L311_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.77/29.95 apply (zenon_L159_); trivial. % 29.77/29.95 apply (zenon_L314_); trivial. % 29.77/29.95 (* end of lemma zenon_L315_ *) % 29.77/29.95 assert (zenon_L316_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_Hb8 zenon_H231 zenon_H10d zenon_H3f zenon_He9 zenon_Hf9 zenon_H18e zenon_H135 zenon_He2 zenon_H1d8 zenon_He1 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H218 zenon_H16b zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H1e zenon_H42 zenon_H108 zenon_Hfe zenon_H1ca zenon_H6c zenon_H5e zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H159 zenon_H3c zenon_H101 zenon_H19a zenon_H200 zenon_Hde zenon_Hda zenon_H14b zenon_H20d zenon_H18c zenon_Hd1 zenon_H6b zenon_H1dc zenon_H173 zenon_Hb1 zenon_H2d. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 29.77/29.95 apply (zenon_L300_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 29.77/29.95 exact (zenon_H18e zenon_H40). % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 29.77/29.95 apply (zenon_L315_); trivial. % 29.77/29.95 apply (zenon_L107_); trivial. % 29.77/29.95 (* end of lemma zenon_L316_ *) % 29.77/29.95 assert (zenon_L317_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H234 zenon_H37. % 29.77/29.95 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 29.77/29.95 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 29.77/29.95 congruence. % 29.77/29.95 exact (zenon_H103 zenon_H37). % 29.77/29.95 exact (zenon_H103 zenon_H37). % 29.77/29.95 (* end of lemma zenon_L317_ *) % 29.77/29.95 assert (zenon_L318_ : (~((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H235 zenon_H37. % 29.77/29.95 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.77/29.95 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 29.77/29.95 congruence. % 29.77/29.95 exact (zenon_H103 zenon_H37). % 29.77/29.95 apply zenon_H22. apply refl_equal. % 29.77/29.95 (* end of lemma zenon_L318_ *) % 29.77/29.95 assert (zenon_L319_ : ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (op (op (e1) (e1)) (e1)))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H9d zenon_H37 zenon_H236. % 29.77/29.95 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 29.77/29.95 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e2) = (op (op (e1) (e1)) (e1)))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H236. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_H13e. % 29.77/29.95 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 29.77/29.95 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H237]. % 29.77/29.95 congruence. % 29.77/29.95 cut (((op (e3) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H237. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_H9d. % 29.77/29.95 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.77/29.95 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H238]. % 29.77/29.95 congruence. % 29.77/29.95 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 29.77/29.95 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H238. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_H13e. % 29.77/29.95 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 29.77/29.95 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H235]. % 29.77/29.95 congruence. % 29.77/29.95 apply (zenon_L318_); trivial. % 29.77/29.95 apply zenon_H13f. apply refl_equal. % 29.77/29.95 apply zenon_H13f. apply refl_equal. % 29.77/29.95 apply zenon_H57. apply refl_equal. % 29.77/29.95 apply zenon_H13f. apply refl_equal. % 29.77/29.95 apply zenon_H13f. apply refl_equal. % 29.77/29.95 (* end of lemma zenon_L319_ *) % 29.77/29.95 assert (zenon_L320_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False). % 29.77/29.95 do 0 intro. intros zenon_Hb1 zenon_H9d zenon_H37. % 29.77/29.95 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H144 | zenon_intro zenon_H239 ]. % 29.77/29.95 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 29.77/29.95 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H144. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_H145. % 29.77/29.95 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 29.77/29.95 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 29.77/29.95 congruence. % 29.77/29.95 cut (((op (e3) (e3)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H147. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_Hb1. % 29.77/29.95 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.77/29.95 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 29.77/29.95 congruence. % 29.77/29.95 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 29.77/29.95 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))))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.95 apply zenon_H23a. % 29.77/29.95 rewrite <- zenon_D_pnotp. % 29.77/29.95 exact zenon_H145. % 29.77/29.95 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 29.77/29.95 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H234]. % 29.77/29.95 congruence. % 29.77/29.95 apply (zenon_L317_); trivial. % 29.77/29.95 apply zenon_H146. apply refl_equal. % 29.77/29.95 apply zenon_H146. apply refl_equal. % 29.77/29.95 apply zenon_H1d. apply refl_equal. % 29.77/29.95 apply zenon_H146. apply refl_equal. % 29.77/29.95 apply zenon_H146. apply refl_equal. % 29.77/29.95 apply (zenon_notand_s _ _ zenon_H239); [ zenon_intro zenon_H236 | zenon_intro zenon_H38 ]. % 29.77/29.95 apply (zenon_L319_); trivial. % 29.77/29.95 apply zenon_H38. apply sym_equal. exact zenon_H37. % 29.77/29.95 (* end of lemma zenon_L320_ *) % 29.77/29.95 assert (zenon_L321_ : ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.95 do 0 intro. intros zenon_Hdf zenon_H231 zenon_Hb8 zenon_Had zenon_H6e zenon_H18e zenon_He1 zenon_H112 zenon_H6f zenon_H37 zenon_H10d zenon_H3f zenon_He9 zenon_Hf9 zenon_H135 zenon_H1d8 zenon_Hd0 zenon_Hd6 zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H1e zenon_H42 zenon_H108 zenon_Hfe zenon_H1ca zenon_H6c zenon_H5e zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H159 zenon_H3c zenon_H101 zenon_H19a zenon_H200 zenon_Hde zenon_Hda zenon_H14b zenon_H20d zenon_H18c zenon_Hd1 zenon_H6b zenon_H1dc zenon_H173 zenon_H2d zenon_H5c zenon_H27 zenon_H174 zenon_H102 zenon_H35 zenon_Hfc zenon_H20e zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_H125 zenon_He4 zenon_H225 zenon_Hdc zenon_Hb5 zenon_Hbd zenon_H1af zenon_H16b zenon_H218. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.95 apply (zenon_L49_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.95 apply (zenon_L217_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.95 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.95 apply (zenon_L193_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.95 apply (zenon_L144_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.77/29.95 apply (zenon_L299_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.77/29.95 apply (zenon_L29_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.77/29.95 apply (zenon_L198_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.77/29.95 apply (zenon_L316_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.77/29.95 apply (zenon_L320_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.77/29.95 apply (zenon_L233_); trivial. % 29.77/29.95 exact (zenon_H231 zenon_Hf4). % 29.77/29.95 apply (zenon_L245_); trivial. % 29.77/29.95 (* end of lemma zenon_L321_ *) % 29.77/29.95 assert (zenon_L322_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H42 zenon_H2d zenon_He1 zenon_H1af zenon_H1bd zenon_Hfd zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.95 apply (zenon_L4_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.95 apply (zenon_L158_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.95 apply (zenon_L49_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.95 apply (zenon_L207_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.95 apply (zenon_L79_); trivial. % 29.77/29.95 apply (zenon_L209_); trivial. % 29.77/29.95 exact (zenon_H18e zenon_H40). % 29.77/29.95 (* end of lemma zenon_L322_ *) % 29.77/29.95 assert (zenon_L323_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H37 zenon_H19e zenon_H156 zenon_H155 zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H142 zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.95 apply (zenon_L273_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.95 apply (zenon_L131_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.95 apply (zenon_L179_); trivial. % 29.77/29.95 apply (zenon_L168_); trivial. % 29.77/29.95 (* end of lemma zenon_L323_ *) % 29.77/29.95 assert (zenon_L324_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H200 zenon_Hde zenon_H1c7 zenon_H60 zenon_Hd6 zenon_H155 zenon_H156 zenon_H19e zenon_H37 zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.95 apply (zenon_L49_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.95 apply (zenon_L207_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.95 apply (zenon_L323_); trivial. % 29.77/29.95 apply (zenon_L210_); trivial. % 29.77/29.95 (* end of lemma zenon_L324_ *) % 29.77/29.95 assert (zenon_L325_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H1d5 zenon_H6b zenon_Hd6 zenon_Hf5 zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1e zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1af zenon_H16c zenon_H156. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.95 apply (zenon_L193_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.95 apply (zenon_L144_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.95 apply (zenon_L202_); trivial. % 29.77/29.95 apply (zenon_L290_); trivial. % 29.77/29.95 (* end of lemma zenon_L325_ *) % 29.77/29.95 assert (zenon_L326_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H135 zenon_Hde zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1e zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1af zenon_H16c zenon_H156. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.95 apply (zenon_L49_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.95 apply (zenon_L88_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.95 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.95 apply (zenon_L325_); trivial. % 29.77/29.95 (* end of lemma zenon_L326_ *) % 29.77/29.95 assert (zenon_L327_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H200 zenon_H16c zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_H112 zenon_Hb8 zenon_He7 zenon_H89 zenon_H18e zenon_H1dc zenon_H2d zenon_H6b zenon_Hd0 zenon_Hde zenon_H135 zenon_H1c7 zenon_H60 zenon_Hd6 zenon_H155 zenon_H156 zenon_H19e zenon_H37 zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.95 apply (zenon_L326_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.95 apply (zenon_L207_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.95 apply (zenon_L323_); trivial. % 29.77/29.95 apply (zenon_L210_); trivial. % 29.77/29.95 (* end of lemma zenon_L327_ *) % 29.77/29.95 assert (zenon_L328_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 29.77/29.95 do 0 intro. intros zenon_H200 zenon_H156 zenon_H16c zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H89 zenon_H18e zenon_H1dc zenon_H2d zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_He9 zenon_Hde zenon_H135 zenon_H1e zenon_H3c zenon_H19e zenon_H19a zenon_Hfc zenon_H155 zenon_H112 zenon_H102 zenon_H1bd zenon_H1af zenon_H3d. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.95 apply (zenon_L326_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.95 apply (zenon_L207_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.95 apply (zenon_L280_); trivial. % 29.77/29.95 apply (zenon_L209_); trivial. % 29.77/29.95 (* end of lemma zenon_L328_ *) % 29.77/29.95 assert (zenon_L329_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H16f zenon_H15a zenon_H6f zenon_H42 zenon_H5e zenon_H6c zenon_H1ca zenon_He1 zenon_Hc9 zenon_H60 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H135 zenon_Hde zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H2d zenon_H1dc zenon_H89 zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H156 zenon_H200 zenon_H18e. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.77/29.95 apply (zenon_L241_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.77/29.95 apply (zenon_L324_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.77/29.95 apply (zenon_L235_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.95 apply (zenon_L4_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.95 apply (zenon_L327_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.95 apply (zenon_L328_); trivial. % 29.77/29.95 exact (zenon_H18e zenon_H40). % 29.77/29.95 (* end of lemma zenon_L329_ *) % 29.77/29.95 assert (zenon_L330_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H135 zenon_He1 zenon_H76 zenon_H9d zenon_H222 zenon_Hde zenon_H142 zenon_H155 zenon_H156. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.95 apply (zenon_L273_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.95 apply (zenon_L264_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.95 apply (zenon_L89_); trivial. % 29.77/29.95 apply (zenon_L90_); trivial. % 29.77/29.95 (* end of lemma zenon_L330_ *) % 29.77/29.95 assert (zenon_L331_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.77/29.95 do 0 intro. intros zenon_H1d5 zenon_H156 zenon_H155 zenon_Hde zenon_H222 zenon_H9d zenon_He1 zenon_H135 zenon_H37 zenon_H19e zenon_H2d zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H142 zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.95 apply (zenon_L330_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.95 apply (zenon_L131_); trivial. % 29.77/29.95 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.95 apply (zenon_L175_); trivial. % 29.77/29.95 apply (zenon_L168_); trivial. % 29.77/29.95 (* end of lemma zenon_L331_ *) % 29.77/29.95 assert (zenon_L332_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 29.77/29.95 do 0 intro. intros zenon_Hc8 zenon_H89 zenon_H76. % 29.77/29.95 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 29.77/29.95 intro zenon_D_pnotp. % 29.77/29.96 apply zenon_Hc8. % 29.77/29.96 rewrite <- zenon_D_pnotp. % 29.77/29.96 exact zenon_H89. % 29.77/29.96 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 29.77/29.96 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 29.77/29.96 congruence. % 29.77/29.96 apply zenon_Hcb. apply refl_equal. % 29.77/29.96 apply zenon_H1da. apply sym_equal. exact zenon_H76. % 29.77/29.96 (* end of lemma zenon_L332_ *) % 29.77/29.96 assert (zenon_L333_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.77/29.96 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_H6c zenon_Hd6 zenon_H2d zenon_H19e zenon_H37 zenon_H135 zenon_He1 zenon_Hde zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H1bd zenon_H156 zenon_H155 zenon_H60 zenon_H1ca zenon_H1e zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H222 zenon_H1af zenon_H1c7. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.96 apply (zenon_L49_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.96 apply (zenon_L207_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.96 apply (zenon_L331_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.96 apply (zenon_L332_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.96 apply (zenon_L209_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.96 apply (zenon_L179_); trivial. % 29.77/29.96 apply (zenon_L265_); trivial. % 29.77/29.96 (* end of lemma zenon_L333_ *) % 29.77/29.96 assert (zenon_L334_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.96 do 0 intro. intros zenon_H42 zenon_H1c7 zenon_H222 zenon_H9d zenon_H5e zenon_H1f zenon_H1ca zenon_H60 zenon_H156 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde zenon_He1 zenon_H135 zenon_H2d zenon_Hd6 zenon_H6c zenon_Hc9 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.96 apply (zenon_L4_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.96 apply (zenon_L333_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.96 apply (zenon_L281_); trivial. % 29.77/29.96 exact (zenon_H18e zenon_H40). % 29.77/29.96 (* end of lemma zenon_L334_ *) % 29.77/29.96 assert (zenon_L335_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.96 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hcd zenon_H101 zenon_Hbd zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_Hd0 zenon_H6f zenon_H15a zenon_H16f zenon_H159 zenon_H42 zenon_H1c7 zenon_H222 zenon_H5e zenon_H1f zenon_H1ca zenon_H60 zenon_H156 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde zenon_He1 zenon_H135 zenon_H2d zenon_Hd6 zenon_H6c zenon_Hc9 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.77/29.96 apply (zenon_L142_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.77/29.96 apply (zenon_L322_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.77/29.96 apply (zenon_L159_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.77/29.96 apply (zenon_L329_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.77/29.96 apply (zenon_L93_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.77/29.96 apply (zenon_L282_); trivial. % 29.77/29.96 apply (zenon_L334_); trivial. % 29.77/29.96 (* end of lemma zenon_L335_ *) % 29.77/29.96 assert (zenon_L336_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 29.77/29.96 do 0 intro. intros zenon_H3f zenon_H1f zenon_H98. % 29.77/29.96 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 29.77/29.96 intro zenon_D_pnotp. % 29.77/29.96 apply zenon_H3f. % 29.77/29.96 rewrite <- zenon_D_pnotp. % 29.77/29.96 exact zenon_H1f. % 29.77/29.96 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 29.77/29.96 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 29.77/29.96 congruence. % 29.77/29.96 apply zenon_H3b. apply refl_equal. % 29.77/29.96 apply zenon_H99. apply sym_equal. exact zenon_H98. % 29.77/29.96 (* end of lemma zenon_L336_ *) % 29.77/29.96 assert (zenon_L337_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 29.77/29.96 do 0 intro. intros zenon_Hee zenon_H19a zenon_H1a0. % 29.77/29.96 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 29.77/29.96 intro zenon_D_pnotp. % 29.77/29.96 apply zenon_Hee. % 29.77/29.96 rewrite <- zenon_D_pnotp. % 29.77/29.96 exact zenon_H19a. % 29.77/29.96 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 29.77/29.96 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 29.77/29.96 congruence. % 29.77/29.96 apply zenon_H19c. apply refl_equal. % 29.77/29.96 apply zenon_H1a1. apply sym_equal. exact zenon_H1a0. % 29.77/29.96 (* end of lemma zenon_L337_ *) % 29.77/29.96 assert (zenon_L338_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 29.77/29.96 do 0 intro. intros zenon_H23b zenon_H20 zenon_H8b zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hb8 zenon_Had zenon_H6e zenon_H100 zenon_H37 zenon_H10d zenon_H117 zenon_H6f. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 29.77/29.96 apply (zenon_L27_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 29.77/29.96 apply (zenon_L336_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 29.77/29.96 apply (zenon_L337_); trivial. % 29.77/29.96 apply (zenon_L153_); trivial. % 29.77/29.96 (* end of lemma zenon_L338_ *) % 29.77/29.96 assert (zenon_L339_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 29.77/29.96 do 0 intro. intros zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H18e zenon_H10d zenon_H117 zenon_H112 zenon_H6f. % 29.77/29.96 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 29.77/29.96 apply (zenon_L174_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 29.77/29.96 exact (zenon_H18e zenon_H40). % 29.77/29.96 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 29.77/29.96 apply (zenon_L151_); trivial. % 29.77/29.96 apply (zenon_L152_); trivial. % 29.77/29.96 (* end of lemma zenon_L339_ *) % 29.77/29.96 assert (zenon_L340_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.96 do 0 intro. intros zenon_Hbd zenon_He7 zenon_H1dc zenon_H6b zenon_Hc8 zenon_Hb8 zenon_H100 zenon_Had zenon_Hee zenon_H3f zenon_H20 zenon_H23b zenon_H8d zenon_H8b zenon_Hb5 zenon_H108 zenon_H135 zenon_H18c zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_He1 zenon_H208 zenon_H6f zenon_Hcd zenon_H1d5 zenon_Hd0 zenon_Hde zenon_H225 zenon_He4 zenon_H2d zenon_H200 zenon_H1d8 zenon_H156 zenon_H125 zenon_H231 zenon_H10d zenon_Hf9 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H42 zenon_H222 zenon_H1f zenon_H3c zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_H174 zenon_H27 zenon_H5c zenon_H14b zenon_H112 zenon_H20d zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.96 apply (zenon_L4_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.96 apply (zenon_L194_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.96 apply (zenon_L207_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.96 apply (zenon_L335_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.96 apply (zenon_L165_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.96 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.96 apply (zenon_L223_); trivial. % 29.77/29.96 apply (zenon_L298_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.96 apply (zenon_L155_); trivial. % 29.77/29.96 exact (zenon_H18e zenon_H40). % 29.77/29.96 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.77/29.96 apply (zenon_L4_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.77/29.96 apply (zenon_L149_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.96 apply (zenon_L4_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.96 apply (zenon_L338_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.96 apply (zenon_L145_); trivial. % 29.77/29.96 exact (zenon_H18e zenon_H40). % 29.77/29.96 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.77/29.96 apply (zenon_L339_); trivial. % 29.77/29.96 apply (zenon_L25_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.96 apply (zenon_L4_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.96 apply (zenon_L299_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.96 apply (zenon_L155_); trivial. % 29.77/29.96 exact (zenon_H18e zenon_H40). % 29.77/29.96 (* end of lemma zenon_L340_ *) % 29.77/29.96 assert (zenon_L341_ : ((op (e2) (e3)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.77/29.96 do 0 intro. intros zenon_Hf5 zenon_H37 zenon_H9d zenon_H112 zenon_H3f zenon_H1e zenon_Hbd zenon_He7 zenon_H1dc zenon_H6b zenon_Hc8 zenon_Hb8 zenon_H100 zenon_Had zenon_Hee zenon_H20 zenon_H23b zenon_H8d zenon_Hb5 zenon_H108 zenon_H135 zenon_H18c zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_He1 zenon_H208 zenon_H6f zenon_Hcd zenon_H1d5 zenon_Hd0 zenon_Hde zenon_H225 zenon_He4 zenon_H2d zenon_H200 zenon_H1d8 zenon_H156 zenon_H125 zenon_H231 zenon_H10d zenon_Hf9 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H42 zenon_H222 zenon_H1f zenon_H3c zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_H174 zenon_H27 zenon_H5c zenon_H14b zenon_H20d zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H35 zenon_H102 zenon_H18e zenon_H1af zenon_H16b zenon_H218. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.96 apply (zenon_L193_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.96 apply (zenon_L144_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.96 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.77/29.96 apply (zenon_L340_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.77/29.96 apply (zenon_L29_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.77/29.96 apply (zenon_L198_); trivial. % 29.77/29.96 apply (zenon_L320_); trivial. % 29.77/29.96 apply (zenon_L245_); trivial. % 29.77/29.96 (* end of lemma zenon_L341_ *) % 29.77/29.96 assert (zenon_L342_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.96 do 0 intro. intros zenon_H218 zenon_H16b zenon_H1af zenon_H20d zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H2d zenon_He4 zenon_H225 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H18c zenon_H135 zenon_H108 zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_H100 zenon_Hb8 zenon_Hc8 zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H3f zenon_H112 zenon_H9d zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.96 apply (zenon_L4_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.96 apply (zenon_L142_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.96 apply (zenon_L264_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.96 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.96 apply (zenon_L341_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.96 apply (zenon_L155_); trivial. % 29.77/29.96 exact (zenon_H18e zenon_H40). % 29.77/29.96 (* end of lemma zenon_L342_ *) % 29.77/29.96 assert (zenon_L343_ : ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.96 do 0 intro. intros zenon_Hdf zenon_H6e zenon_Hda zenon_Hfe zenon_H218 zenon_H16b zenon_H1af zenon_H20d zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H2d zenon_He4 zenon_H225 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H18c zenon_H135 zenon_H108 zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_H100 zenon_Hb8 zenon_Hc8 zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H3f zenon_H112 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.96 apply (zenon_L4_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.96 apply (zenon_L321_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.96 apply (zenon_L145_); trivial. % 29.77/29.96 exact (zenon_H18e zenon_H40). % 29.77/29.96 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.77/29.96 apply (zenon_L154_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.77/29.96 apply (zenon_L309_); trivial. % 29.77/29.96 apply (zenon_L342_); trivial. % 29.77/29.96 (* end of lemma zenon_L343_ *) % 29.77/29.96 assert (zenon_L344_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 29.77/29.96 do 0 intro. intros zenon_H102 zenon_H35 zenon_H1e zenon_Hfc zenon_Hdc zenon_Hd1 zenon_H19e zenon_H3f zenon_Hbd zenon_He7 zenon_H1dc zenon_H6b zenon_Hc8 zenon_H100 zenon_Hee zenon_H20 zenon_H23b zenon_H8d zenon_Hb5 zenon_H108 zenon_H135 zenon_H18c zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H1d5 zenon_Hde zenon_H225 zenon_He4 zenon_H2d zenon_H200 zenon_H1d8 zenon_H156 zenon_H125 zenon_H231 zenon_H10d zenon_Hf9 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H42 zenon_H222 zenon_H1f zenon_H3c zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_H174 zenon_H27 zenon_H5c zenon_H14b zenon_H20d zenon_H1af zenon_H16b zenon_H218 zenon_Hfe zenon_Hdf zenon_Hcd zenon_H19a zenon_Hd0 zenon_Hb8 zenon_Had zenon_H6e zenon_H18e zenon_He1 zenon_H112 zenon_H6f. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.77/29.96 apply (zenon_L343_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.77/29.96 apply (zenon_L159_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.77/29.96 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.96 apply (zenon_L233_); trivial. % 29.77/29.96 (* end of lemma zenon_L344_ *) % 29.77/29.96 assert (zenon_L345_ : ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.77/29.96 do 0 intro. intros zenon_H112 zenon_Hd0 zenon_H20e zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_H1f zenon_H3c zenon_He9 zenon_H1d5 zenon_H18c zenon_H135 zenon_Hdf zenon_H6b zenon_H3f zenon_Hbd zenon_He7 zenon_H1dc zenon_Hc8 zenon_H100 zenon_Hee zenon_H20 zenon_H23b zenon_H8d zenon_Hb5 zenon_H108 zenon_Hde zenon_H225 zenon_He4 zenon_H2d zenon_H200 zenon_H1d8 zenon_H156 zenon_H125 zenon_H231 zenon_H10d zenon_Hf9 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H42 zenon_H222 zenon_H173 zenon_H101 zenon_H159 zenon_H174 zenon_H27 zenon_H5c zenon_H14b zenon_H20d zenon_H16b zenon_H218 zenon_Hcd zenon_Hb8 zenon_Had zenon_H6e zenon_He1 zenon_H92 zenon_H69 zenon_H16a zenon_H83 zenon_H84 zenon_H17d zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.77/29.96 apply (zenon_L4_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.77/29.96 apply (zenon_L271_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.77/29.96 apply (zenon_L344_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.77/29.96 apply (zenon_L303_); trivial. % 29.77/29.96 apply (zenon_L228_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.77/29.96 apply (zenon_L155_); trivial. % 29.77/29.96 exact (zenon_H18e zenon_H40). % 29.77/29.96 (* end of lemma zenon_L345_ *) % 29.77/29.96 assert (zenon_L346_ : (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.77/29.96 do 0 intro. intros zenon_H18e zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hd1 zenon_H19e zenon_H17d zenon_H84 zenon_H83 zenon_H16a zenon_H69 zenon_H92 zenon_He1 zenon_H6e zenon_Had zenon_Hb8 zenon_Hcd zenon_H218 zenon_H16b zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H159 zenon_H101 zenon_H173 zenon_H222 zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H2d zenon_He4 zenon_H225 zenon_Hde zenon_H108 zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_H100 zenon_Hc8 zenon_H1dc zenon_He7 zenon_Hbd zenon_H3f zenon_H6b zenon_H1d5 zenon_H1f zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_Hd6 zenon_H20e zenon_H112 zenon_H60 zenon_H20d zenon_Hd0 zenon_Hdc zenon_H18c zenon_H135 zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.96 apply (zenon_L345_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.96 apply (zenon_L207_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.96 apply (zenon_L224_); trivial. % 29.77/29.96 apply (zenon_L210_); trivial. % 29.77/29.96 (* end of lemma zenon_L346_ *) % 29.77/29.96 assert (zenon_L347_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 29.77/29.96 do 0 intro. intros zenon_H19e zenon_Hc3 zenon_H1ba. % 29.77/29.96 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 29.77/29.96 intro zenon_D_pnotp. % 29.77/29.96 apply zenon_H19e. % 29.77/29.96 rewrite <- zenon_D_pnotp. % 29.77/29.96 exact zenon_Hc3. % 29.77/29.96 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 29.77/29.96 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 29.77/29.96 congruence. % 29.77/29.96 apply zenon_Hc5. apply refl_equal. % 29.77/29.96 apply zenon_H1bb. apply sym_equal. exact zenon_H1ba. % 29.77/29.96 (* end of lemma zenon_L347_ *) % 29.77/29.96 assert (zenon_L348_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 29.77/29.96 do 0 intro. intros zenon_H1ca zenon_Hc3 zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H1c7 zenon_H1b9 zenon_H60 zenon_H1af zenon_Hf5 zenon_Hd6. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1cb ]. % 29.77/29.96 apply (zenon_L347_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H1cc ]. % 29.77/29.96 apply (zenon_L163_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H55 | zenon_intro zenon_H3d ]. % 29.77/29.96 apply (zenon_L216_); trivial. % 29.77/29.96 apply (zenon_L144_); trivial. % 29.77/29.96 (* end of lemma zenon_L348_ *) % 29.77/29.96 assert (zenon_L349_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 29.77/29.96 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1af zenon_H60 zenon_H1c7 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_He1. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.77/29.96 apply (zenon_L142_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.77/29.96 apply (zenon_L88_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.77/29.96 exact (zenon_Hd0 zenon_Hcc). % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.77/29.96 apply (zenon_L193_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.77/29.96 apply (zenon_L144_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.77/29.96 apply (zenon_L348_); trivial. % 29.77/29.96 apply (zenon_L221_); trivial. % 29.77/29.96 (* end of lemma zenon_L349_ *) % 29.77/29.96 assert (zenon_L350_ : ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 29.77/29.96 do 0 intro. intros zenon_H142 zenon_Hfe zenon_H20e. % 29.77/29.96 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.77/29.96 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 29.77/29.96 intro zenon_D_pnotp. % 29.77/29.96 apply zenon_H20e. % 29.77/29.96 rewrite <- zenon_D_pnotp. % 29.77/29.96 exact zenon_H28. % 29.77/29.96 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.77/29.96 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 29.77/29.96 congruence. % 29.77/29.96 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 29.77/29.96 intro zenon_D_pnotp. % 29.77/29.96 apply zenon_H20f. % 29.77/29.96 rewrite <- zenon_D_pnotp. % 29.77/29.96 exact zenon_H142. % 29.77/29.96 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 29.77/29.96 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.77/29.96 congruence. % 29.77/29.96 apply zenon_H29. apply refl_equal. % 29.77/29.96 apply zenon_Hff. apply sym_equal. exact zenon_Hfe. % 29.77/29.96 apply zenon_H29. apply refl_equal. % 29.77/29.96 apply zenon_H29. apply refl_equal. % 29.77/29.96 (* end of lemma zenon_L350_ *) % 29.77/29.96 assert (zenon_L351_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.77/29.96 do 0 intro. intros zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H20e zenon_Hfe zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.77/29.96 apply (zenon_L194_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.77/29.96 apply (zenon_L207_); trivial. % 29.77/29.96 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.77/29.96 apply (zenon_L350_); trivial. % 29.77/29.96 apply (zenon_L210_); trivial. % 29.77/29.96 (* end of lemma zenon_L351_ *) % 29.77/29.96 assert (zenon_L352_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H14f zenon_H14e zenon_H112 zenon_H3f zenon_H1e zenon_H200 zenon_H5c zenon_H1d8 zenon_H20e zenon_Hfe zenon_H1ca zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af zenon_Hbd zenon_He1. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.97 apply (zenon_L142_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.97 apply (zenon_L88_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.97 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/29.97 apply (zenon_L193_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/29.97 apply (zenon_L144_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.81/29.97 apply (zenon_L351_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.81/29.97 apply (zenon_L29_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.81/29.97 apply (zenon_L198_); trivial. % 29.81/29.97 apply (zenon_L84_); trivial. % 29.81/29.97 apply (zenon_L221_); trivial. % 29.81/29.97 (* end of lemma zenon_L352_ *) % 29.81/29.97 assert (zenon_L353_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H42 zenon_H112 zenon_Hd0 zenon_H20e zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_H1f zenon_H3c zenon_He9 zenon_H1d5 zenon_H18c zenon_H135 zenon_H20d zenon_H6b zenon_H14f zenon_H14e zenon_H3f zenon_H200 zenon_H5c zenon_H1d8 zenon_Hbd zenon_He1 zenon_H8d zenon_H16a zenon_H108 zenon_H1fd zenon_H1dc zenon_H2d zenon_H15a zenon_H16f zenon_Had zenon_Hb8 zenon_Hcd zenon_Hde zenon_H125 zenon_H27 zenon_He7 zenon_H84 zenon_Hd9 zenon_H83 zenon_H16b zenon_H218 zenon_H14b zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/29.97 apply (zenon_L4_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/29.97 apply (zenon_L247_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/29.97 apply (zenon_L352_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/29.97 apply (zenon_L224_); trivial. % 29.81/29.97 apply (zenon_L228_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/29.97 apply (zenon_L155_); trivial. % 29.81/29.97 exact (zenon_H18e zenon_H40). % 29.81/29.97 (* end of lemma zenon_L353_ *) % 29.81/29.97 assert (zenon_L354_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H83 zenon_Hd9 zenon_H10e zenon_H84 zenon_H74 zenon_H8a zenon_He7. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 29.81/29.97 apply (zenon_L242_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 29.81/29.97 exact (zenon_H84 zenon_H88). % 29.81/29.97 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 29.81/29.97 exact (zenon_H74 zenon_H73). % 29.81/29.97 apply (zenon_L199_); trivial. % 29.81/29.97 (* end of lemma zenon_L354_ *) % 29.81/29.97 assert (zenon_L355_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 29.81/29.97 do 0 intro. intros zenon_Hb8 zenon_He2 zenon_He1 zenon_H100 zenon_H37 zenon_H9c zenon_H2d zenon_H112 zenon_H6f. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 29.81/29.97 apply (zenon_L50_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 29.81/29.97 apply (zenon_L150_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 29.81/29.97 apply (zenon_L304_); trivial. % 29.81/29.97 apply (zenon_L152_); trivial. % 29.81/29.97 (* end of lemma zenon_L355_ *) % 29.81/29.97 assert (zenon_L356_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 29.81/29.97 do 0 intro. intros zenon_Hf9 zenon_H6f zenon_H112 zenon_H2d zenon_H9c zenon_H37 zenon_H100 zenon_He1 zenon_Hb8 zenon_H55 zenon_H222 zenon_Hda zenon_H10d zenon_H231. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.81/29.97 apply (zenon_L355_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.81/29.97 apply (zenon_L264_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.81/29.97 apply (zenon_L64_); trivial. % 29.81/29.97 exact (zenon_H231 zenon_Hf4). % 29.81/29.97 (* end of lemma zenon_L356_ *) % 29.81/29.97 assert (zenon_L357_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H14b zenon_He7 zenon_H8a zenon_H74 zenon_H84 zenon_Hd9 zenon_H83 zenon_H18e zenon_H1d5 zenon_H19e zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_Hd0 zenon_H108 zenon_H1e zenon_H42 zenon_H60 zenon_H1bd zenon_Hf9 zenon_H6f zenon_H112 zenon_H2d zenon_H37 zenon_H100 zenon_He1 zenon_Hb8 zenon_H55 zenon_H222 zenon_Hda zenon_H10d zenon_H231. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/29.97 apply (zenon_L354_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/29.97 apply (zenon_L309_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/29.97 apply (zenon_L165_); trivial. % 29.81/29.97 apply (zenon_L356_); trivial. % 29.81/29.97 (* end of lemma zenon_L357_ *) % 29.81/29.97 assert (zenon_L358_ : ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H1af zenon_Hf5 zenon_H15e zenon_H20e. % 29.81/29.97 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.81/29.97 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 29.81/29.97 intro zenon_D_pnotp. % 29.81/29.97 apply zenon_H20e. % 29.81/29.97 rewrite <- zenon_D_pnotp. % 29.81/29.97 exact zenon_H28. % 29.81/29.97 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.81/29.97 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 29.81/29.97 congruence. % 29.81/29.97 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 29.81/29.97 intro zenon_D_pnotp. % 29.81/29.97 apply zenon_H20f. % 29.81/29.97 rewrite <- zenon_D_pnotp. % 29.81/29.97 exact zenon_H1af. % 29.81/29.97 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 29.81/29.97 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 29.81/29.97 congruence. % 29.81/29.97 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.81/29.97 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e2)))). % 29.81/29.97 intro zenon_D_pnotp. % 29.81/29.97 apply zenon_H1b0. % 29.81/29.97 rewrite <- zenon_D_pnotp. % 29.81/29.97 exact zenon_H28. % 29.81/29.97 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.81/29.97 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 29.81/29.97 congruence. % 29.81/29.97 apply (zenon_L143_); trivial. % 29.81/29.97 apply zenon_H29. apply refl_equal. % 29.81/29.97 apply zenon_H29. apply refl_equal. % 29.81/29.97 apply zenon_H1fb. apply sym_equal. exact zenon_H15e. % 29.81/29.97 apply zenon_H29. apply refl_equal. % 29.81/29.97 apply zenon_H29. apply refl_equal. % 29.81/29.97 (* end of lemma zenon_L358_ *) % 29.81/29.97 assert (zenon_L359_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H9d zenon_H222 zenon_Hd0 zenon_H1af zenon_H15e zenon_H20e. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.97 apply (zenon_L49_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.97 apply (zenon_L264_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.97 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.97 apply (zenon_L358_); trivial. % 29.81/29.97 (* end of lemma zenon_L359_ *) % 29.81/29.97 assert (zenon_L360_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.81/29.97 do 0 intro. intros zenon_H218 zenon_H18e zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hdc zenon_Hd1 zenon_H19e zenon_H20d zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H159 zenon_H101 zenon_H173 zenon_H3c zenon_H1f zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H2d zenon_He4 zenon_H225 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H18c zenon_H108 zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_H100 zenon_Hb8 zenon_Hc8 zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H1e zenon_H3f zenon_H112 zenon_H8a zenon_H74 zenon_H84 zenon_H83 zenon_Hda zenon_H20e zenon_H1af zenon_Hd0 zenon_H222 zenon_H9d zenon_Hde zenon_Hdf zenon_H135 zenon_H16a zenon_H16b. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/29.97 apply (zenon_L34_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.97 apply (zenon_L142_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.97 apply (zenon_L357_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.97 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.97 apply (zenon_L341_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/29.97 apply (zenon_L359_); trivial. % 29.81/29.97 apply (zenon_L101_); trivial. % 29.81/29.97 (* end of lemma zenon_L360_ *) % 29.81/29.97 assert (zenon_L361_ : ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.81/29.97 do 0 intro. intros zenon_Hfe zenon_H218 zenon_H18e zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hdc zenon_Hd1 zenon_H19e zenon_H20d zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H159 zenon_H101 zenon_H173 zenon_H3c zenon_H1f zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H2d zenon_He4 zenon_H225 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H18c zenon_H108 zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_H100 zenon_Hb8 zenon_Hc8 zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H1e zenon_H3f zenon_H112 zenon_H8a zenon_H74 zenon_H84 zenon_H83 zenon_Hda zenon_H20e zenon_H1af zenon_Hd0 zenon_H222 zenon_Hde zenon_Hdf zenon_H135 zenon_H16a zenon_H16b. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/29.97 apply (zenon_L300_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/29.97 apply (zenon_L154_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/29.97 apply (zenon_L309_); trivial. % 29.81/29.97 apply (zenon_L360_); trivial. % 29.81/29.97 (* end of lemma zenon_L361_ *) % 29.81/29.97 assert (zenon_L362_ : ((op (e1) (e1)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H37 zenon_H16b zenon_H16a zenon_H135 zenon_Hdf zenon_Hde zenon_H222 zenon_H20e zenon_Hc8 zenon_H100 zenon_Had zenon_Hee zenon_H20 zenon_H23b zenon_H8d zenon_Hb5 zenon_H108 zenon_H18c zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_H225 zenon_He4 zenon_H200 zenon_H1d8 zenon_H156 zenon_H125 zenon_H231 zenon_Hf9 zenon_H1fd zenon_H15a zenon_H16f zenon_H42 zenon_H1f zenon_H3c zenon_H173 zenon_H101 zenon_H159 zenon_H174 zenon_H5c zenon_H14b zenon_H20d zenon_H19e zenon_Hd1 zenon_Hdc zenon_Hfc zenon_H35 zenon_H102 zenon_H218 zenon_Hfe zenon_Hcd zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1af zenon_H2d zenon_H1dc zenon_H18e zenon_He7 zenon_Hb8 zenon_H74 zenon_H84 zenon_H11e zenon_Hd9 zenon_H1a5 zenon_H19a zenon_H10d zenon_H27 zenon_H83 zenon_H112 zenon_H3f zenon_H1e zenon_H8a zenon_Hbd zenon_He1. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.97 apply (zenon_L49_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.97 apply (zenon_L217_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.97 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.97 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.81/29.97 apply (zenon_L361_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.81/29.97 apply (zenon_L159_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.81/29.97 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/29.97 apply (zenon_L193_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/29.97 apply (zenon_L144_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.81/29.97 apply (zenon_L25_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.81/29.97 apply (zenon_L29_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.81/29.97 apply (zenon_L198_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H10e | zenon_intro zenon_H11f ]. % 29.81/29.97 apply (zenon_L242_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H26 | zenon_intro zenon_H120 ]. % 29.81/29.97 apply (zenon_L136_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hda | zenon_intro zenon_H117 ]. % 29.81/29.97 apply (zenon_L64_); trivial. % 29.81/29.97 apply (zenon_L160_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 29.81/29.97 exact (zenon_H84 zenon_H88). % 29.81/29.97 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 29.81/29.97 exact (zenon_H74 zenon_H73). % 29.81/29.97 apply (zenon_L201_); trivial. % 29.81/29.97 apply (zenon_L221_); trivial. % 29.81/29.97 (* end of lemma zenon_L362_ *) % 29.81/29.97 assert (zenon_L363_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H3c zenon_He9 zenon_Hd0 zenon_H1af zenon_H15e zenon_H20e. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.97 apply (zenon_L49_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.97 apply (zenon_L88_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.97 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.97 apply (zenon_L358_); trivial. % 29.81/29.97 (* end of lemma zenon_L363_ *) % 29.81/29.97 assert (zenon_L364_ : ((op (e1) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 29.81/29.97 do 0 intro. intros zenon_Hc3 zenon_H37 zenon_H2d. % 29.81/29.97 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.81/29.97 cut (((e3) = (e3)) = ((e0) = (e3))). % 29.81/29.97 intro zenon_D_pnotp. % 29.81/29.97 apply zenon_H2d. % 29.81/29.97 rewrite <- zenon_D_pnotp. % 29.81/29.97 exact zenon_H2e. % 29.81/29.97 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.81/29.97 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 29.81/29.97 congruence. % 29.81/29.97 cut (((op (e1) (e1)) = (e0)) = ((e3) = (e0))). % 29.81/29.97 intro zenon_D_pnotp. % 29.81/29.97 apply zenon_H30. % 29.81/29.97 rewrite <- zenon_D_pnotp. % 29.81/29.97 exact zenon_Hc3. % 29.81/29.97 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.81/29.97 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 29.81/29.97 congruence. % 29.81/29.97 exact (zenon_H103 zenon_H37). % 29.81/29.97 apply zenon_H1d. apply refl_equal. % 29.81/29.97 apply zenon_H2f. apply refl_equal. % 29.81/29.97 apply zenon_H2f. apply refl_equal. % 29.81/29.97 (* end of lemma zenon_L364_ *) % 29.81/29.97 assert (zenon_L365_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H8a zenon_He1 zenon_H1c7 zenon_H55 zenon_H60 zenon_H1af zenon_H16c zenon_H156. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/29.97 apply (zenon_L174_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/29.97 apply (zenon_L126_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/29.97 apply (zenon_L216_); trivial. % 29.81/29.97 apply (zenon_L290_); trivial. % 29.81/29.97 (* end of lemma zenon_L365_ *) % 29.81/29.97 assert (zenon_L366_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H16f zenon_Had zenon_H2d zenon_Hc3 zenon_H6f zenon_H19a zenon_H1d5 zenon_H1d8 zenon_H8a zenon_He1 zenon_H1c7 zenon_H55 zenon_H60 zenon_H1af zenon_H156. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/29.97 apply (zenon_L34_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/29.97 apply (zenon_L364_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/29.97 apply (zenon_L235_); trivial. % 29.81/29.97 apply (zenon_L365_); trivial. % 29.81/29.97 (* end of lemma zenon_L366_ *) % 29.81/29.97 assert (zenon_L367_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H1d5 zenon_H6b zenon_Hd6 zenon_Hf5 zenon_H60 zenon_H1c7 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H1af zenon_H16c zenon_H156. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/29.97 apply (zenon_L193_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/29.97 apply (zenon_L144_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/29.97 apply (zenon_L348_); trivial. % 29.81/29.97 apply (zenon_L290_); trivial. % 29.81/29.97 (* end of lemma zenon_L367_ *) % 29.81/29.97 assert (zenon_L368_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_He1 zenon_H8a zenon_H1d8 zenon_H19a zenon_H6f zenon_H2d zenon_Had zenon_H16f zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H60 zenon_H1c7 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H1af zenon_H16c zenon_H156. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.97 apply (zenon_L49_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.97 apply (zenon_L366_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.97 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.97 apply (zenon_L367_); trivial. % 29.81/29.97 (* end of lemma zenon_L368_ *) % 29.81/29.97 assert (zenon_L369_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_He1 zenon_H8a zenon_H1d8 zenon_H19a zenon_H6f zenon_H2d zenon_Had zenon_H16f zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H60 zenon_H1c7 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H1af zenon_H156. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/29.97 apply (zenon_L34_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/29.97 apply (zenon_L364_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/29.97 apply (zenon_L235_); trivial. % 29.81/29.97 apply (zenon_L368_); trivial. % 29.81/29.97 (* end of lemma zenon_L369_ *) % 29.81/29.97 assert (zenon_L370_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 29.81/29.97 do 0 intro. intros zenon_Hbd zenon_H8a zenon_H2d zenon_H1e zenon_H3f zenon_H1b9 zenon_H112 zenon_H14e zenon_H14f. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.81/29.97 apply (zenon_L25_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.81/29.97 apply (zenon_L29_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.81/29.97 apply (zenon_L198_); trivial. % 29.81/29.97 apply (zenon_L84_); trivial. % 29.81/29.97 (* end of lemma zenon_L370_ *) % 29.81/29.97 assert (zenon_L371_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_Hd6 zenon_H1af zenon_H14f zenon_H14e zenon_H112 zenon_H3f zenon_H1e zenon_H2d zenon_H8a zenon_Hbd zenon_Hf5 zenon_He1. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/29.97 apply (zenon_L174_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/29.97 apply (zenon_L144_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/29.97 apply (zenon_L370_); trivial. % 29.81/29.97 apply (zenon_L221_); trivial. % 29.81/29.97 (* end of lemma zenon_L371_ *) % 29.81/29.97 assert (zenon_L372_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H1d8 zenon_Hd6 zenon_H1af zenon_H14f zenon_H14e zenon_H112 zenon_H3f zenon_H1e zenon_H2d zenon_H8a zenon_Hbd zenon_He1. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.97 apply (zenon_L49_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.97 apply (zenon_L88_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.97 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.97 apply (zenon_L371_); trivial. % 29.81/29.97 (* end of lemma zenon_L372_ *) % 29.81/29.97 assert (zenon_L373_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H172 zenon_H17d zenon_H92 zenon_H16b zenon_H16a zenon_H19a zenon_H6f zenon_H222 zenon_H20e zenon_Hc8 zenon_H100 zenon_Had zenon_Hee zenon_H20 zenon_H23b zenon_H8d zenon_Hb5 zenon_H108 zenon_H18c zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H225 zenon_He4 zenon_H200 zenon_H156 zenon_H125 zenon_H231 zenon_Hf9 zenon_H1fd zenon_H15a zenon_H16f zenon_H42 zenon_H1f zenon_H173 zenon_H101 zenon_H159 zenon_H174 zenon_H5c zenon_H14b zenon_H20d zenon_H19e zenon_Hd1 zenon_Hdc zenon_Hfc zenon_H35 zenon_H102 zenon_H218 zenon_Hcd zenon_H6b zenon_H1dc zenon_H18e zenon_He7 zenon_Hb8 zenon_H74 zenon_H84 zenon_H11e zenon_Hd9 zenon_H1a5 zenon_H10d zenon_H27 zenon_H83 zenon_H135 zenon_Hdf zenon_Hde zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H1d8 zenon_Hd6 zenon_H1af zenon_H14e zenon_H112 zenon_H3f zenon_H1e zenon_H2d zenon_H8a zenon_Hbd zenon_He1. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/29.97 apply (zenon_L34_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/29.97 apply (zenon_L271_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/29.97 apply (zenon_L362_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/29.97 apply (zenon_L176_); trivial. % 29.81/29.97 apply (zenon_L228_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/29.97 apply (zenon_L363_); trivial. % 29.81/29.97 apply (zenon_L101_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/29.97 apply (zenon_L369_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/29.97 apply (zenon_L34_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/29.97 apply (zenon_L362_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/29.97 apply (zenon_L235_); trivial. % 29.81/29.97 apply (zenon_L101_); trivial. % 29.81/29.97 apply (zenon_L372_); trivial. % 29.81/29.97 (* end of lemma zenon_L373_ *) % 29.81/29.97 assert (zenon_L374_ : (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 29.81/29.97 do 0 intro. intros zenon_He1 zenon_Hbd zenon_H2d zenon_H3f zenon_H112 zenon_H14e zenon_Hd6 zenon_H1d5 zenon_Hde zenon_H83 zenon_H27 zenon_H10d zenon_H1a5 zenon_Hd9 zenon_H11e zenon_H84 zenon_H74 zenon_Hb8 zenon_He7 zenon_H18e zenon_H1dc zenon_H6b zenon_Hcd zenon_H218 zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H14b zenon_H5c zenon_H174 zenon_H159 zenon_H101 zenon_H173 zenon_H1f zenon_H42 zenon_H16f zenon_H15a zenon_H1fd zenon_Hf9 zenon_H231 zenon_H125 zenon_H156 zenon_H200 zenon_He4 zenon_H225 zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H5e zenon_H6c zenon_H1ca zenon_H108 zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_H100 zenon_Hc8 zenon_H20e zenon_H222 zenon_H6f zenon_H19a zenon_H16a zenon_H16b zenon_H92 zenon_H17d zenon_H172 zenon_H1e zenon_H60 zenon_H20d zenon_Hd0 zenon_He9 zenon_H3c zenon_Hdc zenon_H18c zenon_H135 zenon_H1d8 zenon_H1af zenon_H8a. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/29.97 apply (zenon_L373_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/29.97 apply (zenon_L207_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/29.97 apply (zenon_L224_); trivial. % 29.81/29.97 apply (zenon_L186_); trivial. % 29.81/29.97 (* end of lemma zenon_L374_ *) % 29.81/29.97 assert (zenon_L375_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 29.81/29.97 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_H1e zenon_H3c zenon_H19e zenon_H19a zenon_Hfc zenon_H155 zenon_H112 zenon_H102 zenon_H1bd zenon_H1af zenon_H3d. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/29.97 apply (zenon_L49_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/29.97 apply (zenon_L207_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/29.97 apply (zenon_L280_); trivial. % 29.81/29.97 apply (zenon_L209_); trivial. % 29.81/29.97 (* end of lemma zenon_L375_ *) % 29.81/29.97 assert (zenon_L376_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/29.97 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hcd zenon_H101 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_Hd0 zenon_H6f zenon_H15a zenon_H16f zenon_H159 zenon_H42 zenon_H1c7 zenon_H222 zenon_H5e zenon_H1f zenon_H1ca zenon_H60 zenon_H156 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_He1 zenon_H135 zenon_H2d zenon_Hd6 zenon_H6c zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/29.97 apply (zenon_L142_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/29.97 apply (zenon_L322_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/29.97 apply (zenon_L159_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/29.97 apply (zenon_L329_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/29.97 apply (zenon_L93_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/29.97 apply (zenon_L282_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/29.97 apply (zenon_L4_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/29.97 apply (zenon_L333_); trivial. % 29.81/29.97 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/29.97 apply (zenon_L375_); trivial. % 29.81/29.97 exact (zenon_H18e zenon_H40). % 29.81/29.97 (* end of lemma zenon_L376_ *) % 29.81/29.97 assert (zenon_L377_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/29.98 do 0 intro. intros zenon_H173 zenon_H18c zenon_He1 zenon_Hcd zenon_H42 zenon_H2d zenon_H6f zenon_H117 zenon_H10d zenon_H100 zenon_H6e zenon_Had zenon_Hb8 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/29.98 apply (zenon_L142_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/29.98 apply (zenon_L322_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/29.98 apply (zenon_L159_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/29.98 apply (zenon_L4_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/29.98 apply (zenon_L153_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/29.98 apply (zenon_L375_); trivial. % 29.81/29.98 exact (zenon_H18e zenon_H40). % 29.81/29.98 (* end of lemma zenon_L377_ *) % 29.81/29.98 assert (zenon_L378_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 29.81/29.98 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H3c zenon_He9 zenon_Hd0 zenon_H1af zenon_H117 zenon_H27. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.98 apply (zenon_L49_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.98 apply (zenon_L88_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.98 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.98 apply (zenon_L183_); trivial. % 29.81/29.98 (* end of lemma zenon_L378_ *) % 29.81/29.98 assert (zenon_L379_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e0) (e0)))) -> ((op (e1) (e1)) = (e0)) -> False). % 29.81/29.98 do 0 intro. intros zenon_H23e zenon_Hc3. % 29.81/29.98 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 29.81/29.98 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 29.81/29.98 congruence. % 29.81/29.98 exact (zenon_H19f zenon_Hc3). % 29.81/29.98 exact (zenon_H19f zenon_Hc3). % 29.81/29.98 (* end of lemma zenon_L379_ *) % 29.81/29.98 assert (zenon_L380_ : (~((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))) -> ((op (e1) (e1)) = (e0)) -> False). % 29.81/29.98 do 0 intro. intros zenon_H23f zenon_Hc3. % 29.81/29.98 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.81/29.98 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 29.81/29.98 congruence. % 29.81/29.98 exact (zenon_H19f zenon_Hc3). % 29.81/29.98 apply zenon_H22. apply refl_equal. % 29.81/29.98 (* end of lemma zenon_L380_ *) % 29.81/29.98 assert (zenon_L381_ : ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((e2) = (op (op (e1) (e1)) (e1)))) -> False). % 29.81/29.98 do 0 intro. intros zenon_He9 zenon_Hc3 zenon_H236. % 29.81/29.98 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 29.81/29.98 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e2) = (op (op (e1) (e1)) (e1)))). % 29.81/29.98 intro zenon_D_pnotp. % 29.81/29.98 apply zenon_H236. % 29.81/29.98 rewrite <- zenon_D_pnotp. % 29.81/29.98 exact zenon_H13e. % 29.81/29.98 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 29.81/29.98 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H237]. % 29.81/29.98 congruence. % 29.81/29.98 cut (((op (e0) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 29.81/29.98 intro zenon_D_pnotp. % 29.81/29.98 apply zenon_H237. % 29.81/29.98 rewrite <- zenon_D_pnotp. % 29.81/29.98 exact zenon_He9. % 29.81/29.98 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.81/29.98 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 29.81/29.98 congruence. % 29.81/29.98 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 29.81/29.98 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 29.81/29.98 intro zenon_D_pnotp. % 29.81/29.98 apply zenon_H240. % 29.81/29.98 rewrite <- zenon_D_pnotp. % 29.81/29.98 exact zenon_H13e. % 29.81/29.98 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 29.81/29.98 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23f]. % 29.81/29.98 congruence. % 29.81/29.98 apply (zenon_L380_); trivial. % 29.81/29.98 apply zenon_H13f. apply refl_equal. % 29.81/29.98 apply zenon_H13f. apply refl_equal. % 29.81/29.98 apply zenon_H57. apply refl_equal. % 29.81/29.98 apply zenon_H13f. apply refl_equal. % 29.81/29.98 apply zenon_H13f. apply refl_equal. % 29.81/29.98 (* end of lemma zenon_L381_ *) % 29.81/29.98 assert (zenon_L382_ : ((op (e0) (e0)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 29.81/29.98 do 0 intro. intros zenon_H89 zenon_He9 zenon_Hc3. % 29.81/29.98 apply (zenon_notand_s _ _ ax17); [ zenon_intro zenon_H242 | zenon_intro zenon_H241 ]. % 29.81/29.98 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 29.81/29.98 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e3) = (op (op (e1) (e1)) (op (e1) (e1))))). % 29.81/29.98 intro zenon_D_pnotp. % 29.81/29.98 apply zenon_H242. % 29.81/29.98 rewrite <- zenon_D_pnotp. % 29.81/29.98 exact zenon_H145. % 29.81/29.98 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 29.81/29.98 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 29.81/29.98 congruence. % 29.81/29.98 cut (((op (e0) (e0)) = (e3)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e3))). % 29.81/29.98 intro zenon_D_pnotp. % 29.81/29.98 apply zenon_H243. % 29.81/29.98 rewrite <- zenon_D_pnotp. % 29.81/29.98 exact zenon_H89. % 29.81/29.98 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.81/29.98 cut (((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H244]. % 29.81/29.98 congruence. % 29.81/29.98 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 29.81/29.98 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 29.81/29.98 intro zenon_D_pnotp. % 29.81/29.98 apply zenon_H244. % 29.81/29.98 rewrite <- zenon_D_pnotp. % 29.81/29.98 exact zenon_H145. % 29.81/29.98 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 29.81/29.98 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 29.81/29.98 congruence. % 29.81/29.98 apply (zenon_L379_); trivial. % 29.81/29.98 apply zenon_H146. apply refl_equal. % 29.81/29.98 apply zenon_H146. apply refl_equal. % 29.81/29.98 apply zenon_H2f. apply refl_equal. % 29.81/29.98 apply zenon_H146. apply refl_equal. % 29.81/29.98 apply zenon_H146. apply refl_equal. % 29.81/29.98 apply (zenon_notand_s _ _ zenon_H241); [ zenon_intro zenon_H236 | zenon_intro zenon_H245 ]. % 29.81/29.98 apply (zenon_L381_); trivial. % 29.81/29.98 apply zenon_H245. apply sym_equal. exact zenon_Hc3. % 29.81/29.98 (* end of lemma zenon_L382_ *) % 29.81/29.98 assert (zenon_L383_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.81/29.98 do 0 intro. intros zenon_H200 zenon_H156 zenon_H16c zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_H112 zenon_Hb8 zenon_He7 zenon_H89 zenon_H18e zenon_H1dc zenon_H2d zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_Hde zenon_H135 zenon_H20e zenon_Hfe zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/29.98 apply (zenon_L326_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/29.98 apply (zenon_L207_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/29.98 apply (zenon_L350_); trivial. % 29.81/29.98 apply (zenon_L210_); trivial. % 29.81/29.98 (* end of lemma zenon_L383_ *) % 29.81/29.98 assert (zenon_L384_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.81/29.98 do 0 intro. intros zenon_H16f zenon_H15a zenon_He1 zenon_Hdf zenon_H208 zenon_H1f zenon_H60 zenon_H19e zenon_Hcd zenon_H1d2 zenon_H1c7 zenon_H108 zenon_H6f zenon_H19a zenon_H200 zenon_H156 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_H112 zenon_Hb8 zenon_He7 zenon_H89 zenon_H18e zenon_H1dc zenon_H2d zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_Hde zenon_H135 zenon_H20e zenon_Hfe zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/29.98 apply (zenon_L241_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/29.98 apply (zenon_L222_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/29.98 apply (zenon_L235_); trivial. % 29.81/29.98 apply (zenon_L383_); trivial. % 29.81/29.98 (* end of lemma zenon_L384_ *) % 29.81/29.98 assert (zenon_L385_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 29.81/29.98 do 0 intro. intros zenon_H8d zenon_Hd9 zenon_H18e zenon_H135 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H117 zenon_H112 zenon_H1e zenon_H2d zenon_H42 zenon_H6f zenon_H6c zenon_He1 zenon_He2. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/29.98 apply (zenon_L149_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/29.98 apply (zenon_L4_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/29.98 apply (zenon_L153_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/29.98 apply (zenon_L308_); trivial. % 29.81/29.98 exact (zenon_H18e zenon_H40). % 29.81/29.98 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/29.98 apply (zenon_L157_); trivial. % 29.81/29.98 apply (zenon_L50_); trivial. % 29.81/29.98 (* end of lemma zenon_L385_ *) % 29.81/29.98 assert (zenon_L386_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 29.81/29.98 do 0 intro. intros zenon_H90 zenon_He2 zenon_Hcd. % 29.81/29.98 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 29.81/29.98 cut (((e2) = (e2)) = ((e1) = (e2))). % 29.81/29.98 intro zenon_D_pnotp. % 29.81/29.98 apply zenon_Hcd. % 29.81/29.98 rewrite <- zenon_D_pnotp. % 29.81/29.98 exact zenon_Hce. % 29.81/29.98 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.81/29.98 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 29.81/29.98 congruence. % 29.81/29.98 cut (((op (e3) (e0)) = (e1)) = ((e2) = (e1))). % 29.81/29.98 intro zenon_D_pnotp. % 29.81/29.98 apply zenon_Hcf. % 29.81/29.98 rewrite <- zenon_D_pnotp. % 29.81/29.98 exact zenon_H90. % 29.81/29.98 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.81/29.98 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 29.81/29.98 congruence. % 29.81/29.98 exact (zenon_He3 zenon_He2). % 29.81/29.98 apply zenon_H22. apply refl_equal. % 29.81/29.98 apply zenon_H57. apply refl_equal. % 29.81/29.98 apply zenon_H57. apply refl_equal. % 29.81/29.98 (* end of lemma zenon_L386_ *) % 29.81/29.98 assert (zenon_L387_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 29.81/29.98 do 0 intro. intros zenon_H23b zenon_Hcd zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_He2 zenon_H89. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 29.81/29.98 apply (zenon_L386_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 29.81/29.98 apply (zenon_L336_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 29.81/29.98 apply (zenon_L337_); trivial. % 29.81/29.98 apply (zenon_L252_); trivial. % 29.81/29.98 (* end of lemma zenon_L387_ *) % 29.81/29.98 assert (zenon_L388_ : (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 29.81/29.98 do 0 intro. intros zenon_H2d zenon_H173 zenon_H1dc zenon_H6b zenon_Hd1 zenon_H18c zenon_H20d zenon_H14b zenon_Hda zenon_Hde zenon_H200 zenon_H19a zenon_H101 zenon_H3c zenon_H159 zenon_Hcd zenon_H6f zenon_H208 zenon_H42 zenon_H1e zenon_H156 zenon_H222 zenon_H1d5 zenon_H19e zenon_H16b zenon_H218 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e zenon_Hf9 zenon_He9 zenon_H3f zenon_H10d zenon_H231 zenon_Hb8 zenon_H112 zenon_H5c zenon_H27 zenon_H174 zenon_H102 zenon_H35 zenon_Hfc zenon_H20e zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_H125 zenon_He4 zenon_H225 zenon_Hdc zenon_Hb5 zenon_Hbd zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_Hfe zenon_H37 zenon_Hd0 zenon_H108. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.98 apply (zenon_L142_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.98 apply (zenon_L217_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.98 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.98 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/29.98 apply (zenon_L193_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/29.98 apply (zenon_L144_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/29.98 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.81/29.98 apply (zenon_L299_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.81/29.98 apply (zenon_L29_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.81/29.98 apply (zenon_L198_); trivial. % 29.81/29.98 apply (zenon_L316_); trivial. % 29.81/29.98 apply (zenon_L172_); trivial. % 29.81/29.98 (* end of lemma zenon_L388_ *) % 29.81/29.98 assert (zenon_L389_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 29.81/29.98 do 0 intro. intros zenon_H108 zenon_H37 zenon_Hfe zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_Hbd zenon_Hb5 zenon_Hdc zenon_H225 zenon_He4 zenon_H125 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H1f zenon_H20e zenon_Hfc zenon_H35 zenon_H102 zenon_H174 zenon_H27 zenon_H5c zenon_H231 zenon_H10d zenon_H3f zenon_He9 zenon_Hf9 zenon_H135 zenon_He2 zenon_H1d8 zenon_H218 zenon_H16b zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H1e zenon_H42 zenon_H208 zenon_H159 zenon_H3c zenon_H101 zenon_H200 zenon_Hde zenon_H14b zenon_H20d zenon_H18c zenon_Hd1 zenon_H6b zenon_H1dc zenon_H173 zenon_H2d zenon_Hcd zenon_H19a zenon_Hd0 zenon_Hb8 zenon_Had zenon_H6e zenon_H18e zenon_He1 zenon_H112 zenon_H6f. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.81/29.98 apply (zenon_L388_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.81/29.98 apply (zenon_L159_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.81/29.98 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.98 apply (zenon_L233_); trivial. % 29.81/29.98 (* end of lemma zenon_L389_ *) % 29.81/29.98 assert (zenon_L390_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/29.98 do 0 intro. intros zenon_H102 zenon_Hfc zenon_Hd1 zenon_H17d zenon_H84 zenon_H83 zenon_H16a zenon_H8d zenon_He7 zenon_H20 zenon_H69 zenon_H92 zenon_H6e zenon_Had zenon_H173 zenon_H1dc zenon_H6b zenon_H14b zenon_Hde zenon_H200 zenon_H101 zenon_H159 zenon_H208 zenon_H222 zenon_Hf9 zenon_H3f zenon_H10d zenon_H231 zenon_H5c zenon_H27 zenon_H174 zenon_H20e zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_H125 zenon_He4 zenon_H225 zenon_Hb5 zenon_Hbd zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H5e zenon_H6c zenon_H1ca zenon_H108 zenon_H20d zenon_H18c zenon_Hb8 zenon_H100 zenon_H112 zenon_H6f zenon_H35 zenon_Hcd zenon_H19a zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_He9 zenon_H3c zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/29.98 apply (zenon_L4_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/29.98 apply (zenon_L271_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/29.98 apply (zenon_L389_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/29.98 apply (zenon_L224_); trivial. % 29.81/29.98 apply (zenon_L355_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/29.98 apply (zenon_L155_); trivial. % 29.81/29.98 exact (zenon_H18e zenon_H40). % 29.81/29.98 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/29.98 apply (zenon_L95_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/29.98 apply (zenon_L159_); trivial. % 29.81/29.98 apply (zenon_L312_); trivial. % 29.81/29.98 (* end of lemma zenon_L390_ *) % 29.81/29.98 assert (zenon_L391_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/29.98 do 0 intro. intros zenon_Hbd zenon_Hb5 zenon_H225 zenon_He4 zenon_H125 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H1f zenon_H20e zenon_Hfc zenon_H35 zenon_H102 zenon_H174 zenon_H27 zenon_H5c zenon_H231 zenon_H10d zenon_H3f zenon_He9 zenon_Hf9 zenon_H200 zenon_Hde zenon_H14b zenon_H20d zenon_H18c zenon_Hd1 zenon_H6b zenon_H1dc zenon_H173 zenon_Hb8 zenon_Had zenon_H6e zenon_H112 zenon_H19a zenon_H101 zenon_H3c zenon_H159 zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H5e zenon_H6c zenon_H1ca zenon_Hfe zenon_H108 zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_H222 zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/29.98 apply (zenon_L4_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/29.98 apply (zenon_L389_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/29.98 apply (zenon_L308_); trivial. % 29.81/29.98 exact (zenon_H18e zenon_H40). % 29.81/29.98 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/29.98 apply (zenon_L311_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/29.98 apply (zenon_L159_); trivial. % 29.81/29.98 apply (zenon_L314_); trivial. % 29.81/29.98 (* end of lemma zenon_L391_ *) % 29.81/29.98 assert (zenon_L392_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 29.81/29.98 do 0 intro. intros zenon_Hbd zenon_Hde zenon_H1e zenon_H3f zenon_H6f zenon_H112 zenon_H2d zenon_H37 zenon_H100 zenon_He1 zenon_He2 zenon_Hb8 zenon_H14e zenon_H14f. % 29.81/29.98 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.81/29.98 apply (zenon_L288_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.81/29.98 apply (zenon_L29_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.81/29.98 apply (zenon_L355_); trivial. % 29.81/29.98 apply (zenon_L84_); trivial. % 29.81/29.98 (* end of lemma zenon_L392_ *) % 29.81/29.98 assert (zenon_L393_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/29.98 do 0 intro. intros zenon_H42 zenon_H14f zenon_H14e zenon_Hb8 zenon_H100 zenon_H2d zenon_H112 zenon_H6f zenon_H3f zenon_H1e zenon_Hde zenon_Hbd zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/29.98 apply (zenon_L4_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/29.98 apply (zenon_L392_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/29.98 apply (zenon_L308_); trivial. % 29.81/29.98 exact (zenon_H18e zenon_H40). % 29.81/29.98 (* end of lemma zenon_L393_ *) % 29.81/29.98 assert (zenon_L394_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/29.98 do 0 intro. intros zenon_H172 zenon_H92 zenon_H20 zenon_He7 zenon_H8d zenon_H16a zenon_H83 zenon_H84 zenon_H17d zenon_H218 zenon_H16b zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H108 zenon_H1ca zenon_H6c zenon_H5e zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H159 zenon_H3c zenon_H101 zenon_H19a zenon_H6e zenon_Had zenon_H173 zenon_H1dc zenon_H6b zenon_Hd1 zenon_H18c zenon_H20d zenon_H14b zenon_H200 zenon_Hf9 zenon_He9 zenon_H10d zenon_H231 zenon_H5c zenon_H27 zenon_H174 zenon_H102 zenon_H35 zenon_Hfc zenon_H20e zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_H125 zenon_He4 zenon_H225 zenon_Hb5 zenon_H42 zenon_H14e zenon_Hb8 zenon_H100 zenon_H2d zenon_H112 zenon_H6f zenon_H3f zenon_H1e zenon_Hde zenon_Hbd zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/29.98 apply (zenon_L390_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/29.98 apply (zenon_L42_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/29.98 apply (zenon_L391_); trivial. % 29.81/29.98 apply (zenon_L393_); trivial. % 29.81/29.98 (* end of lemma zenon_L394_ *) % 29.81/29.98 assert (zenon_L395_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 29.81/29.98 do 0 intro. intros zenon_Hee zenon_H23b zenon_H18e zenon_H135 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_Hbd zenon_Hde zenon_H1e zenon_H3f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H42 zenon_Hb5 zenon_H225 zenon_He4 zenon_H125 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H1f zenon_H20e zenon_Hfc zenon_H35 zenon_H102 zenon_H174 zenon_H27 zenon_H5c zenon_H231 zenon_H10d zenon_He9 zenon_Hf9 zenon_H200 zenon_H14b zenon_H20d zenon_H18c zenon_Hd1 zenon_H6b zenon_H1dc zenon_H173 zenon_Had zenon_H19a zenon_H101 zenon_H3c zenon_H159 zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H5e zenon_H1ca zenon_H108 zenon_H156 zenon_H222 zenon_H1d5 zenon_H19e zenon_H60 zenon_H218 zenon_H17d zenon_H84 zenon_H83 zenon_H16a zenon_H8d zenon_He7 zenon_H20 zenon_H92 zenon_H172 zenon_H6f zenon_H6c zenon_He1 zenon_He2. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/29.98 apply (zenon_L252_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/29.98 apply (zenon_L4_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/29.98 apply (zenon_L385_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/29.98 apply (zenon_L387_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/29.98 apply (zenon_L394_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/29.98 apply (zenon_L157_); trivial. % 29.81/29.98 apply (zenon_L50_); trivial. % 29.81/29.98 (* end of lemma zenon_L395_ *) % 29.81/29.98 assert (zenon_L396_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> False). % 29.81/29.98 do 0 intro. intros zenon_H1a5 zenon_H11e zenon_H74 zenon_Hc8 zenon_Hdf zenon_Hee zenon_H23b zenon_H18e zenon_H135 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_Hbd zenon_Hde zenon_H1e zenon_H3f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H42 zenon_Hb5 zenon_H225 zenon_He4 zenon_H125 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H1f zenon_H20e zenon_Hfc zenon_H35 zenon_H102 zenon_H174 zenon_H27 zenon_H5c zenon_H231 zenon_H10d zenon_He9 zenon_Hf9 zenon_H200 zenon_H14b zenon_H20d zenon_H18c zenon_Hd1 zenon_H6b zenon_H1dc zenon_H173 zenon_Had zenon_H19a zenon_H101 zenon_H3c zenon_H159 zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H5e zenon_H1ca zenon_H108 zenon_H156 zenon_H222 zenon_H1d5 zenon_H19e zenon_H60 zenon_H218 zenon_H17d zenon_H84 zenon_H83 zenon_H16a zenon_H8d zenon_He7 zenon_H20 zenon_H92 zenon_H172 zenon_H6f zenon_H6c zenon_He1. % 29.81/29.98 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/29.98 exact (zenon_H74 zenon_H73). % 29.81/29.98 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/29.98 apply (zenon_L241_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/29.98 apply (zenon_L229_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/29.98 apply (zenon_L363_); trivial. % 29.81/29.98 apply (zenon_L326_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/29.98 apply (zenon_L4_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/29.98 apply (zenon_L378_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/29.98 apply (zenon_L345_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/29.98 apply (zenon_L229_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/29.98 apply (zenon_L235_); trivial. % 29.81/29.98 apply (zenon_L326_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/29.98 apply (zenon_L382_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/29.98 apply (zenon_L384_); trivial. % 29.81/29.98 apply (zenon_L353_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/29.98 apply (zenon_L345_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/29.98 apply (zenon_L42_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/29.98 apply (zenon_L344_); trivial. % 29.81/29.98 apply (zenon_L353_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/29.98 apply (zenon_L157_); trivial. % 29.81/29.98 apply (zenon_L373_); trivial. % 29.81/29.98 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/29.98 apply (zenon_L49_); trivial. % 29.81/29.98 apply (zenon_L395_); trivial. % 29.81/29.98 (* end of lemma zenon_L396_ *) % 29.81/29.98 assert (zenon_L397_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/29.99 do 0 intro. intros zenon_Hc9 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1a5 zenon_H11e zenon_H74 zenon_Hc8 zenon_Hee zenon_H23b zenon_H135 zenon_H1d8 zenon_Hd0 zenon_Hd6 zenon_Hbd zenon_Hde zenon_H3f zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H42 zenon_Hb5 zenon_H225 zenon_He4 zenon_H125 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H1f zenon_H20e zenon_H35 zenon_H174 zenon_H27 zenon_H5c zenon_H231 zenon_H10d zenon_He9 zenon_Hf9 zenon_H200 zenon_H14b zenon_H20d zenon_H18c zenon_Hd1 zenon_H6b zenon_H1dc zenon_H173 zenon_Had zenon_H101 zenon_H159 zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H5e zenon_H1ca zenon_H108 zenon_H156 zenon_H222 zenon_H1d5 zenon_H60 zenon_H218 zenon_H17d zenon_H84 zenon_H83 zenon_H16a zenon_H8d zenon_He7 zenon_H20 zenon_H92 zenon_H172 zenon_H6f zenon_H6c zenon_He1 zenon_H18e. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/29.99 apply (zenon_L4_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/29.99 apply (zenon_L324_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/29.99 apply (zenon_L396_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/29.99 apply (zenon_L207_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/29.99 apply (zenon_L280_); trivial. % 29.81/29.99 apply (zenon_L209_); trivial. % 29.81/29.99 exact (zenon_H18e zenon_H40). % 29.81/29.99 (* end of lemma zenon_L397_ *) % 29.81/29.99 assert (zenon_L398_ : ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/29.99 do 0 intro. intros zenon_H6c zenon_H6f zenon_H172 zenon_H92 zenon_H20 zenon_He7 zenon_H8d zenon_H16a zenon_H83 zenon_H84 zenon_H17d zenon_H108 zenon_H1ca zenon_H5e zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H101 zenon_Had zenon_H173 zenon_H1dc zenon_H6b zenon_Hd1 zenon_H18c zenon_H20d zenon_H14b zenon_Hf9 zenon_H10d zenon_H231 zenon_H5c zenon_H27 zenon_H174 zenon_H35 zenon_H20e zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_H125 zenon_He4 zenon_H225 zenon_Hb5 zenon_H14e zenon_Hb8 zenon_H100 zenon_H3f zenon_Hbd zenon_Hd6 zenon_H1d8 zenon_H23b zenon_Hee zenon_Hc8 zenon_H74 zenon_H11e zenon_H1a5 zenon_H159 zenon_H42 zenon_H2d zenon_H156 zenon_Hd0 zenon_H222 zenon_H1d5 zenon_He1 zenon_H60 zenon_H16b zenon_H218 zenon_H135 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/29.99 apply (zenon_L142_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/29.99 apply (zenon_L322_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/29.99 apply (zenon_L159_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/29.99 apply (zenon_L397_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/29.99 apply (zenon_L93_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/29.99 apply (zenon_L282_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/29.99 apply (zenon_L4_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/29.99 apply (zenon_L283_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/29.99 apply (zenon_L375_); trivial. % 29.81/29.99 exact (zenon_H18e zenon_H40). % 29.81/29.99 (* end of lemma zenon_L398_ *) % 29.81/29.99 assert (zenon_L399_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/29.99 do 0 intro. intros zenon_H1e6 zenon_Hf6 zenon_He9 zenon_H6c zenon_H6f zenon_H172 zenon_H92 zenon_H20 zenon_He7 zenon_H8d zenon_H16a zenon_H83 zenon_H84 zenon_H17d zenon_H108 zenon_H1ca zenon_H5e zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H101 zenon_Had zenon_H173 zenon_H1dc zenon_H6b zenon_Hd1 zenon_H18c zenon_H20d zenon_H14b zenon_Hf9 zenon_H10d zenon_H231 zenon_H5c zenon_H27 zenon_H174 zenon_H35 zenon_H20e zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_H125 zenon_He4 zenon_H225 zenon_Hb5 zenon_H14e zenon_Hb8 zenon_H100 zenon_H3f zenon_Hbd zenon_Hd6 zenon_H1d8 zenon_H23b zenon_Hee zenon_Hc8 zenon_H74 zenon_H11e zenon_H1a5 zenon_H159 zenon_H42 zenon_H2d zenon_H156 zenon_Hd0 zenon_H222 zenon_H1d5 zenon_He1 zenon_H60 zenon_H218 zenon_H135 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/29.99 apply (zenon_L376_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/29.99 apply (zenon_L4_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/29.99 apply (zenon_L149_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/29.99 apply (zenon_L377_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/29.99 apply (zenon_L273_); trivial. % 29.81/29.99 apply (zenon_L189_); trivial. % 29.81/29.99 apply (zenon_L398_); trivial. % 29.81/29.99 (* end of lemma zenon_L399_ *) % 29.81/29.99 assert (zenon_L400_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.81/29.99 do 0 intro. intros zenon_Hc0 zenon_H18c zenon_H1c7 zenon_H222 zenon_H101 zenon_H159 zenon_H20e zenon_H208 zenon_H20 zenon_H69 zenon_H1a5 zenon_H92 zenon_H1b1 zenon_Hcd zenon_H10e zenon_Hde zenon_He4 zenon_H60 zenon_H156 zenon_H173 zenon_H218 zenon_H1af zenon_H83 zenon_Hd9 zenon_H84 zenon_He7 zenon_Hd6 zenon_H6b zenon_H1d5 zenon_H3c zenon_H135 zenon_H16f zenon_H15a zenon_H1bd zenon_H5e zenon_H1e zenon_H1ca zenon_H2d zenon_H1dc zenon_H3f zenon_H1d8 zenon_Hbd zenon_H1fd zenon_Hfc zenon_H108 zenon_H200 zenon_H16a zenon_H42 zenon_H19e zenon_Hd1 zenon_H35 zenon_H102 zenon_H174 zenon_H27 zenon_H5c zenon_H8d zenon_H18e zenon_Had zenon_Hb8 zenon_Hd0 zenon_H19a zenon_H125 zenon_H6f zenon_He1 zenon_H225 zenon_H17d zenon_H112. % 29.81/29.99 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.81/29.99 exact (zenon_H84 zenon_H88). % 29.81/29.99 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.81/29.99 apply (zenon_L271_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.81/29.99 apply (zenon_L136_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.81/29.99 exact (zenon_H84 zenon_H88). % 29.81/29.99 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.81/29.99 apply (zenon_L147_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.81/29.99 apply (zenon_L239_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.81/29.99 apply (zenon_L254_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.81/29.99 apply (zenon_L192_); trivial. % 29.81/29.99 apply (zenon_L106_); trivial. % 29.81/29.99 apply (zenon_L139_); trivial. % 29.81/29.99 (* end of lemma zenon_L400_ *) % 29.81/29.99 assert (zenon_L401_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.99 do 0 intro. intros zenon_H16f zenon_H6f zenon_Had zenon_He1 zenon_H108 zenon_Hfc zenon_Hd9 zenon_H1fd zenon_H19a zenon_Hcd zenon_H10e zenon_H125 zenon_H27 zenon_H20e zenon_H135 zenon_Hde zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1e zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1af zenon_H156. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/29.99 apply (zenon_L234_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/29.99 apply (zenon_L206_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/29.99 apply (zenon_L363_); trivial. % 29.81/29.99 apply (zenon_L326_); trivial. % 29.81/29.99 (* end of lemma zenon_L401_ *) % 29.81/29.99 assert (zenon_L402_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.99 do 0 intro. intros zenon_H1d5 zenon_H6b zenon_Hd6 zenon_Hf5 zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1e zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1af zenon_H16b zenon_H218. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/29.99 apply (zenon_L193_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/29.99 apply (zenon_L144_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/29.99 apply (zenon_L202_); trivial. % 29.81/29.99 apply (zenon_L245_); trivial. % 29.81/29.99 (* end of lemma zenon_L402_ *) % 29.81/29.99 assert (zenon_L403_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.99 do 0 intro. intros zenon_H8d zenon_Hbd zenon_Hdf zenon_H1d8 zenon_H1e zenon_H3f zenon_H1dc zenon_H2d zenon_H112 zenon_He1 zenon_H18e zenon_Had zenon_Hb8 zenon_H19a zenon_Hcd zenon_Hde zenon_H125 zenon_H6f zenon_H135 zenon_H27 zenon_H5c zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_He7 zenon_H6c zenon_H84 zenon_H10e zenon_Hd9 zenon_H83 zenon_H1af zenon_H16b zenon_H218. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.99 apply (zenon_L191_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.99 apply (zenon_L88_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.99 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.99 apply (zenon_L402_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/29.99 apply (zenon_L234_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/29.99 apply (zenon_L157_); trivial. % 29.81/29.99 apply (zenon_L246_); trivial. % 29.81/29.99 (* end of lemma zenon_L403_ *) % 29.81/29.99 assert (zenon_L404_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.99 do 0 intro. intros zenon_H174 zenon_H156 zenon_H20e zenon_H1fd zenon_Hfc zenon_H108 zenon_H16f zenon_H8d zenon_Hbd zenon_Hdf zenon_H1d8 zenon_H1e zenon_H3f zenon_H1dc zenon_H2d zenon_H112 zenon_He1 zenon_H18e zenon_Had zenon_Hb8 zenon_H19a zenon_Hcd zenon_Hde zenon_H125 zenon_H6f zenon_H135 zenon_H27 zenon_H5c zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_He7 zenon_H6c zenon_H84 zenon_H10e zenon_Hd9 zenon_H83 zenon_H1af zenon_H218. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/29.99 apply (zenon_L401_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/29.99 apply (zenon_L4_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/29.99 apply (zenon_L378_); trivial. % 29.81/29.99 apply (zenon_L403_); trivial. % 29.81/29.99 (* end of lemma zenon_L404_ *) % 29.81/29.99 assert (zenon_L405_ : ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.99 do 0 intro. intros zenon_Hf5 zenon_H17b zenon_H218. % 29.81/29.99 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 29.81/29.99 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 29.81/29.99 intro zenon_D_pnotp. % 29.81/29.99 apply zenon_H218. % 29.81/29.99 rewrite <- zenon_D_pnotp. % 29.81/29.99 exact zenon_H109. % 29.81/29.99 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.81/29.99 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 29.81/29.99 congruence. % 29.81/29.99 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 29.81/29.99 intro zenon_D_pnotp. % 29.81/29.99 apply zenon_H219. % 29.81/29.99 rewrite <- zenon_D_pnotp. % 29.81/29.99 exact zenon_Hf5. % 29.81/29.99 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 29.81/29.99 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 29.81/29.99 congruence. % 29.81/29.99 apply zenon_H10a. apply refl_equal. % 29.81/29.99 apply zenon_H223. apply sym_equal. exact zenon_H17b. % 29.81/29.99 apply zenon_H10a. apply refl_equal. % 29.81/29.99 apply zenon_H10a. apply refl_equal. % 29.81/29.99 (* end of lemma zenon_L405_ *) % 29.81/29.99 assert (zenon_L406_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.81/29.99 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H9d zenon_H222 zenon_Hd0 zenon_H17b zenon_H218. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.99 apply (zenon_L49_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.99 apply (zenon_L264_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.99 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.99 apply (zenon_L405_); trivial. % 29.81/29.99 (* end of lemma zenon_L406_ *) % 29.81/29.99 assert (zenon_L407_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.81/29.99 do 0 intro. intros zenon_Hc0 zenon_He4 zenon_H19e zenon_H5e zenon_H208 zenon_Hd1 zenon_H101 zenon_H18c zenon_H42 zenon_H222 zenon_H1a5 zenon_H92 zenon_H1b1 zenon_Hcd zenon_H10e zenon_Hde zenon_H174 zenon_H156 zenon_H20e zenon_H1fd zenon_Hfc zenon_H108 zenon_H16f zenon_H8d zenon_Hbd zenon_Hdf zenon_H1d8 zenon_H1e zenon_H3f zenon_H1dc zenon_H2d zenon_He1 zenon_H18e zenon_Had zenon_Hb8 zenon_H19a zenon_H125 zenon_H6f zenon_H135 zenon_H27 zenon_H5c zenon_H3c zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_He7 zenon_H84 zenon_Hd9 zenon_H83 zenon_H1af zenon_H218 zenon_H173 zenon_H15a zenon_H16a zenon_H60 zenon_H225 zenon_H17d zenon_H112. % 29.81/29.99 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.81/29.99 exact (zenon_H84 zenon_H88). % 29.81/29.99 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.81/29.99 exact (zenon_H84 zenon_H88). % 29.81/29.99 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.81/29.99 apply (zenon_L147_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.81/29.99 apply (zenon_L239_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.81/29.99 apply (zenon_L404_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.81/29.99 apply (zenon_L192_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/29.99 apply (zenon_L239_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/29.99 apply (zenon_L404_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/29.99 apply (zenon_L154_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/29.99 apply (zenon_L261_); trivial. % 29.81/29.99 apply (zenon_L406_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/29.99 apply (zenon_L4_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/29.99 apply (zenon_L87_); trivial. % 29.81/29.99 apply (zenon_L267_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/29.99 apply (zenon_L49_); trivial. % 29.81/29.99 apply (zenon_L269_); trivial. % 29.81/29.99 apply (zenon_L139_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.81/29.99 apply (zenon_L136_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.81/29.99 exact (zenon_H84 zenon_H88). % 29.81/29.99 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.81/29.99 apply (zenon_L147_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.81/29.99 apply (zenon_L239_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.81/29.99 apply (zenon_L404_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.81/29.99 apply (zenon_L192_); trivial. % 29.81/29.99 apply (zenon_L106_); trivial. % 29.81/29.99 apply (zenon_L139_); trivial. % 29.81/29.99 (* end of lemma zenon_L407_ *) % 29.81/29.99 assert (zenon_L408_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 29.81/29.99 do 0 intro. intros zenon_H225 zenon_He1 zenon_H60 zenon_H156 zenon_H19a zenon_H6f zenon_H2d zenon_H1fd zenon_Hd0 zenon_Hd9 zenon_H125 zenon_H42 zenon_H18e zenon_H15a zenon_H173 zenon_H1af zenon_H1bd zenon_H3c zenon_H5e zenon_H6c zenon_H1e zenon_H1ca zenon_H27 zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_Hde zenon_H10e zenon_H33 zenon_Hcd. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.81/29.99 apply (zenon_L286_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.81/29.99 apply (zenon_L287_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.81/29.99 apply (zenon_L192_); trivial. % 29.81/29.99 apply (zenon_L106_); trivial. % 29.81/29.99 (* end of lemma zenon_L408_ *) % 29.81/29.99 assert (zenon_L409_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 29.81/29.99 do 0 intro. intros zenon_H246 zenon_H16a zenon_H83 zenon_He7 zenon_Hd6 zenon_H6b zenon_H135 zenon_Hb8 zenon_Had zenon_H1dc zenon_H3f zenon_Hbd zenon_H8d zenon_H18c zenon_Hc0 zenon_H112 zenon_H17d zenon_He4 zenon_H231 zenon_H10d zenon_Hf9 zenon_H108 zenon_H16f zenon_H1c7 zenon_H222 zenon_H218 zenon_H101 zenon_H159 zenon_H20e zenon_H208 zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H174 zenon_H1a5 zenon_H92 zenon_H84 zenon_H1b1 zenon_Hcd zenon_H10e zenon_Hde zenon_H200 zenon_H5c zenon_H1d8 zenon_H27 zenon_H1ca zenon_H1e zenon_H5e zenon_H3c zenon_H1bd zenon_H1af zenon_H173 zenon_H15a zenon_H18e zenon_H42 zenon_H125 zenon_Hd9 zenon_Hd0 zenon_H1fd zenon_H2d zenon_H6f zenon_H19a zenon_H156 zenon_H60 zenon_He1 zenon_H225 zenon_H20. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 29.81/29.99 apply (zenon_L242_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 29.81/29.99 apply (zenon_L400_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 29.81/29.99 apply (zenon_L407_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.81/29.99 exact (zenon_H84 zenon_H88). % 29.81/29.99 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.81/29.99 exact (zenon_H84 zenon_H88). % 29.81/29.99 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.81/29.99 apply (zenon_L147_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.81/29.99 apply (zenon_L293_); trivial. % 29.81/29.99 apply (zenon_L139_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.81/29.99 apply (zenon_L136_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.81/29.99 exact (zenon_H84 zenon_H88). % 29.81/29.99 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.81/29.99 apply (zenon_L147_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.81/29.99 apply (zenon_L408_); trivial. % 29.81/29.99 apply (zenon_L27_); trivial. % 29.81/29.99 (* end of lemma zenon_L409_ *) % 29.81/29.99 assert (zenon_L410_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 29.81/29.99 do 0 intro. intros zenon_H14b zenon_H20 zenon_H225 zenon_H156 zenon_H19a zenon_H1fd zenon_Hd9 zenon_H125 zenon_H15a zenon_H173 zenon_H3c zenon_H27 zenon_H1d8 zenon_H5c zenon_H200 zenon_Hde zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H174 zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H20e zenon_H159 zenon_H101 zenon_H218 zenon_H16f zenon_He4 zenon_H17d zenon_Hc0 zenon_H18c zenon_H8d zenon_Hbd zenon_H3f zenon_H1dc zenon_Had zenon_H135 zenon_H6b zenon_He7 zenon_H83 zenon_H16a zenon_H246 zenon_H18e zenon_H1d5 zenon_H19e zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_Hd0 zenon_H108 zenon_H1e zenon_H42 zenon_H60 zenon_H1bd zenon_Hf9 zenon_H6f zenon_H112 zenon_H2d zenon_H37 zenon_H100 zenon_He1 zenon_Hb8 zenon_H55 zenon_H222 zenon_Hda zenon_H10d zenon_H231. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/29.99 apply (zenon_L409_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/29.99 apply (zenon_L309_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/29.99 apply (zenon_L165_); trivial. % 29.81/29.99 apply (zenon_L356_); trivial. % 29.81/29.99 (* end of lemma zenon_L410_ *) % 29.81/29.99 assert (zenon_L411_ : ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> False). % 29.81/29.99 do 0 intro. intros zenon_Hdf zenon_H231 zenon_H10d zenon_Hda zenon_H222 zenon_Hb8 zenon_He1 zenon_H100 zenon_H2d zenon_Hf9 zenon_H42 zenon_H1e zenon_H108 zenon_Hcd zenon_H18e zenon_H246 zenon_H16a zenon_H83 zenon_He7 zenon_H6b zenon_H135 zenon_Had zenon_H1dc zenon_H3f zenon_Hbd zenon_H8d zenon_H18c zenon_Hc0 zenon_H17d zenon_He4 zenon_H16f zenon_H218 zenon_H101 zenon_H159 zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H174 zenon_H1a5 zenon_H92 zenon_H84 zenon_H1b1 zenon_Hde zenon_H200 zenon_H5c zenon_H1d8 zenon_H27 zenon_H173 zenon_H15a zenon_H125 zenon_Hd9 zenon_H1fd zenon_H156 zenon_H225 zenon_H20 zenon_H14b zenon_H1d5 zenon_H19e zenon_H37 zenon_He9 zenon_H3c zenon_H1f zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H20e zenon_H19a zenon_Hd0 zenon_H112 zenon_H9c. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/29.99 apply (zenon_L49_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/29.99 apply (zenon_L410_); trivial. % 29.81/29.99 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/29.99 exact (zenon_Hd0 zenon_Hcc). % 29.81/29.99 apply (zenon_L227_); trivial. % 29.81/29.99 (* end of lemma zenon_L411_ *) % 29.81/29.99 assert (zenon_L412_ : (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H231 zenon_H10d zenon_Hda zenon_H222 zenon_Hb8 zenon_H100 zenon_H2d zenon_H112 zenon_H6f zenon_Hf9 zenon_H1bd zenon_H60 zenon_H42 zenon_H1e zenon_H108 zenon_Hd0 zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H1af zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H19e zenon_H1d5 zenon_H246 zenon_H16a zenon_H83 zenon_He7 zenon_H6b zenon_H135 zenon_Had zenon_H1dc zenon_H3f zenon_Hbd zenon_H8d zenon_H18c zenon_Hc0 zenon_H17d zenon_He4 zenon_H16f zenon_H218 zenon_H101 zenon_H159 zenon_H20e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H174 zenon_H1a5 zenon_H92 zenon_H84 zenon_H1b1 zenon_Hde zenon_H200 zenon_H5c zenon_H1d8 zenon_H27 zenon_H3c zenon_H173 zenon_H15a zenon_H125 zenon_Hd9 zenon_H1fd zenon_H19a zenon_H156 zenon_H225 zenon_H20 zenon_H14b zenon_He1 zenon_H55 zenon_H18e. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.00 apply (zenon_L4_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.00 apply (zenon_L410_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.00 apply (zenon_L126_); trivial. % 29.81/30.00 exact (zenon_H18e zenon_H40). % 29.81/30.00 (* end of lemma zenon_L412_ *) % 29.81/30.00 assert (zenon_L413_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H1d5 zenon_H6b zenon_Hd6 zenon_Hf5 zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1ca zenon_H1e zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H222 zenon_H1af zenon_H1c7. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/30.00 apply (zenon_L193_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/30.00 apply (zenon_L144_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/30.00 apply (zenon_L202_); trivial. % 29.81/30.00 apply (zenon_L265_); trivial. % 29.81/30.00 (* end of lemma zenon_L413_ *) % 29.81/30.00 assert (zenon_L414_ : ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.81/30.00 do 0 intro. intros zenon_Hdc zenon_He1 zenon_H14b zenon_H20 zenon_H225 zenon_H156 zenon_H19a zenon_H1fd zenon_Hd9 zenon_H125 zenon_H15a zenon_H173 zenon_H27 zenon_H200 zenon_Hde zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H174 zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H20e zenon_H159 zenon_H101 zenon_H218 zenon_H16f zenon_He4 zenon_H17d zenon_Hc0 zenon_H18c zenon_H8d zenon_Had zenon_H135 zenon_H83 zenon_H16a zenon_H246 zenon_H19e zenon_Hcd zenon_H208 zenon_H1d2 zenon_H6c zenon_H108 zenon_H42 zenon_H60 zenon_H1bd zenon_Hf9 zenon_H6f zenon_H100 zenon_Hda zenon_H10d zenon_H231 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1ca zenon_H1e zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H222 zenon_H1af zenon_H1c7. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/30.00 apply (zenon_L142_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/30.00 apply (zenon_L412_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/30.00 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.00 apply (zenon_L413_); trivial. % 29.81/30.00 (* end of lemma zenon_L414_ *) % 29.81/30.00 assert (zenon_L415_ : ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (op (op (e3) (e3)) (e3)))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H14f zenon_H112 zenon_H249. % 29.81/30.00 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 29.81/30.00 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e0) = (op (op (e3) (e3)) (e3)))). % 29.81/30.00 intro zenon_D_pnotp. % 29.81/30.00 apply zenon_H249. % 29.81/30.00 rewrite <- zenon_D_pnotp. % 29.81/30.00 exact zenon_H131. % 29.81/30.00 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 29.81/30.00 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H24a]. % 29.81/30.00 congruence. % 29.81/30.00 cut (((op (e1) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))). % 29.81/30.00 intro zenon_D_pnotp. % 29.81/30.00 apply zenon_H24a. % 29.81/30.00 rewrite <- zenon_D_pnotp. % 29.81/30.00 exact zenon_H14f. % 29.81/30.00 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.81/30.00 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H22c]. % 29.81/30.00 congruence. % 29.81/30.00 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 29.81/30.00 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 29.81/30.00 intro zenon_D_pnotp. % 29.81/30.00 apply zenon_H22c. % 29.81/30.00 rewrite <- zenon_D_pnotp. % 29.81/30.00 exact zenon_H131. % 29.81/30.00 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 29.81/30.00 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H229]. % 29.81/30.00 congruence. % 29.81/30.00 apply (zenon_L277_); trivial. % 29.81/30.00 apply zenon_H132. apply refl_equal. % 29.81/30.00 apply zenon_H132. apply refl_equal. % 29.81/30.00 apply zenon_H1d. apply refl_equal. % 29.81/30.00 apply zenon_H132. apply refl_equal. % 29.81/30.00 apply zenon_H132. apply refl_equal. % 29.81/30.00 (* end of lemma zenon_L415_ *) % 29.81/30.00 assert (zenon_L416_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> False). % 29.81/30.00 do 0 intro. intros zenon_Hfd zenon_H14f zenon_H112. % 29.81/30.00 apply (zenon_notand_s _ _ ax28); [ zenon_intro zenon_H12b | zenon_intro zenon_H24b ]. % 29.81/30.00 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 29.81/30.00 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e2) = (op (op (e3) (e3)) (op (e3) (e3))))). % 29.81/30.00 intro zenon_D_pnotp. % 29.81/30.00 apply zenon_H12b. % 29.81/30.00 rewrite <- zenon_D_pnotp. % 29.81/30.00 exact zenon_H12c. % 29.81/30.00 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 29.81/30.00 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 29.81/30.00 congruence. % 29.81/30.00 cut (((op (e1) (e1)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 29.81/30.00 intro zenon_D_pnotp. % 29.81/30.00 apply zenon_H12e. % 29.81/30.00 rewrite <- zenon_D_pnotp. % 29.81/30.00 exact zenon_Hfd. % 29.81/30.00 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.81/30.00 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H230]. % 29.81/30.00 congruence. % 29.81/30.00 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 29.81/30.00 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))))). % 29.81/30.00 intro zenon_D_pnotp. % 29.81/30.00 apply zenon_H230. % 29.81/30.00 rewrite <- zenon_D_pnotp. % 29.81/30.00 exact zenon_H12c. % 29.81/30.00 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 29.81/30.00 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 29.81/30.00 congruence. % 29.81/30.00 apply (zenon_L276_); trivial. % 29.81/30.00 apply zenon_H12d. apply refl_equal. % 29.81/30.00 apply zenon_H12d. apply refl_equal. % 29.81/30.00 apply zenon_H57. apply refl_equal. % 29.81/30.00 apply zenon_H12d. apply refl_equal. % 29.81/30.00 apply zenon_H12d. apply refl_equal. % 29.81/30.00 apply (zenon_notand_s _ _ zenon_H24b); [ zenon_intro zenon_H249 | zenon_intro zenon_H192 ]. % 29.81/30.00 apply (zenon_L415_); trivial. % 29.81/30.00 apply zenon_H192. apply sym_equal. exact zenon_H112. % 29.81/30.00 (* end of lemma zenon_L416_ *) % 29.81/30.00 assert (zenon_L417_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H172 zenon_H14e zenon_H20d zenon_Hdc zenon_He1 zenon_H14b zenon_H20 zenon_H225 zenon_H156 zenon_H19a zenon_H1fd zenon_Hd9 zenon_H125 zenon_H15a zenon_H173 zenon_H27 zenon_H200 zenon_Hde zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H174 zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H20e zenon_H159 zenon_H101 zenon_H218 zenon_H16f zenon_He4 zenon_H17d zenon_Hc0 zenon_H18c zenon_H8d zenon_Had zenon_H135 zenon_H83 zenon_H16a zenon_H246 zenon_H19e zenon_Hcd zenon_H208 zenon_H1d2 zenon_H6c zenon_H108 zenon_H42 zenon_H60 zenon_H1bd zenon_Hf9 zenon_H6f zenon_H100 zenon_Hda zenon_H10d zenon_H231 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1ca zenon_H1e zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H1af zenon_H1c7. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.00 apply (zenon_L241_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.00 apply (zenon_L271_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.00 apply (zenon_L222_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.00 apply (zenon_L224_); trivial. % 29.81/30.00 apply (zenon_L411_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.00 apply (zenon_L363_); trivial. % 29.81/30.00 apply (zenon_L326_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.00 apply (zenon_L154_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.00 apply (zenon_L412_); trivial. % 29.81/30.00 apply (zenon_L414_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/30.00 apply (zenon_L42_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.00 apply (zenon_L384_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.00 apply (zenon_L154_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.00 apply (zenon_L309_); trivial. % 29.81/30.00 apply (zenon_L414_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.00 apply (zenon_L241_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.00 apply (zenon_L240_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.00 apply (zenon_L352_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.00 apply (zenon_L224_); trivial. % 29.81/30.00 apply (zenon_L411_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.00 apply (zenon_L363_); trivial. % 29.81/30.00 apply (zenon_L326_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.00 apply (zenon_L416_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.00 apply (zenon_L412_); trivial. % 29.81/30.00 apply (zenon_L414_); trivial. % 29.81/30.00 (* end of lemma zenon_L417_ *) % 29.81/30.00 assert (zenon_L418_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H16f zenon_Had zenon_H231 zenon_H10d zenon_Hda zenon_H222 zenon_Hb8 zenon_H100 zenon_H2d zenon_H112 zenon_Hf9 zenon_H1bd zenon_H42 zenon_H1e zenon_H108 zenon_Hd0 zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H1d2 zenon_H208 zenon_Hcd zenon_H19e zenon_H18e zenon_H83 zenon_Hd9 zenon_H84 zenon_H74 zenon_He7 zenon_H14b zenon_H6f zenon_H19a zenon_H1d5 zenon_H1d8 zenon_H8a zenon_He1 zenon_H1c7 zenon_H55 zenon_H60 zenon_H1af zenon_H156. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.00 apply (zenon_L34_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.00 apply (zenon_L357_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.00 apply (zenon_L235_); trivial. % 29.81/30.00 apply (zenon_L365_); trivial. % 29.81/30.00 (* end of lemma zenon_L418_ *) % 29.81/30.00 assert (zenon_L419_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H135 zenon_H156 zenon_H60 zenon_H6b zenon_H6c zenon_H1dc zenon_H1d2 zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H2d zenon_H1ca zenon_Hd6 zenon_H5e zenon_H1bd zenon_H1c7 zenon_H6f zenon_H108 zenon_H14b zenon_H19a zenon_Hcd zenon_He1 zenon_H18c zenon_H173 zenon_H9d zenon_H222 zenon_Hd0 zenon_H1af zenon_H117 zenon_H27. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/30.00 apply (zenon_L182_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/30.00 apply (zenon_L264_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/30.00 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.00 apply (zenon_L183_); trivial. % 29.81/30.00 (* end of lemma zenon_L419_ *) % 29.81/30.00 assert (zenon_L420_ : ((op (e0) (e2)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.00 do 0 intro. intros zenon_Hda zenon_H6c zenon_H6f zenon_H172 zenon_H92 zenon_H20 zenon_He7 zenon_H8d zenon_H16a zenon_H83 zenon_H84 zenon_H17d zenon_H108 zenon_H1ca zenon_H5e zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H101 zenon_Had zenon_H173 zenon_H1dc zenon_H6b zenon_Hd1 zenon_H18c zenon_H20d zenon_H14b zenon_Hf9 zenon_H10d zenon_H231 zenon_H5c zenon_H27 zenon_H174 zenon_H35 zenon_H20e zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_H125 zenon_He4 zenon_H225 zenon_Hb5 zenon_H14e zenon_Hb8 zenon_H100 zenon_H3f zenon_Hbd zenon_Hd6 zenon_H1d8 zenon_H23b zenon_Hee zenon_Hc8 zenon_H74 zenon_H11e zenon_H1a5 zenon_H159 zenon_H42 zenon_H2d zenon_H156 zenon_Hd0 zenon_H222 zenon_H1d5 zenon_He1 zenon_H60 zenon_H218 zenon_H135 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.00 apply (zenon_L376_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.00 apply (zenon_L4_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.00 apply (zenon_L149_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.00 apply (zenon_L377_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.00 apply (zenon_L339_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.00 apply (zenon_L142_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.00 apply (zenon_L322_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.00 apply (zenon_L159_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.00 apply (zenon_L397_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.00 apply (zenon_L93_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.00 apply (zenon_L418_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.00 apply (zenon_L4_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.00 apply (zenon_L419_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.00 apply (zenon_L375_); trivial. % 29.81/30.00 exact (zenon_H18e zenon_H40). % 29.81/30.00 apply (zenon_L398_); trivial. % 29.81/30.00 (* end of lemma zenon_L420_ *) % 29.81/30.00 assert (zenon_L421_ : (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.00 do 0 intro. intros zenon_Hde zenon_Hf9 zenon_H6f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H222 zenon_Hda zenon_H10d zenon_H231 zenon_H173 zenon_Hcd zenon_H101 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_He7 zenon_H1dc zenon_H6b zenon_H15a zenon_H16f zenon_H159 zenon_H42 zenon_H1c7 zenon_H5e zenon_H1f zenon_H1ca zenon_H60 zenon_H156 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6c zenon_H1bd zenon_H102 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H200 zenon_H108 zenon_H1d2 zenon_H208 zenon_H14b zenon_H11e zenon_H74 zenon_Hee zenon_H23b zenon_H14e zenon_Hb5 zenon_H172 zenon_H20 zenon_H225 zenon_H1fd zenon_Hd9 zenon_H125 zenon_H27 zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H174 zenon_H35 zenon_Hd1 zenon_H20e zenon_H218 zenon_He4 zenon_H17d zenon_Hc0 zenon_H8d zenon_Had zenon_H83 zenon_H16a zenon_H246 zenon_H20d zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.00 apply (zenon_L4_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.00 apply (zenon_L417_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.00 apply (zenon_L207_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/30.00 apply (zenon_L420_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/30.00 apply (zenon_L412_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/30.00 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.00 apply (zenon_L223_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.00 apply (zenon_L192_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.00 apply (zenon_L295_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.00 apply (zenon_L296_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/30.00 apply (zenon_L376_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/30.00 apply (zenon_L356_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/30.00 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.00 apply (zenon_L294_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.00 apply (zenon_L145_); trivial. % 29.81/30.00 exact (zenon_H18e zenon_H40). % 29.81/30.00 (* end of lemma zenon_L421_ *) % 29.81/30.00 assert (zenon_L422_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H8d zenon_H102 zenon_H35 zenon_Hfc zenon_H101 zenon_H3f zenon_Hdc zenon_Hd1 zenon_He7 zenon_H74 zenon_H84 zenon_Hd9 zenon_H83 zenon_H208 zenon_Hf9 zenon_H100 zenon_Hb8 zenon_Hda zenon_H10d zenon_H231 zenon_Had zenon_H16f zenon_H42 zenon_H1e zenon_Hd0 zenon_H222 zenon_H173 zenon_H18c zenon_He1 zenon_Hcd zenon_H19a zenon_H14b zenon_H108 zenon_H6f zenon_H1bd zenon_H5e zenon_Hd6 zenon_H1ca zenon_H2d zenon_H19e zenon_H1d5 zenon_H1d2 zenon_H1dc zenon_H6c zenon_H6b zenon_H60 zenon_H156 zenon_H135 zenon_H1c7 zenon_H1af zenon_H117 zenon_H27 zenon_Hf6 zenon_H112 zenon_H1d8 zenon_H1e6 zenon_H18e. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.00 apply (zenon_L149_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.00 apply (zenon_L156_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.00 apply (zenon_L339_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.00 apply (zenon_L300_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.00 apply (zenon_L154_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.00 apply (zenon_L418_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.00 apply (zenon_L4_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.00 apply (zenon_L419_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.00 apply (zenon_L188_); trivial. % 29.81/30.00 exact (zenon_H18e zenon_H40). % 29.81/30.00 (* end of lemma zenon_L422_ *) % 29.81/30.00 assert (zenon_L423_ : ((op (e1) (e0)) = (e3)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H6e zenon_H69 zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H17d zenon_Hc0 zenon_H83 zenon_H16a zenon_H246 zenon_Hda zenon_H218 zenon_H16b zenon_H1af zenon_H20d zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H2d zenon_He4 zenon_H225 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H18c zenon_H135 zenon_H108 zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_H100 zenon_Hb8 zenon_Hc8 zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H3f zenon_H112 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.00 apply (zenon_L346_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.00 apply (zenon_L154_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.00 apply (zenon_L412_); trivial. % 29.81/30.00 apply (zenon_L342_); trivial. % 29.81/30.00 (* end of lemma zenon_L423_ *) % 29.81/30.00 assert (zenon_L424_ : ((op (e1) (e0)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H6e zenon_Hfe zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H17d zenon_Hc0 zenon_H83 zenon_H16a zenon_H246 zenon_Hda zenon_H218 zenon_H16b zenon_H1af zenon_H20d zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H2d zenon_He4 zenon_H225 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H18c zenon_H135 zenon_H108 zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_H100 zenon_Hb8 zenon_Hc8 zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H3f zenon_H112 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.00 apply (zenon_L4_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.00 apply (zenon_L321_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.00 apply (zenon_L207_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.00 apply (zenon_L350_); trivial. % 29.81/30.00 apply (zenon_L295_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.00 apply (zenon_L155_); trivial. % 29.81/30.00 exact (zenon_H18e zenon_H40). % 29.81/30.00 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.00 apply (zenon_L154_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.00 apply (zenon_L412_); trivial. % 29.81/30.00 apply (zenon_L342_); trivial. % 29.81/30.00 (* end of lemma zenon_L424_ *) % 29.81/30.00 assert (zenon_L425_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H16a zenon_H8a zenon_H74 zenon_H84 zenon_H83 zenon_Hda zenon_H218 zenon_H16b zenon_H1af zenon_H20d zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H2d zenon_He4 zenon_H225 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H18c zenon_H135 zenon_H108 zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_H100 zenon_Hb8 zenon_Hc8 zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H3f zenon_H112 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.00 apply (zenon_L300_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.00 apply (zenon_L236_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.00 apply (zenon_L418_); trivial. % 29.81/30.00 apply (zenon_L342_); trivial. % 29.81/30.00 (* end of lemma zenon_L425_ *) % 29.81/30.00 assert (zenon_L426_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H14b zenon_Hde zenon_Hda zenon_H108 zenon_Hd0 zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H1af zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H19e zenon_H1d5 zenon_H55 zenon_H60 zenon_H1bd zenon_Hb8 zenon_He2 zenon_He1 zenon_H100 zenon_H37 zenon_H2d zenon_H112 zenon_H6f. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.00 apply (zenon_L192_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.00 apply (zenon_L217_); trivial. % 29.81/30.00 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.00 apply (zenon_L165_); trivial. % 29.81/30.00 apply (zenon_L355_); trivial. % 29.81/30.00 (* end of lemma zenon_L426_ *) % 29.81/30.00 assert (zenon_L427_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.00 do 0 intro. intros zenon_H42 zenon_H1e zenon_H6f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H1bd zenon_H60 zenon_H55 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H5e zenon_H6c zenon_H1ca zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.01 apply (zenon_L426_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.01 apply (zenon_L308_); trivial. % 29.81/30.01 exact (zenon_H18e zenon_H40). % 29.81/30.01 (* end of lemma zenon_L427_ *) % 29.81/30.01 assert (zenon_L428_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H101 zenon_H3c zenon_H159 zenon_H14b zenon_Hde zenon_Hda zenon_H108 zenon_H1ca zenon_H6c zenon_H5e zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H1bd zenon_Hb8 zenon_H100 zenon_H112 zenon_H6f zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_H155 zenon_H222 zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_L312_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L93_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L427_); trivial. % 29.81/30.01 apply (zenon_L313_); trivial. % 29.81/30.01 (* end of lemma zenon_L428_ *) % 29.81/30.01 assert (zenon_L429_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H3f zenon_Hbd zenon_He7 zenon_H1dc zenon_H6b zenon_Hc8 zenon_Had zenon_Hee zenon_H20 zenon_H23b zenon_H8d zenon_Hb5 zenon_H18c zenon_H225 zenon_He4 zenon_H200 zenon_H125 zenon_H231 zenon_H10d zenon_Hf9 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H1f zenon_H173 zenon_H20e zenon_H174 zenon_H27 zenon_H5c zenon_H20d zenon_H17d zenon_H84 zenon_H83 zenon_H16a zenon_H69 zenon_H92 zenon_H6e zenon_H19a zenon_H101 zenon_H3c zenon_H159 zenon_H14b zenon_Hde zenon_Hda zenon_H108 zenon_H1ca zenon_H6c zenon_H5e zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H1bd zenon_Hb8 zenon_H100 zenon_H112 zenon_H6f zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_H222 zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_L390_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L154_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L427_); trivial. % 29.81/30.01 apply (zenon_L342_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.01 apply (zenon_L311_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.01 apply (zenon_L159_); trivial. % 29.81/30.01 apply (zenon_L428_); trivial. % 29.81/30.01 (* end of lemma zenon_L429_ *) % 29.81/30.01 assert (zenon_L430_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H42 zenon_H6f zenon_H112 zenon_H2d zenon_H100 zenon_He1 zenon_He2 zenon_Hb8 zenon_H1bd zenon_H60 zenon_H55 zenon_H1d5 zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_Hd0 zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.01 apply (zenon_L426_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.01 apply (zenon_L155_); trivial. % 29.81/30.01 exact (zenon_H18e zenon_H40). % 29.81/30.01 (* end of lemma zenon_L430_ *) % 29.81/30.01 assert (zenon_L431_ : ((op (e3) (e0)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.81/30.01 do 0 intro. intros zenon_He2 zenon_Hfe zenon_H37 zenon_H9d zenon_H112 zenon_H3f zenon_H1e zenon_Hbd zenon_He7 zenon_H1dc zenon_H6b zenon_Hc8 zenon_Hb8 zenon_H100 zenon_Had zenon_Hee zenon_H20 zenon_H23b zenon_H8d zenon_Hb5 zenon_H108 zenon_H135 zenon_H18c zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_He1 zenon_H208 zenon_H6f zenon_Hcd zenon_H1d5 zenon_Hd0 zenon_Hde zenon_H225 zenon_He4 zenon_H2d zenon_H200 zenon_H1d8 zenon_H156 zenon_H125 zenon_H231 zenon_H10d zenon_Hf9 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H42 zenon_H222 zenon_H1f zenon_H3c zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_H174 zenon_H27 zenon_H5c zenon_H14b zenon_H20d zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H35 zenon_H102 zenon_H18e zenon_H1af zenon_H16b zenon_H218. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/30.01 apply (zenon_L307_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/30.01 apply (zenon_L217_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/30.01 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.01 apply (zenon_L341_); trivial. % 29.81/30.01 (* end of lemma zenon_L431_ *) % 29.81/30.01 assert (zenon_L432_ : ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H112 zenon_H3f zenon_Hbd zenon_He7 zenon_H1dc zenon_H6b zenon_Hc8 zenon_Hb8 zenon_H100 zenon_Had zenon_Hee zenon_H20 zenon_H23b zenon_H8d zenon_Hb5 zenon_H18c zenon_Hde zenon_H225 zenon_He4 zenon_H200 zenon_H125 zenon_H231 zenon_H10d zenon_Hf9 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H1f zenon_H173 zenon_H20e zenon_H174 zenon_H27 zenon_H5c zenon_H14b zenon_H20d zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_Hda zenon_H19a zenon_H101 zenon_H3c zenon_H159 zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H5e zenon_H6c zenon_H1ca zenon_Hfe zenon_H108 zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_H222 zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.01 apply (zenon_L388_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.01 apply (zenon_L308_); trivial. % 29.81/30.01 exact (zenon_H18e zenon_H40). % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L311_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L430_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.01 apply (zenon_L431_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.01 apply (zenon_L308_); trivial. % 29.81/30.01 exact (zenon_H18e zenon_H40). % 29.81/30.01 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.01 apply (zenon_L311_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.01 apply (zenon_L159_); trivial. % 29.81/30.01 apply (zenon_L314_); trivial. % 29.81/30.01 (* end of lemma zenon_L432_ *) % 29.81/30.01 assert (zenon_L433_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_H3c zenon_He9 zenon_Hd0 zenon_H17b zenon_H218. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/30.01 apply (zenon_L142_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/30.01 apply (zenon_L88_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/30.01 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.01 apply (zenon_L405_); trivial. % 29.81/30.01 (* end of lemma zenon_L433_ *) % 29.81/30.01 assert (zenon_L434_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H125 zenon_H231 zenon_H10d zenon_H55 zenon_Hb8 zenon_H100 zenon_H9c zenon_H2d zenon_H112 zenon_Hf9 zenon_H1d5 zenon_H19e zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H19a zenon_Hd1 zenon_H101 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_Hdc zenon_H18c zenon_H135 zenon_H218 zenon_H17b zenon_H60 zenon_H1fd zenon_H89 zenon_Hd9 zenon_H37 zenon_Hfc zenon_H108 zenon_He1. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 29.81/30.01 apply (zenon_L356_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 29.81/30.01 apply (zenon_L159_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 29.81/30.01 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.01 apply (zenon_L260_); trivial. % 29.81/30.01 (* end of lemma zenon_L434_ *) % 29.81/30.01 assert (zenon_L435_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H108 zenon_Hfc zenon_Hd9 zenon_H89 zenon_H1fd zenon_H60 zenon_H17b zenon_H218 zenon_H135 zenon_H18c zenon_Hdc zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H101 zenon_Hd1 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H19e zenon_H1d5 zenon_Hf9 zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H10d zenon_H231 zenon_H125 zenon_H1bd zenon_H42 zenon_H1e zenon_H1ca zenon_H6c zenon_H1c7 zenon_H1d2 zenon_Hde zenon_H14b zenon_He1 zenon_H55 zenon_H18e. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.01 apply (zenon_L261_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.01 apply (zenon_L309_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.01 apply (zenon_L165_); trivial. % 29.81/30.01 apply (zenon_L434_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.01 apply (zenon_L126_); trivial. % 29.81/30.01 exact (zenon_H18e zenon_H40). % 29.81/30.01 (* end of lemma zenon_L435_ *) % 29.81/30.01 assert (zenon_L436_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H14b zenon_Hde zenon_H1d2 zenon_H6c zenon_H1bd zenon_H125 zenon_H231 zenon_H10d zenon_Hb8 zenon_H100 zenon_H112 zenon_Hf9 zenon_Hd6 zenon_Hd0 zenon_H18c zenon_H135 zenon_H1fd zenon_H89 zenon_Hd9 zenon_H108 zenon_H42 zenon_H2d zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_H1ca zenon_H60 zenon_H17b zenon_H218 zenon_H173 zenon_He1 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_L433_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L154_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L435_); trivial. % 29.81/30.01 apply (zenon_L266_); trivial. % 29.81/30.01 (* end of lemma zenon_L436_ *) % 29.81/30.01 assert (zenon_L437_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_Hb8 zenon_H1c7 zenon_H3d zenon_H1af zenon_H117 zenon_H27 zenon_Hf6 zenon_H1d8 zenon_H1e6 zenon_H18e zenon_H9c zenon_H2d zenon_H112 zenon_H6f. % 29.81/30.01 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 29.81/30.01 apply (zenon_L188_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 29.81/30.01 exact (zenon_H18e zenon_H40). % 29.81/30.01 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 29.81/30.01 apply (zenon_L304_); trivial. % 29.81/30.01 apply (zenon_L152_); trivial. % 29.81/30.01 (* end of lemma zenon_L437_ *) % 29.81/30.01 assert (zenon_L438_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.81/30.01 do 0 intro. intros zenon_H14b zenon_He1 zenon_H17b zenon_H1e zenon_H200 zenon_Hbd zenon_H5c zenon_H3f zenon_He7 zenon_H1dc zenon_H125 zenon_Hde zenon_H18c zenon_H135 zenon_H1fd zenon_Hd9 zenon_H42 zenon_H222 zenon_H1f zenon_H3c zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_Hd1 zenon_Hdc zenon_Hfc zenon_H35 zenon_H102 zenon_H174 zenon_H108 zenon_H6b zenon_Hdf zenon_H1d5 zenon_H19e zenon_H37 zenon_Hcd zenon_H55 zenon_H208 zenon_H6f zenon_H2d zenon_H18e zenon_H1e6 zenon_H1d8 zenon_Hf6 zenon_H27 zenon_H117 zenon_Hb8 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H20e zenon_H19a zenon_Hd0 zenon_H112. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.01 apply (zenon_L268_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.01 apply (zenon_L173_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.01 apply (zenon_L303_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/30.01 apply (zenon_L255_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/30.01 apply (zenon_L437_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/30.01 apply (zenon_L198_); trivial. % 29.81/30.01 apply (zenon_L226_); trivial. % 29.81/30.01 (* end of lemma zenon_L438_ *) % 29.81/30.01 assert (zenon_L439_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H1d5 zenon_H19e zenon_H37 zenon_H6f zenon_H208 zenon_H1e1 zenon_H1bd zenon_H218 zenon_H17b zenon_H60 zenon_H1ca zenon_H1e zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H222 zenon_H1af zenon_H1c7. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/30.01 apply (zenon_L257_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/30.01 apply (zenon_L209_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/30.01 apply (zenon_L259_); trivial. % 29.81/30.01 apply (zenon_L265_); trivial. % 29.81/30.01 (* end of lemma zenon_L439_ *) % 29.81/30.01 assert (zenon_L440_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H42 zenon_H1c7 zenon_H5e zenon_H1f zenon_H1ca zenon_H60 zenon_H208 zenon_H6f zenon_H1d5 zenon_H156 zenon_He1 zenon_H2d zenon_Hd6 zenon_H6c zenon_Hc9 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H135 zenon_Hde zenon_H9d zenon_H222 zenon_Hd0 zenon_H17b zenon_H218 zenon_H200 zenon_H18e. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.01 apply (zenon_L49_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.01 apply (zenon_L207_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.01 apply (zenon_L331_); trivial. % 29.81/30.01 apply (zenon_L439_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.01 apply (zenon_L406_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.01 apply (zenon_L207_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.01 apply (zenon_L280_); trivial. % 29.81/30.01 apply (zenon_L209_); trivial. % 29.81/30.01 exact (zenon_H18e zenon_H40). % 29.81/30.01 (* end of lemma zenon_L440_ *) % 29.81/30.01 assert (zenon_L441_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H174 zenon_He2 zenon_H6c zenon_H6f zenon_H42 zenon_H2d zenon_H1e zenon_H112 zenon_H10d zenon_H100 zenon_Had zenon_Hb8 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_H1d8 zenon_H135 zenon_H18e zenon_Hd9 zenon_H8d zenon_H17b zenon_He1. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.01 apply (zenon_L252_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.01 apply (zenon_L385_); trivial. % 29.81/30.01 apply (zenon_L267_); trivial. % 29.81/30.01 (* end of lemma zenon_L441_ *) % 29.81/30.01 assert (zenon_L442_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_Hf6 zenon_H1e6 zenon_H200 zenon_H218 zenon_H222 zenon_Hde zenon_H3c zenon_H19e zenon_H19a zenon_Hfc zenon_H102 zenon_H1bd zenon_H156 zenon_H1d5 zenon_H208 zenon_H60 zenon_H1ca zenon_H1f zenon_H5e zenon_H1c7 zenon_H159 zenon_H1a5 zenon_H11e zenon_H74 zenon_Hc8 zenon_Hee zenon_H23b zenon_Hbd zenon_H3f zenon_H14e zenon_Hb5 zenon_H225 zenon_He4 zenon_H125 zenon_H1fd zenon_H15a zenon_H16f zenon_H20e zenon_H35 zenon_H27 zenon_H5c zenon_H231 zenon_Hf9 zenon_H14b zenon_H20d zenon_H18c zenon_Hd1 zenon_H6b zenon_H1dc zenon_H173 zenon_H101 zenon_Hcd zenon_H1d2 zenon_H108 zenon_H17d zenon_H84 zenon_H83 zenon_H16a zenon_He7 zenon_H20 zenon_H92 zenon_H172 zenon_H174 zenon_H6c zenon_H6f zenon_H42 zenon_H2d zenon_H1e zenon_H112 zenon_H10d zenon_H100 zenon_Had zenon_Hb8 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_H1d8 zenon_H135 zenon_H18e zenon_Hd9 zenon_H8d zenon_H17b zenon_He1. % 29.81/30.01 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.01 exact (zenon_H74 zenon_H73). % 29.81/30.01 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.01 apply (zenon_L436_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.01 apply (zenon_L149_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_L433_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L154_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.01 apply (zenon_L153_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.01 apply (zenon_L126_); trivial. % 29.81/30.01 exact (zenon_H18e zenon_H40). % 29.81/30.01 apply (zenon_L266_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.01 apply (zenon_L157_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_L189_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L154_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.01 apply (zenon_L34_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.01 apply (zenon_L438_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.01 apply (zenon_L207_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.01 apply (zenon_L176_); trivial. % 29.81/30.01 apply (zenon_L186_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.01 apply (zenon_L235_); trivial. % 29.81/30.01 apply (zenon_L365_); trivial. % 29.81/30.01 apply (zenon_L266_); trivial. % 29.81/30.01 apply (zenon_L267_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.01 apply (zenon_L142_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.01 apply (zenon_L322_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.01 apply (zenon_L159_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_L397_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L93_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L282_); trivial. % 29.81/30.01 apply (zenon_L440_); trivial. % 29.81/30.01 apply (zenon_L441_); trivial. % 29.81/30.01 (* end of lemma zenon_L442_ *) % 29.81/30.01 assert (zenon_L443_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.81/30.01 do 0 intro. intros zenon_Hc8 zenon_H100 zenon_Hee zenon_H20 zenon_H23b zenon_H8d zenon_Hb5 zenon_H225 zenon_He4 zenon_H156 zenon_H231 zenon_H10d zenon_Hf9 zenon_H15a zenon_H16f zenon_H42 zenon_H222 zenon_H173 zenon_H101 zenon_H159 zenon_H174 zenon_H218 zenon_Had zenon_H92 zenon_H69 zenon_H83 zenon_H84 zenon_H17d zenon_Hd1 zenon_H35 zenon_H102 zenon_H1af zenon_H1bd zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1e zenon_H1ca zenon_H135 zenon_H18c zenon_Hdc zenon_Hd0 zenon_H20d zenon_H60 zenon_H14b zenon_H27 zenon_H125 zenon_H6b zenon_H1fd zenon_Hd9 zenon_Hfc zenon_H200 zenon_He1 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H89 zenon_H18e zenon_H1dc zenon_H2d zenon_Hcd zenon_H108 zenon_Hde zenon_H1d5 zenon_H19e zenon_H1f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_Hd6 zenon_H20e zenon_H112 zenon_H6f zenon_H19a zenon_H16a zenon_H16b. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.01 apply (zenon_L346_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.01 apply (zenon_L230_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.01 apply (zenon_L235_); trivial. % 29.81/30.01 apply (zenon_L101_); trivial. % 29.81/30.01 (* end of lemma zenon_L443_ *) % 29.81/30.01 assert (zenon_L444_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H9d zenon_H222 zenon_Hd0 zenon_H1af zenon_H117 zenon_H27. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/30.01 apply (zenon_L49_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/30.01 apply (zenon_L264_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/30.01 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.01 apply (zenon_L183_); trivial. % 29.81/30.01 (* end of lemma zenon_L444_ *) % 29.81/30.01 assert (zenon_L445_ : ((op (e3) (e3)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H112 zenon_H19a zenon_H20e zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_H1f zenon_H3c zenon_He9 zenon_H19e zenon_H1d5 zenon_H14b zenon_H20 zenon_H225 zenon_H156 zenon_H1fd zenon_Hd9 zenon_H125 zenon_H15a zenon_H173 zenon_H27 zenon_H1d8 zenon_H5c zenon_H200 zenon_Hde zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H174 zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H159 zenon_H101 zenon_H218 zenon_H16f zenon_He4 zenon_H17d zenon_Hc0 zenon_H8d zenon_Hbd zenon_H3f zenon_H1dc zenon_Had zenon_H6b zenon_He7 zenon_H83 zenon_H16a zenon_H246 zenon_Hcd zenon_H108 zenon_H1e zenon_H42 zenon_Hf9 zenon_H2d zenon_H100 zenon_Hb8 zenon_H222 zenon_Hda zenon_H10d zenon_H231 zenon_Hdf zenon_H20d zenon_H6e zenon_Hb5 zenon_H16b zenon_H69 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.01 apply (zenon_L271_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.01 apply (zenon_L321_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.01 apply (zenon_L224_); trivial. % 29.81/30.01 apply (zenon_L411_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.01 apply (zenon_L145_); trivial. % 29.81/30.01 exact (zenon_H18e zenon_H40). % 29.81/30.01 (* end of lemma zenon_L445_ *) % 29.81/30.01 assert (zenon_L446_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_H108 zenon_H37 zenon_Hfe zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_He1 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1e zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1af zenon_H16b zenon_H218. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/30.01 apply (zenon_L142_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/30.01 apply (zenon_L217_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/30.01 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.01 apply (zenon_L402_); trivial. % 29.81/30.01 (* end of lemma zenon_L446_ *) % 29.81/30.01 assert (zenon_L447_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H14e zenon_Hdf zenon_H14f zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H17d zenon_Hc0 zenon_H83 zenon_H16a zenon_H246 zenon_Hda zenon_H218 zenon_H16b zenon_H1af zenon_H20d zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H156 zenon_H1d8 zenon_H200 zenon_H2d zenon_He4 zenon_H225 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H18c zenon_H135 zenon_H108 zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_H100 zenon_Hb8 zenon_Hc8 zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H3f zenon_H112 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.01 apply (zenon_L403_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.01 apply (zenon_L352_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.01 apply (zenon_L303_); trivial. % 29.81/30.01 apply (zenon_L411_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.01 apply (zenon_L155_); trivial. % 29.81/30.01 exact (zenon_H18e zenon_H40). % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L416_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L412_); trivial. % 29.81/30.01 apply (zenon_L342_); trivial. % 29.81/30.01 (* end of lemma zenon_L447_ *) % 29.81/30.01 assert (zenon_L448_ : (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> False). % 29.81/30.01 do 0 intro. intros zenon_H74 zenon_H172 zenon_H14e zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H17d zenon_Hc0 zenon_H246 zenon_H18e zenon_H135 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H218 zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H1e zenon_H2d zenon_H42 zenon_H112 zenon_H100 zenon_Hb8 zenon_H1bd zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H5e zenon_H1ca zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_H159 zenon_H3c zenon_H101 zenon_H19a zenon_H83 zenon_H84 zenon_H16a zenon_Hdf zenon_H6b zenon_H3f zenon_Hbd zenon_He7 zenon_H1dc zenon_Hc8 zenon_Had zenon_Hee zenon_H20 zenon_H23b zenon_H8d zenon_Hb5 zenon_H18c zenon_H225 zenon_He4 zenon_H200 zenon_H125 zenon_H231 zenon_H10d zenon_Hf9 zenon_H1fd zenon_Hd9 zenon_H15a zenon_H16f zenon_H1f zenon_H173 zenon_H20e zenon_H174 zenon_H27 zenon_H5c zenon_H20d zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H6f zenon_H6c zenon_He1. % 29.81/30.01 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.01 exact (zenon_H74 zenon_H73). % 29.81/30.01 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.01 apply (zenon_L417_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_L378_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L154_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L412_); trivial. % 29.81/30.01 apply (zenon_L444_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.01 apply (zenon_L445_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.01 apply (zenon_L271_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.01 apply (zenon_L446_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.01 apply (zenon_L224_); trivial. % 29.81/30.01 apply (zenon_L411_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.01 apply (zenon_L235_); trivial. % 29.81/30.01 apply (zenon_L101_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L154_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L412_); trivial. % 29.81/30.01 apply (zenon_L342_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/30.01 apply (zenon_L42_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.01 apply (zenon_L343_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.01 apply (zenon_L446_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.01 apply (zenon_L363_); trivial. % 29.81/30.01 apply (zenon_L383_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L154_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L309_); trivial. % 29.81/30.01 apply (zenon_L342_); trivial. % 29.81/30.01 apply (zenon_L447_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_L445_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L154_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L412_); trivial. % 29.81/30.01 apply (zenon_L342_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/30.01 apply (zenon_L42_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/30.01 apply (zenon_L343_); trivial. % 29.81/30.01 apply (zenon_L447_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.01 apply (zenon_L157_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.01 apply (zenon_L300_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.01 apply (zenon_L236_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.01 apply (zenon_L418_); trivial. % 29.81/30.01 apply (zenon_L360_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.01 apply (zenon_L49_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.01 apply (zenon_L387_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.01 apply (zenon_L4_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.01 apply (zenon_L385_); trivial. % 29.81/30.01 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.02 apply (zenon_L252_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.02 apply (zenon_L248_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.02 apply (zenon_L388_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.02 apply (zenon_L224_); trivial. % 29.81/30.02 apply (zenon_L355_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L145_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.02 apply (zenon_L311_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.02 apply (zenon_L427_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.02 apply (zenon_L234_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.02 apply (zenon_L431_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.02 apply (zenon_L303_); trivial. % 29.81/30.02 apply (zenon_L355_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L308_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.02 apply (zenon_L311_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.02 apply (zenon_L159_); trivial. % 29.81/30.02 apply (zenon_L428_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.02 apply (zenon_L157_); trivial. % 29.81/30.02 apply (zenon_L50_); trivial. % 29.81/30.02 (* end of lemma zenon_L448_ *) % 29.81/30.02 assert (zenon_L449_ : ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H112 zenon_Hd0 zenon_H19a zenon_H20e zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_Hb8 zenon_H117 zenon_H27 zenon_Hf6 zenon_H1d8 zenon_H1e6 zenon_H2d zenon_H6f zenon_H208 zenon_Hcd zenon_H19e zenon_H1d5 zenon_Hdf zenon_H6b zenon_H108 zenon_H174 zenon_H102 zenon_H35 zenon_Hfc zenon_Hdc zenon_Hd1 zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_Hd9 zenon_H1fd zenon_H135 zenon_H18c zenon_Hde zenon_H125 zenon_H1dc zenon_He7 zenon_H3f zenon_H5c zenon_Hbd zenon_H200 zenon_H1e zenon_H17b zenon_H14b zenon_He1 zenon_H55 zenon_H18e. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_L438_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L126_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 (* end of lemma zenon_L449_ *) % 29.81/30.02 assert (zenon_L450_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.81/30.02 do 0 intro. intros zenon_H8d zenon_Hd9 zenon_H18e zenon_H200 zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_H19e zenon_H19a zenon_Hfc zenon_H112 zenon_H102 zenon_H1bd zenon_H1af zenon_H23b zenon_H20 zenon_H1f zenon_H3f zenon_Hee zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H117 zenon_H6f zenon_H42 zenon_Hcd zenon_Hde zenon_H18c zenon_H173 zenon_He1 zenon_Hc9 zenon_H2d zenon_H8b. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.02 apply (zenon_L149_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.02 apply (zenon_L142_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.02 apply (zenon_L322_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.02 apply (zenon_L159_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_L338_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L281_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.02 apply (zenon_L273_); trivial. % 29.81/30.02 apply (zenon_L25_); trivial. % 29.81/30.02 (* end of lemma zenon_L450_ *) % 29.81/30.02 assert (zenon_L451_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H92 zenon_H84 zenon_H1b1 zenon_Hde zenon_H174 zenon_Hd6 zenon_Hc8 zenon_H1ca zenon_H5e zenon_H1c7 zenon_H16f zenon_H15a zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H6f zenon_H10d zenon_H100 zenon_Had zenon_Hb8 zenon_Hee zenon_H3f zenon_H1f zenon_H23b zenon_Hd9 zenon_H8d zenon_H173 zenon_H18c zenon_Hcd zenon_H101 zenon_H159 zenon_H42 zenon_H2d zenon_H156 zenon_Hd0 zenon_H222 zenon_H1d5 zenon_He1 zenon_H60 zenon_H218 zenon_H135 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H200 zenon_H18e zenon_Hb5 zenon_H108 zenon_H1d2 zenon_H208 zenon_H225 zenon_He4 zenon_H125 zenon_H231 zenon_Hf9 zenon_H1fd zenon_H20e zenon_H27 zenon_H14b zenon_H20d zenon_Hd1 zenon_H35 zenon_H74 zenon_H8b zenon_H20. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.81/30.02 exact (zenon_H84 zenon_H88). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.81/30.02 apply (zenon_L147_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.02 exact (zenon_H74 zenon_H73). % 29.81/30.02 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.02 apply (zenon_L340_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.02 apply (zenon_L335_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.02 apply (zenon_L450_); trivial. % 29.81/30.02 apply (zenon_L285_); trivial. % 29.81/30.02 apply (zenon_L288_); trivial. % 29.81/30.02 apply (zenon_L27_); trivial. % 29.81/30.02 (* end of lemma zenon_L451_ *) % 29.81/30.02 assert (zenon_L452_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.81/30.02 do 0 intro. intros zenon_Hf6 zenon_H1e6 zenon_H172 zenon_H14e zenon_H246 zenon_H83 zenon_H16a zenon_H11e zenon_H17d zenon_Hc0 zenon_H20 zenon_H74 zenon_H35 zenon_Hd1 zenon_H20d zenon_H14b zenon_H27 zenon_H20e zenon_H1fd zenon_Hf9 zenon_H231 zenon_H125 zenon_He4 zenon_H225 zenon_H208 zenon_H1d2 zenon_H108 zenon_Hb5 zenon_H18e zenon_H200 zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_H19e zenon_Hfc zenon_H102 zenon_H1bd zenon_H1af zenon_H135 zenon_H218 zenon_H60 zenon_He1 zenon_H1d5 zenon_H222 zenon_Hd0 zenon_H156 zenon_H2d zenon_H42 zenon_H159 zenon_H101 zenon_Hcd zenon_H18c zenon_H173 zenon_H8d zenon_Hd9 zenon_H23b zenon_H3f zenon_Hee zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H6f zenon_Hbd zenon_He7 zenon_H1dc zenon_H6b zenon_H15a zenon_H16f zenon_H1c7 zenon_H5e zenon_H1ca zenon_Hc8 zenon_Hd6 zenon_H174 zenon_Hde zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H19a zenon_H112 zenon_Ha4. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.81/30.02 exact (zenon_H84 zenon_H88). % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.81/30.02 exact (zenon_H84 zenon_H88). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.81/30.02 apply (zenon_L147_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.81/30.02 exact (zenon_H74 zenon_H73). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.02 exact (zenon_H74 zenon_H73). % 29.81/30.02 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.02 apply (zenon_L148_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.02 apply (zenon_L190_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.02 apply (zenon_L231_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/30.02 apply (zenon_L346_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/30.02 apply (zenon_L349_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.02 apply (zenon_L344_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.02 apply (zenon_L207_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.02 apply (zenon_L350_); trivial. % 29.81/30.02 apply (zenon_L295_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L145_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 apply (zenon_L353_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.02 apply (zenon_L157_); trivial. % 29.81/30.02 apply (zenon_L374_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.02 apply (zenon_L399_); trivial. % 29.81/30.02 apply (zenon_L395_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.02 exact (zenon_H74 zenon_H73). % 29.81/30.02 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.02 apply (zenon_L421_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.02 apply (zenon_L422_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.02 apply (zenon_L148_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/30.02 apply (zenon_L423_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/30.02 apply (zenon_L42_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/30.02 apply (zenon_L424_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.02 apply (zenon_L353_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.02 apply (zenon_L416_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.02 apply (zenon_L412_); trivial. % 29.81/30.02 apply (zenon_L342_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.02 apply (zenon_L157_); trivial. % 29.81/30.02 apply (zenon_L425_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.02 apply (zenon_L420_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.02 apply (zenon_L252_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.02 apply (zenon_L385_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.02 apply (zenon_L252_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/30.02 apply (zenon_L429_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/30.02 apply (zenon_L42_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/30.02 apply (zenon_L432_); trivial. % 29.81/30.02 apply (zenon_L393_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.02 apply (zenon_L157_); trivial. % 29.81/30.02 apply (zenon_L50_); trivial. % 29.81/30.02 apply (zenon_L442_); trivial. % 29.81/30.02 apply (zenon_L139_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.81/30.02 apply (zenon_L136_); trivial. % 29.81/30.02 apply (zenon_L140_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.81/30.02 exact (zenon_H84 zenon_H88). % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.81/30.02 exact (zenon_H84 zenon_H88). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.81/30.02 apply (zenon_L147_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.81/30.02 exact (zenon_H74 zenon_H73). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.02 exact (zenon_H74 zenon_H73). % 29.81/30.02 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.02 apply (zenon_L231_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.02 apply (zenon_L190_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.02 apply (zenon_L443_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.02 apply (zenon_L346_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.02 apply (zenon_L157_); trivial. % 29.81/30.02 apply (zenon_L374_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.02 apply (zenon_L399_); trivial. % 29.81/30.02 apply (zenon_L395_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.02 exact (zenon_H74 zenon_H73). % 29.81/30.02 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.02 apply (zenon_L421_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.02 apply (zenon_L422_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.02 apply (zenon_L443_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.02 apply (zenon_L154_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.02 apply (zenon_L412_); trivial. % 29.81/30.02 apply (zenon_L342_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.02 apply (zenon_L423_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.02 apply (zenon_L157_); trivial. % 29.81/30.02 apply (zenon_L425_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.02 apply (zenon_L420_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.02 apply (zenon_L252_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.02 apply (zenon_L385_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.02 apply (zenon_L252_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.02 apply (zenon_L429_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.02 apply (zenon_L157_); trivial. % 29.81/30.02 apply (zenon_L50_); trivial. % 29.81/30.02 apply (zenon_L442_); trivial. % 29.81/30.02 apply (zenon_L139_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.81/30.02 apply (zenon_L136_); trivial. % 29.81/30.02 apply (zenon_L140_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.81/30.02 exact (zenon_H84 zenon_H88). % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.81/30.02 exact (zenon_H84 zenon_H88). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.81/30.02 apply (zenon_L147_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.81/30.02 exact (zenon_H74 zenon_H73). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.81/30.02 apply (zenon_L396_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.81/30.02 apply (zenon_L448_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.02 exact (zenon_H74 zenon_H73). % 29.81/30.02 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.02 apply (zenon_L436_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.02 apply (zenon_L378_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.02 apply (zenon_L154_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.02 apply (zenon_L449_); trivial. % 29.81/30.02 apply (zenon_L444_); trivial. % 29.81/30.02 apply (zenon_L267_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.02 apply (zenon_L49_); trivial. % 29.81/30.02 apply (zenon_L441_); trivial. % 29.81/30.02 apply (zenon_L139_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.81/30.02 apply (zenon_L136_); trivial. % 29.81/30.02 apply (zenon_L140_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.81/30.02 exact (zenon_H84 zenon_H88). % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.81/30.02 apply (zenon_L451_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.81/30.02 apply (zenon_L136_); trivial. % 29.81/30.02 apply (zenon_L140_); trivial. % 29.81/30.02 (* end of lemma zenon_L452_ *) % 29.81/30.02 assert (zenon_L453_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H1a8 zenon_Hdc zenon_Ha4 zenon_H1a5 zenon_H92 zenon_H84 zenon_H1b1 zenon_Hde zenon_H174 zenon_Hd6 zenon_Hc8 zenon_H1ca zenon_H5e zenon_H1c7 zenon_H16f zenon_H15a zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H6f zenon_H10d zenon_H100 zenon_Had zenon_Hb8 zenon_Hee zenon_H3f zenon_H23b zenon_Hd9 zenon_H8d zenon_H173 zenon_H18c zenon_Hcd zenon_H101 zenon_H159 zenon_H42 zenon_H2d zenon_H156 zenon_Hd0 zenon_H222 zenon_H1d5 zenon_He1 zenon_H60 zenon_H218 zenon_H135 zenon_H1af zenon_H1bd zenon_H102 zenon_Hfc zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H200 zenon_H18e zenon_Hb5 zenon_H108 zenon_H1d2 zenon_H208 zenon_H225 zenon_He4 zenon_H125 zenon_H231 zenon_Hf9 zenon_H1fd zenon_H20e zenon_H27 zenon_H14b zenon_H20d zenon_Hd1 zenon_H35 zenon_H74 zenon_H20 zenon_Hc0 zenon_H17d zenon_H11e zenon_H16a zenon_H83 zenon_H246 zenon_H172 zenon_H1e6 zenon_Hf6 zenon_H112 zenon_H14e. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.81/30.02 apply (zenon_L48_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.81/30.02 apply (zenon_L146_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.81/30.02 apply (zenon_L452_); trivial. % 29.81/30.02 apply (zenon_L137_); trivial. % 29.81/30.02 (* end of lemma zenon_L453_ *) % 29.81/30.02 assert (zenon_L454_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H1f zenon_H5e zenon_H3c zenon_He9 zenon_H60 zenon_H1af zenon_H37 zenon_H19e. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.81/30.02 apply (zenon_L120_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.81/30.02 apply (zenon_L218_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.81/30.02 apply (zenon_L219_); trivial. % 29.81/30.02 apply (zenon_L214_); trivial. % 29.81/30.02 (* end of lemma zenon_L454_ *) % 29.81/30.02 assert (zenon_L455_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H1e6 zenon_H142 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1af zenon_H3d zenon_H1c7. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 29.81/30.02 apply (zenon_L296_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 29.81/30.02 apply (zenon_L187_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 29.81/30.02 apply (zenon_L144_); trivial. % 29.81/30.02 apply (zenon_L167_); trivial. % 29.81/30.02 (* end of lemma zenon_L455_ *) % 29.81/30.02 assert (zenon_L456_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 29.81/30.02 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_H1e zenon_H3c zenon_H1c7 zenon_Hd6 zenon_Hf6 zenon_H112 zenon_H108 zenon_H1e6 zenon_H1bd zenon_H1af zenon_H3d. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.02 apply (zenon_L49_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.02 apply (zenon_L207_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.02 apply (zenon_L455_); trivial. % 29.81/30.02 apply (zenon_L209_); trivial. % 29.81/30.02 (* end of lemma zenon_L456_ *) % 29.81/30.02 assert (zenon_L457_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H42 zenon_H2d zenon_H19e zenon_H60 zenon_He9 zenon_H5e zenon_H1f zenon_H18c zenon_H68 zenon_H208 zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_L454_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L456_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 (* end of lemma zenon_L457_ *) % 29.81/30.02 assert (zenon_L458_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H42 zenon_H2d zenon_Hd2 zenon_H6f zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_L125_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L456_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 (* end of lemma zenon_L458_ *) % 29.81/30.02 assert (zenon_L459_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 29.81/30.02 do 0 intro. intros zenon_H14b zenon_H112 zenon_H18e zenon_H6e zenon_Had zenon_Hb8 zenon_H19a zenon_H125 zenon_He1 zenon_H1dc zenon_H1af zenon_Hd6 zenon_H1d5 zenon_Hd0 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_H1ca zenon_H37 zenon_H108 zenon_Hde zenon_H135 zenon_H6b zenon_Hdf zenon_H2d zenon_Hb6. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.02 apply (zenon_L234_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.02 apply (zenon_L302_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.02 apply (zenon_L303_); trivial. % 29.81/30.02 apply (zenon_L304_); trivial. % 29.81/30.02 (* end of lemma zenon_L459_ *) % 29.81/30.02 assert (zenon_L460_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H42 zenon_H1e zenon_Hb6 zenon_H2d zenon_Hdf zenon_H6b zenon_Hde zenon_H108 zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_H1dc zenon_H125 zenon_H19a zenon_Hb8 zenon_Had zenon_H6e zenon_H112 zenon_H14b zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_L459_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L145_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 (* end of lemma zenon_L460_ *) % 29.81/30.02 assert (zenon_L461_ : ((op (e3) (e2)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 29.81/30.02 do 0 intro. intros zenon_Hb6 zenon_H8a zenon_Hb5. % 29.81/30.02 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 29.81/30.02 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e0)) = (op (e3) (e2)))). % 29.81/30.02 intro zenon_D_pnotp. % 29.81/30.02 apply zenon_Hb5. % 29.81/30.02 rewrite <- zenon_D_pnotp. % 29.81/30.02 exact zenon_Hef. % 29.81/30.02 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.81/30.02 cut (((op (e3) (e2)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H24c]. % 29.81/30.02 congruence. % 29.81/30.02 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e0)))). % 29.81/30.02 intro zenon_D_pnotp. % 29.81/30.02 apply zenon_H24c. % 29.81/30.02 rewrite <- zenon_D_pnotp. % 29.81/30.02 exact zenon_Hb6. % 29.81/30.02 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 29.81/30.02 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.81/30.02 congruence. % 29.81/30.02 apply zenon_Hf0. apply refl_equal. % 29.81/30.02 apply zenon_H1e3. apply sym_equal. exact zenon_H8a. % 29.81/30.02 apply zenon_Hf0. apply refl_equal. % 29.81/30.02 apply zenon_Hf0. apply refl_equal. % 29.81/30.02 (* end of lemma zenon_L461_ *) % 29.81/30.02 assert (zenon_L462_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H8d zenon_H156 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_He7 zenon_He9 zenon_H3c zenon_H20e zenon_H27 zenon_H1fd zenon_Hd9 zenon_Hfc zenon_H200 zenon_H20d zenon_H15a zenon_H16f zenon_H18e zenon_H135 zenon_H18c zenon_Hdc zenon_He1 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H14b zenon_H112 zenon_Had zenon_Hb8 zenon_H19a zenon_H125 zenon_H1dc zenon_H1d5 zenon_H19e zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H1ca zenon_H108 zenon_Hde zenon_H6b zenon_Hdf zenon_H2d zenon_H1e zenon_H42 zenon_H6f zenon_H6c zenon_Hb6 zenon_Hb5. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.02 apply (zenon_L241_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.02 apply (zenon_L211_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.02 apply (zenon_L302_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.02 apply (zenon_L224_); trivial. % 29.81/30.02 apply (zenon_L304_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.02 apply (zenon_L363_); trivial. % 29.81/30.02 apply (zenon_L326_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.02 apply (zenon_L460_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.02 apply (zenon_L157_); trivial. % 29.81/30.02 apply (zenon_L461_); trivial. % 29.81/30.02 (* end of lemma zenon_L462_ *) % 29.81/30.02 assert (zenon_L463_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H14b zenon_H17d zenon_H225 zenon_H125 zenon_H19a zenon_Had zenon_H18e zenon_H8d zenon_H5c zenon_H27 zenon_H174 zenon_H102 zenon_H35 zenon_Hd1 zenon_H42 zenon_H16a zenon_H200 zenon_Hfc zenon_H1fd zenon_Hbd zenon_H1d8 zenon_H3f zenon_H1e zenon_H15a zenon_H16f zenon_H3c zenon_He7 zenon_H84 zenon_Hd9 zenon_H83 zenon_H218 zenon_H173 zenon_H156 zenon_He4 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H69 zenon_H20 zenon_H20e zenon_H159 zenon_H101 zenon_H222 zenon_H18c zenon_Hc0 zenon_Hb6 zenon_H1dc zenon_H1af zenon_Hd6 zenon_H1d5 zenon_Hd0 zenon_H19e zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_H1ca zenon_H108 zenon_Hde zenon_H135 zenon_H6b zenon_Hdf zenon_Hb8 zenon_He2 zenon_He1 zenon_H100 zenon_H37 zenon_H2d zenon_H112 zenon_H6f. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.02 apply (zenon_L400_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.02 apply (zenon_L302_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.02 apply (zenon_L303_); trivial. % 29.81/30.02 apply (zenon_L355_); trivial. % 29.81/30.02 (* end of lemma zenon_L463_ *) % 29.81/30.02 assert (zenon_L464_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H42 zenon_H2d zenon_He1 zenon_Hb6 zenon_H1dc zenon_H1af zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_H1ca zenon_Hfe zenon_H108 zenon_Hde zenon_Hdf zenon_H135 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_L302_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L155_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 (* end of lemma zenon_L464_ *) % 29.81/30.02 assert (zenon_L465_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H173 zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_Hdf zenon_Hde zenon_H6b zenon_H1dc zenon_Hb6 zenon_H19a zenon_H101 zenon_H3c zenon_H159 zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H5e zenon_H6c zenon_H1ca zenon_Hfe zenon_H108 zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_H222 zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.02 apply (zenon_L464_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.02 apply (zenon_L311_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.02 apply (zenon_L159_); trivial. % 29.81/30.02 apply (zenon_L314_); trivial. % 29.81/30.02 (* end of lemma zenon_L465_ *) % 29.81/30.02 assert (zenon_L466_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.02 do 0 intro. intros zenon_Hee zenon_H1f zenon_H23b zenon_H10d zenon_H172 zenon_H14b zenon_H17d zenon_H225 zenon_H125 zenon_Had zenon_H8d zenon_H5c zenon_H27 zenon_H174 zenon_H16a zenon_H200 zenon_H1fd zenon_H15a zenon_H16f zenon_He7 zenon_H84 zenon_Hd9 zenon_H83 zenon_He4 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H20 zenon_H20e zenon_H18c zenon_Hc0 zenon_H218 zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H108 zenon_H1ca zenon_H6c zenon_H5e zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H159 zenon_H3c zenon_H101 zenon_H19a zenon_Hb6 zenon_H1dc zenon_H6b zenon_Hdf zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H173 zenon_H42 zenon_H14e zenon_Hb8 zenon_H100 zenon_H2d zenon_H112 zenon_H6f zenon_H3f zenon_H1e zenon_Hde zenon_Hbd zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.02 apply (zenon_L387_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.02 apply (zenon_L151_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_L463_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L308_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/30.02 apply (zenon_L42_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/30.02 apply (zenon_L465_); trivial. % 29.81/30.02 apply (zenon_L393_); trivial. % 29.81/30.02 (* end of lemma zenon_L466_ *) % 29.81/30.02 assert (zenon_L467_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.02 do 0 intro. intros zenon_H42 zenon_Hb6 zenon_H2d zenon_Hdf zenon_H6b zenon_H135 zenon_Hde zenon_H108 zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_Hd0 zenon_H1d5 zenon_Hd6 zenon_H1af zenon_H1dc zenon_He1 zenon_Hda zenon_H14b zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.02 apply (zenon_L4_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.02 apply (zenon_L305_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.02 apply (zenon_L155_); trivial. % 29.81/30.02 exact (zenon_H18e zenon_H40). % 29.81/30.02 (* end of lemma zenon_L467_ *) % 29.81/30.02 assert (zenon_L468_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 29.81/30.02 do 0 intro. intros zenon_H14b zenon_H18e zenon_H125 zenon_Hde zenon_H222 zenon_H1f zenon_H3c zenon_H20e zenon_H19a zenon_Hd1 zenon_H101 zenon_Hdc zenon_H18c zenon_H135 zenon_H218 zenon_H17b zenon_H1fd zenon_H89 zenon_Hd9 zenon_Hfc zenon_H1e zenon_H42 zenon_H108 zenon_Hd0 zenon_H37 zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H1af zenon_H1c7 zenon_H1d2 zenon_He1 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_H55 zenon_H60 zenon_H1bd zenon_H2d zenon_Hb6. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.02 apply (zenon_L261_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.02 apply (zenon_L217_); trivial. % 29.81/30.02 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.03 apply (zenon_L165_); trivial. % 29.81/30.03 apply (zenon_L304_); trivial. % 29.81/30.03 (* end of lemma zenon_L468_ *) % 29.81/30.03 assert (zenon_L469_ : ((op (e2) (e0)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.81/30.03 do 0 intro. intros zenon_Hdf zenon_Hb6 zenon_H2d zenon_H1bd zenon_H60 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H37 zenon_H108 zenon_H42 zenon_H1e zenon_Hfc zenon_Hd9 zenon_H89 zenon_H1fd zenon_H135 zenon_H18c zenon_Hdc zenon_H101 zenon_Hd1 zenon_H19a zenon_H20e zenon_H3c zenon_H1f zenon_H222 zenon_Hde zenon_H125 zenon_H18e zenon_H14b zenon_Hd0 zenon_H17b zenon_H218. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/30.03 apply (zenon_L49_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/30.03 apply (zenon_L468_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/30.03 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.03 apply (zenon_L405_); trivial. % 29.81/30.03 (* end of lemma zenon_L469_ *) % 29.81/30.03 assert (zenon_L470_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.81/30.03 do 0 intro. intros zenon_H16f zenon_H15a zenon_H218 zenon_H17b zenon_H14b zenon_H125 zenon_H222 zenon_H1f zenon_H19a zenon_Hd1 zenon_H101 zenon_Hdc zenon_H18c zenon_H1fd zenon_Hd9 zenon_Hfc zenon_H42 zenon_H108 zenon_H1ca zenon_H6c zenon_H5e zenon_H1c7 zenon_H1d2 zenon_He1 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H60 zenon_H1bd zenon_Hb6 zenon_H20e zenon_H135 zenon_Hde zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H2d zenon_H1dc zenon_H18e zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1e zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1af zenon_H156. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.03 apply (zenon_L241_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.03 apply (zenon_L469_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.03 apply (zenon_L363_); trivial. % 29.81/30.03 apply (zenon_L326_); trivial. % 29.81/30.03 (* end of lemma zenon_L470_ *) % 29.81/30.03 assert (zenon_L471_ : ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.03 do 0 intro. intros zenon_Hb6 zenon_H2d zenon_H1bd zenon_H60 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_Hd0 zenon_H108 zenon_H42 zenon_H1e zenon_Hfc zenon_Hd9 zenon_H89 zenon_H1fd zenon_H17b zenon_H218 zenon_H135 zenon_H18c zenon_Hdc zenon_H101 zenon_Hd1 zenon_H19a zenon_H20e zenon_H3c zenon_H1f zenon_H222 zenon_Hde zenon_H125 zenon_H14b zenon_He1 zenon_H55 zenon_H18e. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.03 apply (zenon_L4_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.03 apply (zenon_L468_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.03 apply (zenon_L126_); trivial. % 29.81/30.03 exact (zenon_H18e zenon_H40). % 29.81/30.03 (* end of lemma zenon_L471_ *) % 29.81/30.03 assert (zenon_L472_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.81/30.03 do 0 intro. intros zenon_H174 zenon_He2 zenon_H112 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_H17b zenon_He1. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.03 apply (zenon_L252_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.03 apply (zenon_L4_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.03 apply (zenon_L151_); trivial. % 29.81/30.03 apply (zenon_L267_); trivial. % 29.81/30.03 (* end of lemma zenon_L472_ *) % 29.81/30.03 assert (zenon_L473_ : (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.81/30.03 do 0 intro. intros zenon_He1 zenon_Hb6 zenon_H10d zenon_H1e zenon_H2d zenon_H174 zenon_Hde zenon_Hdf zenon_H218 zenon_Hd0 zenon_H222 zenon_H135 zenon_H1bd zenon_H60 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H5e zenon_Hd6 zenon_H1ca zenon_H108 zenon_H42 zenon_Hfc zenon_Hd9 zenon_H1fd zenon_H18c zenon_H101 zenon_Hd1 zenon_H19a zenon_H20e zenon_H3c zenon_H1f zenon_H125 zenon_H14b zenon_H18e zenon_H16f zenon_H15a zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H156 zenon_H74 zenon_He4 zenon_Hee zenon_H23b zenon_H172 zenon_H225 zenon_Had zenon_H8d zenon_H27 zenon_H16a zenon_H200 zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H20 zenon_Hc0 zenon_H159 zenon_H35 zenon_H102 zenon_H173 zenon_H14e zenon_H100 zenon_Hb5 zenon_H20d zenon_H17d zenon_H112. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.81/30.03 exact (zenon_H84 zenon_H88). % 29.81/30.03 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.81/30.03 apply (zenon_L147_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.81/30.03 exact (zenon_H74 zenon_H73). % 29.81/30.03 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.81/30.03 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.03 exact (zenon_H74 zenon_H73). % 29.81/30.03 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.03 apply (zenon_L462_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.03 apply (zenon_L49_); trivial. % 29.81/30.03 apply (zenon_L466_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.81/30.03 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.03 exact (zenon_H74 zenon_H73). % 29.81/30.03 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.03 apply (zenon_L467_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.03 apply (zenon_L49_); trivial. % 29.81/30.03 apply (zenon_L466_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.03 exact (zenon_H74 zenon_H73). % 29.81/30.03 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.03 apply (zenon_L470_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.03 apply (zenon_L154_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.03 apply (zenon_L471_); trivial. % 29.81/30.03 apply (zenon_L406_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.03 apply (zenon_L4_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.03 apply (zenon_L151_); trivial. % 29.81/30.03 apply (zenon_L267_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.03 apply (zenon_L49_); trivial. % 29.81/30.03 apply (zenon_L472_); trivial. % 29.81/30.03 apply (zenon_L139_); trivial. % 29.81/30.03 (* end of lemma zenon_L473_ *) % 29.81/30.03 assert (zenon_L474_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 29.81/30.03 do 0 intro. intros zenon_H17d zenon_H20d zenon_Hb5 zenon_H100 zenon_H14e zenon_H173 zenon_H35 zenon_H159 zenon_Hc0 zenon_H20 zenon_H1a5 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H200 zenon_H16a zenon_H27 zenon_H8d zenon_Had zenon_H225 zenon_H172 zenon_H23b zenon_Hee zenon_He4 zenon_H74 zenon_H156 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_H15a zenon_H16f zenon_H18e zenon_H14b zenon_H125 zenon_H1f zenon_H20e zenon_Hd1 zenon_H101 zenon_H18c zenon_H1fd zenon_Hd9 zenon_H42 zenon_H108 zenon_H1ca zenon_Hd6 zenon_H5e zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H1d5 zenon_H60 zenon_H135 zenon_H222 zenon_Hd0 zenon_H218 zenon_Hde zenon_H174 zenon_H2d zenon_H10d zenon_Hb6 zenon_He1 zenon_H1e zenon_H3c zenon_H19e zenon_H19a zenon_Hfc zenon_H155 zenon_H112 zenon_H102 zenon_H1bd zenon_H1af zenon_H3d. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.03 apply (zenon_L473_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.03 apply (zenon_L207_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.03 apply (zenon_L280_); trivial. % 29.81/30.03 apply (zenon_L209_); trivial. % 29.81/30.03 (* end of lemma zenon_L474_ *) % 29.81/30.03 assert (zenon_L475_ : ((op (e0) (e3)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.03 do 0 intro. intros zenon_H16b zenon_Hc9 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_He1 zenon_Hb6 zenon_H10d zenon_H2d zenon_H174 zenon_Hde zenon_H218 zenon_Hd0 zenon_H222 zenon_H135 zenon_H60 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H5e zenon_Hd6 zenon_H1ca zenon_H108 zenon_H42 zenon_Hd9 zenon_H1fd zenon_H18c zenon_H101 zenon_Hd1 zenon_H20e zenon_H1f zenon_H125 zenon_H14b zenon_H16f zenon_H15a zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H156 zenon_H74 zenon_He4 zenon_Hee zenon_H23b zenon_H172 zenon_H225 zenon_Had zenon_H8d zenon_H27 zenon_H16a zenon_H200 zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H20 zenon_Hc0 zenon_H159 zenon_H35 zenon_H173 zenon_H14e zenon_H100 zenon_Hb5 zenon_H20d zenon_H17d zenon_H18e. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.03 apply (zenon_L142_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.03 apply (zenon_L322_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.03 apply (zenon_L159_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.03 apply (zenon_L4_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.03 apply (zenon_L274_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.03 apply (zenon_L474_); trivial. % 29.81/30.03 exact (zenon_H18e zenon_H40). % 29.81/30.03 (* end of lemma zenon_L475_ *) % 29.81/30.03 assert (zenon_L476_ : (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> False). % 29.81/30.03 do 0 intro. intros zenon_H18e zenon_H17d zenon_Hb5 zenon_H100 zenon_H14e zenon_H173 zenon_H35 zenon_H159 zenon_Hc0 zenon_H20 zenon_H1a5 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H200 zenon_H16a zenon_H27 zenon_H8d zenon_Had zenon_H225 zenon_H172 zenon_H23b zenon_Hee zenon_He4 zenon_H74 zenon_H156 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_H15a zenon_H16f zenon_H14b zenon_H125 zenon_H1f zenon_H20e zenon_Hd1 zenon_H101 zenon_H18c zenon_H1fd zenon_Hd9 zenon_H42 zenon_H108 zenon_H1ca zenon_Hd6 zenon_H5e zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H1d5 zenon_H135 zenon_H222 zenon_H218 zenon_Hde zenon_H174 zenon_H2d zenon_H10d zenon_Hb6 zenon_He1 zenon_H1e zenon_H3c zenon_H19e zenon_H19a zenon_Hfc zenon_H112 zenon_H102 zenon_H1af zenon_H16b zenon_H1bd zenon_Hd0 zenon_H20d zenon_H60 zenon_H142. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.81/30.03 apply (zenon_L475_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.81/30.03 apply (zenon_L165_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.81/30.03 exact (zenon_Hd0 zenon_Hcc). % 29.81/30.03 apply (zenon_L223_); trivial. % 29.81/30.03 (* end of lemma zenon_L476_ *) % 29.81/30.03 assert (zenon_L477_ : ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.03 do 0 intro. intros zenon_Hb6 zenon_H2d zenon_H108 zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_Hde zenon_H64 zenon_Hd9 zenon_H14b zenon_H17d zenon_Hb5 zenon_H100 zenon_H14e zenon_H173 zenon_H35 zenon_H159 zenon_Hc0 zenon_H20 zenon_H1a5 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H200 zenon_H16a zenon_H27 zenon_H8d zenon_Had zenon_H225 zenon_H172 zenon_H23b zenon_Hee zenon_He4 zenon_H74 zenon_H156 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_H15a zenon_H16f zenon_H125 zenon_H1f zenon_H20e zenon_Hd1 zenon_H101 zenon_H1fd zenon_H42 zenon_H222 zenon_H218 zenon_H174 zenon_H10d zenon_H1e zenon_H3c zenon_H19a zenon_Hfc zenon_H112 zenon_H102 zenon_H16b zenon_H20d zenon_H6e zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.03 apply (zenon_L4_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.03 apply (zenon_L459_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.03 apply (zenon_L207_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.03 apply (zenon_L476_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.03 apply (zenon_L242_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.03 apply (zenon_L295_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.03 apply (zenon_L296_); trivial. % 29.81/30.03 apply (zenon_L304_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.03 apply (zenon_L145_); trivial. % 29.81/30.03 exact (zenon_H18e zenon_H40). % 29.81/30.03 (* end of lemma zenon_L477_ *) % 29.81/30.03 assert (zenon_L478_ : (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 29.81/30.03 do 0 intro. intros zenon_H18e zenon_H135 zenon_H18c zenon_Hdc zenon_He1 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H20d zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H3c zenon_H1e zenon_H10d zenon_H174 zenon_H218 zenon_H222 zenon_H42 zenon_H1fd zenon_H101 zenon_Hd1 zenon_H20e zenon_H1f zenon_H125 zenon_H16f zenon_H15a zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H156 zenon_H74 zenon_He4 zenon_Hee zenon_H23b zenon_H172 zenon_H225 zenon_Had zenon_H8d zenon_H27 zenon_H16a zenon_H200 zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H20 zenon_Hc0 zenon_H159 zenon_H35 zenon_H173 zenon_H14e zenon_H100 zenon_H17d zenon_H14b zenon_Hd9 zenon_H64 zenon_Hde zenon_H1d5 zenon_H19e zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H1ca zenon_H108 zenon_H2d zenon_H6f zenon_H6c zenon_Hb6 zenon_Hb5. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.03 apply (zenon_L148_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.03 apply (zenon_L4_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.03 apply (zenon_L151_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.03 apply (zenon_L148_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.03 apply (zenon_L477_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.03 apply (zenon_L157_); trivial. % 29.81/30.03 apply (zenon_L461_); trivial. % 29.81/30.03 (* end of lemma zenon_L478_ *) % 29.81/30.03 assert (zenon_L479_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.81/30.03 do 0 intro. intros zenon_H17d zenon_H20d zenon_Hb5 zenon_H100 zenon_H14e zenon_H173 zenon_H102 zenon_H35 zenon_H159 zenon_Hc0 zenon_H20 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H200 zenon_H16a zenon_H27 zenon_H8d zenon_Had zenon_H225 zenon_H172 zenon_H23b zenon_Hee zenon_He4 zenon_H74 zenon_H156 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_H15a zenon_H16f zenon_H18e zenon_H14b zenon_H125 zenon_H3c zenon_H20e zenon_Hd1 zenon_H101 zenon_H18c zenon_H1fd zenon_Hd9 zenon_Hfc zenon_H42 zenon_H108 zenon_H1ca zenon_Hd6 zenon_H5e zenon_H1af zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_H60 zenon_H1bd zenon_H135 zenon_H222 zenon_Hd0 zenon_H218 zenon_Hdf zenon_Hde zenon_H174 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_He1 zenon_H1a5 zenon_H19a zenon_H112 zenon_Ha4. % 29.81/30.03 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.81/30.03 exact (zenon_H84 zenon_H88). % 29.81/30.03 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.81/30.03 apply (zenon_L473_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.81/30.03 apply (zenon_L136_); trivial. % 29.81/30.03 apply (zenon_L140_); trivial. % 29.81/30.03 (* end of lemma zenon_L479_ *) % 29.81/30.03 assert (zenon_L480_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 29.81/30.03 do 0 intro. intros zenon_H1d5 zenon_H37 zenon_He9 zenon_H3c zenon_H1f zenon_H6f zenon_H208 zenon_H19e zenon_H19a zenon_Hfc zenon_H155 zenon_H112 zenon_H102 zenon_H1dc zenon_Hb6 zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H142 zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/30.03 apply (zenon_L220_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/30.03 apply (zenon_L280_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/30.03 apply (zenon_L200_); trivial. % 29.81/30.03 apply (zenon_L168_); trivial. % 29.81/30.03 (* end of lemma zenon_L480_ *) % 29.81/30.03 assert (zenon_L481_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.81/30.03 do 0 intro. intros zenon_H200 zenon_H156 zenon_H16c zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H89 zenon_H18e zenon_H2d zenon_H6b zenon_Hd0 zenon_Hde zenon_H135 zenon_H1c7 zenon_H60 zenon_Hd6 zenon_Hb6 zenon_H1dc zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H208 zenon_H6f zenon_H1f zenon_H37 zenon_H1d5 zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.03 apply (zenon_L326_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.03 apply (zenon_L207_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.03 apply (zenon_L480_); trivial. % 29.81/30.03 apply (zenon_L210_); trivial. % 29.81/30.03 (* end of lemma zenon_L481_ *) % 29.81/30.03 assert (zenon_L482_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.03 do 0 intro. intros zenon_H17d zenon_H20d zenon_Hb5 zenon_H100 zenon_H14e zenon_H173 zenon_H35 zenon_H159 zenon_Hc0 zenon_H20 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H16a zenon_H27 zenon_H8d zenon_Had zenon_H225 zenon_H172 zenon_H23b zenon_Hee zenon_He4 zenon_H74 zenon_H15a zenon_H16f zenon_H14b zenon_H125 zenon_H20e zenon_Hd1 zenon_H101 zenon_H18c zenon_H1fd zenon_Hd9 zenon_H108 zenon_H1d2 zenon_Hcd zenon_H222 zenon_H218 zenon_H174 zenon_H10d zenon_He1 zenon_H1a5 zenon_Ha4 zenon_H42 zenon_H5e zenon_H6c zenon_H1ca zenon_H1f zenon_H6f zenon_H208 zenon_Hb6 zenon_H60 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H135 zenon_Hde zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H2d zenon_H1dc zenon_H89 zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H156 zenon_H200 zenon_H18e. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.03 apply (zenon_L241_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.03 apply (zenon_L479_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.03 apply (zenon_L207_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.03 apply (zenon_L480_); trivial. % 29.81/30.03 apply (zenon_L210_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.03 apply (zenon_L235_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.03 apply (zenon_L4_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.03 apply (zenon_L481_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.03 apply (zenon_L328_); trivial. % 29.81/30.03 exact (zenon_H18e zenon_H40). % 29.81/30.03 (* end of lemma zenon_L482_ *) % 29.81/30.03 assert (zenon_L483_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.03 do 0 intro. intros zenon_Ha4 zenon_Hc8 zenon_H89 zenon_H6c zenon_Hc9 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_He1 zenon_Hb6 zenon_H10d zenon_H2d zenon_H174 zenon_Hde zenon_H218 zenon_Hd0 zenon_H222 zenon_H135 zenon_H60 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H5e zenon_Hd6 zenon_H1ca zenon_H108 zenon_H42 zenon_Hd9 zenon_H1fd zenon_H18c zenon_H101 zenon_Hd1 zenon_H20e zenon_H1f zenon_H125 zenon_H14b zenon_H16f zenon_H15a zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H156 zenon_H74 zenon_He4 zenon_Hee zenon_H23b zenon_H172 zenon_H225 zenon_Had zenon_H8d zenon_H27 zenon_H16a zenon_H200 zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H20 zenon_Hc0 zenon_H159 zenon_H35 zenon_H173 zenon_H14e zenon_H100 zenon_Hb5 zenon_H20d zenon_H17d zenon_H18e. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.03 apply (zenon_L142_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.03 apply (zenon_L322_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.03 apply (zenon_L159_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.03 apply (zenon_L482_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.03 apply (zenon_L93_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.03 apply (zenon_L282_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.03 apply (zenon_L4_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.03 apply (zenon_L333_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.03 apply (zenon_L474_); trivial. % 29.81/30.03 exact (zenon_H18e zenon_H40). % 29.81/30.03 (* end of lemma zenon_L483_ *) % 29.81/30.03 assert (zenon_L484_ : ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.03 do 0 intro. intros zenon_H6c zenon_Hc8 zenon_Ha4 zenon_Hc9 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_He1 zenon_Hb6 zenon_H10d zenon_H2d zenon_H174 zenon_Hde zenon_H218 zenon_Hd0 zenon_H222 zenon_H135 zenon_H60 zenon_H1d5 zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H5e zenon_Hd6 zenon_H1ca zenon_H108 zenon_H42 zenon_Hd9 zenon_H1fd zenon_H18c zenon_H101 zenon_Hd1 zenon_H20e zenon_H1f zenon_H125 zenon_H14b zenon_H16f zenon_H15a zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H156 zenon_H74 zenon_He4 zenon_Hee zenon_H23b zenon_H172 zenon_H225 zenon_Had zenon_H8d zenon_H27 zenon_H16a zenon_H200 zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H20 zenon_Hc0 zenon_H159 zenon_H35 zenon_H173 zenon_H14e zenon_H100 zenon_Hb5 zenon_H20d zenon_H17d zenon_H18e. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.03 apply (zenon_L483_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.03 apply (zenon_L4_); trivial. % 29.81/30.03 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.03 apply (zenon_L151_); trivial. % 29.81/30.03 apply (zenon_L475_); trivial. % 29.81/30.03 (* end of lemma zenon_L484_ *) % 29.81/30.03 assert (zenon_L485_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.04 do 0 intro. intros zenon_H18c zenon_H6e zenon_H20d zenon_H102 zenon_H112 zenon_Hfc zenon_H10d zenon_H174 zenon_H222 zenon_H1fd zenon_H101 zenon_Hd1 zenon_H20e zenon_H1f zenon_H125 zenon_H16f zenon_H15a zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H5c zenon_Hbd zenon_H74 zenon_He4 zenon_Hee zenon_H23b zenon_H172 zenon_H225 zenon_Had zenon_H8d zenon_H27 zenon_H16a zenon_H200 zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H20 zenon_Hc0 zenon_H159 zenon_H35 zenon_H173 zenon_H14e zenon_H100 zenon_Hb5 zenon_H17d zenon_H14b zenon_Hd9 zenon_H64 zenon_Hde zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H5e zenon_H6c zenon_H1ca zenon_H108 zenon_Hb6 zenon_Hcd zenon_H19a zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_He9 zenon_H3c zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.04 apply (zenon_L477_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.04 apply (zenon_L311_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.04 apply (zenon_L159_); trivial. % 29.81/30.04 apply (zenon_L312_); trivial. % 29.81/30.04 (* end of lemma zenon_L485_ *) % 29.81/30.04 assert (zenon_L486_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.04 do 0 intro. intros zenon_H1bd zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1e zenon_H1ca zenon_H18c zenon_Hdc zenon_H20d zenon_H60 zenon_H14b zenon_H17d zenon_H225 zenon_H125 zenon_H19a zenon_Had zenon_H8d zenon_H5c zenon_H27 zenon_H174 zenon_H102 zenon_H35 zenon_Hd1 zenon_H42 zenon_H16a zenon_H200 zenon_Hfc zenon_H1fd zenon_Hbd zenon_H3f zenon_H15a zenon_H16f zenon_He7 zenon_H84 zenon_Hd9 zenon_H83 zenon_H218 zenon_H173 zenon_H156 zenon_He4 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H69 zenon_H20 zenon_H20e zenon_H159 zenon_H101 zenon_H222 zenon_Hc0 zenon_Hb6 zenon_H1dc zenon_H1d5 zenon_H19e zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H108 zenon_Hde zenon_H6b zenon_Hb8 zenon_H100 zenon_H2d zenon_H112 zenon_H6f zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.04 apply (zenon_L4_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.04 apply (zenon_L463_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.04 apply (zenon_L207_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.04 apply (zenon_L224_); trivial. % 29.81/30.04 apply (zenon_L210_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.04 apply (zenon_L308_); trivial. % 29.81/30.04 exact (zenon_H18e zenon_H40). % 29.81/30.04 (* end of lemma zenon_L486_ *) % 29.81/30.04 assert (zenon_L487_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.81/30.04 do 0 intro. intros zenon_H14b zenon_H112 zenon_H17d zenon_H225 zenon_H125 zenon_H19a zenon_Hb8 zenon_Had zenon_H18e zenon_H8d zenon_H5c zenon_H27 zenon_H174 zenon_H102 zenon_H35 zenon_Hd1 zenon_H42 zenon_H16a zenon_H200 zenon_Hfc zenon_H1fd zenon_Hbd zenon_H1d8 zenon_H3f zenon_H2d zenon_H1e zenon_H15a zenon_H16f zenon_H3c zenon_He7 zenon_H84 zenon_Hd9 zenon_H83 zenon_H218 zenon_H173 zenon_He4 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H69 zenon_H20 zenon_H20e zenon_H159 zenon_H101 zenon_H222 zenon_H18c zenon_Hc0 zenon_He1 zenon_Hb6 zenon_H1af zenon_Hd6 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_H1c7 zenon_H5e zenon_H1ca zenon_H37 zenon_H108 zenon_Hde zenon_Hdf zenon_H135 zenon_H55 zenon_H1bd zenon_H1d2 zenon_H1dc zenon_H6c zenon_H6b zenon_Hd0 zenon_H60 zenon_H155 zenon_H156. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.04 apply (zenon_L400_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.04 apply (zenon_L302_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.04 apply (zenon_L165_); trivial. % 29.81/30.04 apply (zenon_L180_); trivial. % 29.81/30.04 (* end of lemma zenon_L487_ *) % 29.81/30.04 assert (zenon_L488_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.81/30.04 do 0 intro. intros zenon_H1d5 zenon_H19e zenon_H37 zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H19a zenon_H159 zenon_H101 zenon_H1e1 zenon_H1bd zenon_H156 zenon_H155 zenon_H60 zenon_H1af zenon_H16b zenon_H218. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/30.04 apply (zenon_L262_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/30.04 apply (zenon_L209_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/30.04 apply (zenon_L179_); trivial. % 29.81/30.04 apply (zenon_L245_); trivial. % 29.81/30.04 (* end of lemma zenon_L488_ *) % 29.81/30.04 assert (zenon_L489_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.04 do 0 intro. intros zenon_H100 zenon_Hda zenon_H20d zenon_H6b zenon_H6c zenon_H1dc zenon_H1d2 zenon_Hde zenon_H108 zenon_H1ca zenon_H1c7 zenon_Hb6 zenon_Hc0 zenon_H18c zenon_H20 zenon_H69 zenon_H1a5 zenon_H92 zenon_H1b1 zenon_He4 zenon_H173 zenon_H83 zenon_Hd9 zenon_H84 zenon_He7 zenon_H16f zenon_H15a zenon_H3f zenon_Hbd zenon_H1fd zenon_Hfc zenon_H200 zenon_H16a zenon_Hd1 zenon_H35 zenon_H102 zenon_H174 zenon_H27 zenon_H5c zenon_H8d zenon_Had zenon_Hb8 zenon_H125 zenon_H225 zenon_H17d zenon_H112 zenon_H14b zenon_H5e zenon_H1f zenon_H3c zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H19a zenon_H159 zenon_H101 zenon_H1bd zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_H222 zenon_H1d5 zenon_H19e zenon_H60 zenon_H16b zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.04 apply (zenon_L486_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.04 apply (zenon_L154_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.04 apply (zenon_L430_); trivial. % 29.81/30.04 apply (zenon_L310_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.04 apply (zenon_L311_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.04 apply (zenon_L159_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.04 apply (zenon_L312_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.04 apply (zenon_L93_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.04 apply (zenon_L4_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.04 apply (zenon_L487_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.04 apply (zenon_L207_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.04 apply (zenon_L165_); trivial. % 29.81/30.04 apply (zenon_L488_); trivial. % 29.81/30.04 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.04 apply (zenon_L308_); trivial. % 29.81/30.04 exact (zenon_H18e zenon_H40). % 29.81/30.04 apply (zenon_L313_); trivial. % 29.81/30.04 (* end of lemma zenon_L489_ *) % 29.81/30.04 assert (zenon_L490_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 29.81/30.04 do 0 intro. intros zenon_Hb6 zenon_H15e zenon_Hee. % 29.81/30.04 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 29.81/30.04 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 29.81/30.04 intro zenon_D_pnotp. % 29.81/30.04 apply zenon_Hee. % 29.81/30.04 rewrite <- zenon_D_pnotp. % 29.81/30.04 exact zenon_Hef. % 29.81/30.04 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.81/30.04 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 29.81/30.04 congruence. % 29.81/30.04 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 29.81/30.04 intro zenon_D_pnotp. % 29.81/30.04 apply zenon_Hf1. % 29.81/30.04 rewrite <- zenon_D_pnotp. % 29.81/30.04 exact zenon_Hb6. % 29.81/30.04 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 29.81/30.04 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 29.81/30.04 congruence. % 29.81/30.04 apply zenon_Hf0. apply refl_equal. % 29.81/30.04 apply zenon_H1fb. apply sym_equal. exact zenon_H15e. % 29.81/30.04 apply zenon_Hf0. apply refl_equal. % 29.81/30.04 apply zenon_Hf0. apply refl_equal. % 29.81/30.04 (* end of lemma zenon_L490_ *) % 29.81/30.04 assert (zenon_L491_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.81/30.05 do 0 intro. intros zenon_H1d5 zenon_H19e zenon_H37 zenon_H222 zenon_H60 zenon_H5e zenon_H1f zenon_H3c zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H19a zenon_Hd1 zenon_Hdc zenon_H101 zenon_H1e1 zenon_H1bd zenon_H1dc zenon_Hb6 zenon_H1af zenon_H16c zenon_H156. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.81/30.05 apply (zenon_L258_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.81/30.05 apply (zenon_L209_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.81/30.05 apply (zenon_L200_); trivial. % 29.81/30.05 apply (zenon_L290_); trivial. % 29.81/30.05 (* end of lemma zenon_L491_ *) % 29.81/30.05 assert (zenon_L492_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.05 do 0 intro. intros zenon_H42 zenon_H156 zenon_H16c zenon_H1af zenon_Hb6 zenon_H1dc zenon_H1bd zenon_H101 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H1d5 zenon_H135 zenon_H18c zenon_He9 zenon_Hd0 zenon_H20d zenon_Hde zenon_H6b zenon_Hd6 zenon_H2d zenon_H89 zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H200 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.05 apply (zenon_L4_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.05 apply (zenon_L326_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.05 apply (zenon_L207_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.05 apply (zenon_L224_); trivial. % 29.81/30.05 apply (zenon_L491_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.05 apply (zenon_L155_); trivial. % 29.81/30.05 exact (zenon_H18e zenon_H40). % 29.81/30.05 (* end of lemma zenon_L492_ *) % 29.81/30.05 assert (zenon_L493_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.81/30.05 do 0 intro. intros zenon_H174 zenon_H18e zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hdc zenon_Hd1 zenon_H19e zenon_H1d5 zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H60 zenon_H1ca zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H42 zenon_H1bd zenon_H1d2 zenon_H6c zenon_Hd6 zenon_Hd0 zenon_H108 zenon_Hd9 zenon_H1fd zenon_H135 zenon_H18c zenon_Hde zenon_H125 zenon_H14b zenon_H16f zenon_H15a zenon_Hee zenon_H156 zenon_H1dc zenon_H20d zenon_H6b zenon_He7 zenon_Hb8 zenon_H112 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H200 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_H17b zenon_He1. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.81/30.05 apply (zenon_L241_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.05 apply (zenon_L469_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.05 apply (zenon_L207_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.05 apply (zenon_L224_); trivial. % 29.81/30.05 apply (zenon_L210_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.81/30.05 apply (zenon_L490_); trivial. % 29.81/30.05 apply (zenon_L492_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.05 apply (zenon_L154_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.05 apply (zenon_L471_); trivial. % 29.81/30.05 apply (zenon_L266_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.05 apply (zenon_L4_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.05 apply (zenon_L151_); trivial. % 29.81/30.05 apply (zenon_L267_); trivial. % 29.81/30.05 (* end of lemma zenon_L493_ *) % 29.81/30.05 assert (zenon_L494_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.81/30.05 do 0 intro. intros zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_Ha4 zenon_H1a5 zenon_Hcd zenon_H1d2 zenon_H108 zenon_Hd9 zenon_H1fd zenon_H18c zenon_H101 zenon_Hd1 zenon_H20e zenon_H125 zenon_H14b zenon_H16f zenon_H15a zenon_H74 zenon_He4 zenon_Hee zenon_H23b zenon_H172 zenon_H225 zenon_Had zenon_H8d zenon_H27 zenon_H16a zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_H20 zenon_Hc0 zenon_H35 zenon_H173 zenon_H14e zenon_H100 zenon_Hb5 zenon_H20d zenon_H17d zenon_H159 zenon_H42 zenon_H1c7 zenon_H5e zenon_H1f zenon_H1ca zenon_H60 zenon_H208 zenon_H6f zenon_H1d5 zenon_H156 zenon_Hd6 zenon_H6c zenon_H1af zenon_H1bd zenon_H102 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H135 zenon_Hde zenon_H222 zenon_Hd0 zenon_H218 zenon_H200 zenon_H18e zenon_H174 zenon_H112 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_H17b zenon_He1. % 29.81/30.05 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.05 exact (zenon_H74 zenon_H73). % 29.81/30.05 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.05 apply (zenon_L493_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.05 apply (zenon_L142_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.05 apply (zenon_L322_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.05 apply (zenon_L159_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.81/30.05 apply (zenon_L482_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.81/30.05 apply (zenon_L93_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.81/30.05 apply (zenon_L282_); trivial. % 29.81/30.05 apply (zenon_L440_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.05 apply (zenon_L4_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.05 apply (zenon_L151_); trivial. % 29.81/30.05 apply (zenon_L267_); trivial. % 29.81/30.05 apply (zenon_L472_); trivial. % 29.81/30.05 (* end of lemma zenon_L494_ *) % 29.81/30.05 assert (zenon_L495_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.81/30.05 do 0 intro. intros zenon_Hc8 zenon_H64 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_Ha4 zenon_H1a5 zenon_Hcd zenon_H1d2 zenon_H108 zenon_Hd9 zenon_H1fd zenon_H18c zenon_H101 zenon_Hd1 zenon_H20e zenon_H125 zenon_H14b zenon_H16f zenon_H15a zenon_H74 zenon_He4 zenon_Hee zenon_H23b zenon_H172 zenon_H225 zenon_Had zenon_H8d zenon_H27 zenon_H16a zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_H20 zenon_Hc0 zenon_H35 zenon_H173 zenon_H14e zenon_H100 zenon_Hb5 zenon_H20d zenon_H17d zenon_H159 zenon_H42 zenon_H1c7 zenon_H5e zenon_H1f zenon_H1ca zenon_H60 zenon_H208 zenon_H6f zenon_H1d5 zenon_H156 zenon_Hd6 zenon_H6c zenon_H1af zenon_H1bd zenon_H102 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H135 zenon_Hde zenon_H222 zenon_Hd0 zenon_H218 zenon_H200 zenon_H18e zenon_H174 zenon_H112 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_He1. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.81/30.05 exact (zenon_H74 zenon_H73). % 29.81/30.05 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.81/30.05 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.05 exact (zenon_H74 zenon_H73). % 29.81/30.05 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.05 apply (zenon_L478_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.05 apply (zenon_L484_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.05 apply (zenon_L387_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.05 apply (zenon_L4_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.05 apply (zenon_L151_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.81/30.05 apply (zenon_L387_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.81/30.05 apply (zenon_L485_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.81/30.05 apply (zenon_L157_); trivial. % 29.81/30.05 apply (zenon_L50_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.81/30.05 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.05 exact (zenon_H74 zenon_H73). % 29.81/30.05 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.05 apply (zenon_L478_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.05 apply (zenon_L484_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.05 apply (zenon_L387_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.05 apply (zenon_L4_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.05 apply (zenon_L151_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.81/30.05 apply (zenon_L489_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.81/30.05 apply (zenon_L42_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.81/30.05 apply (zenon_L315_); trivial. % 29.81/30.05 apply (zenon_L393_); trivial. % 29.81/30.05 apply (zenon_L494_); trivial. % 29.81/30.05 (* end of lemma zenon_L495_ *) % 29.81/30.05 assert (zenon_L496_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 29.81/30.05 do 0 intro. intros zenon_H14b zenon_H112 zenon_H17d zenon_H225 zenon_H84 zenon_H83 zenon_He4 zenon_H156 zenon_H16f zenon_Had zenon_H16a zenon_H15a zenon_H8d zenon_H200 zenon_Hbd zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_H125 zenon_H1fd zenon_Hd9 zenon_H42 zenon_H222 zenon_H1f zenon_H3c zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_Hd1 zenon_H19a zenon_Hfc zenon_H35 zenon_H102 zenon_H18e zenon_H27 zenon_H5c zenon_H174 zenon_H1e zenon_H20 zenon_H69 zenon_H92 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H37 zenon_Hdc zenon_H18c zenon_H135 zenon_H1e1 zenon_H108 zenon_H2d zenon_Hb6. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.81/30.05 apply (zenon_L271_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.81/30.05 apply (zenon_L295_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.81/30.05 apply (zenon_L296_); trivial. % 29.81/30.05 apply (zenon_L304_); trivial. % 29.81/30.05 (* end of lemma zenon_L496_ *) % 29.81/30.05 assert (zenon_L497_ : ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.05 do 0 intro. intros zenon_Hb6 zenon_H2d zenon_H108 zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_Hde zenon_H92 zenon_H69 zenon_H20 zenon_H1e zenon_H174 zenon_H5c zenon_H27 zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hd1 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_Hd9 zenon_H1fd zenon_H125 zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_Hbd zenon_H200 zenon_H8d zenon_H15a zenon_H16a zenon_Had zenon_H16f zenon_H156 zenon_He4 zenon_H83 zenon_H84 zenon_H225 zenon_H17d zenon_H112 zenon_H14b zenon_He9 zenon_H20d zenon_Hb5 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.81/30.05 apply (zenon_L4_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.81/30.05 apply (zenon_L462_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.81/30.05 apply (zenon_L207_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.81/30.05 apply (zenon_L224_); trivial. % 29.81/30.05 apply (zenon_L496_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.81/30.05 apply (zenon_L145_); trivial. % 29.81/30.05 exact (zenon_H18e zenon_H40). % 29.81/30.05 (* end of lemma zenon_L497_ *) % 29.81/30.05 assert (zenon_L498_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.81/30.05 do 0 intro. intros zenon_Hb5 zenon_H14e zenon_H172 zenon_H74 zenon_Ha4 zenon_Hc8 zenon_Hee zenon_H1f zenon_H23b zenon_H10d zenon_H6f zenon_H112 zenon_H100 zenon_Hb8 zenon_H6b zenon_Hde zenon_H108 zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H1dc zenon_Hb6 zenon_Hc0 zenon_H222 zenon_H101 zenon_H159 zenon_H20e zenon_H20 zenon_H69 zenon_H1a5 zenon_H92 zenon_H1b1 zenon_He4 zenon_H173 zenon_H83 zenon_Hd9 zenon_H84 zenon_He7 zenon_H16f zenon_H15a zenon_H3f zenon_Hbd zenon_H1fd zenon_Hfc zenon_H200 zenon_H16a zenon_Hd1 zenon_H35 zenon_H102 zenon_H174 zenon_H27 zenon_H5c zenon_H8d zenon_Had zenon_H125 zenon_H225 zenon_H17d zenon_H14b zenon_H20d zenon_H18c zenon_H1ca zenon_H6c zenon_H5e zenon_H1bd zenon_Hcd zenon_H19a zenon_H42 zenon_H2d zenon_H1e zenon_H156 zenon_He9 zenon_H3c zenon_H1d5 zenon_H19e zenon_H60 zenon_H218 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_H135 zenon_H18e. % 29.81/30.05 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.81/30.05 exact (zenon_H74 zenon_H73). % 29.81/30.05 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.81/30.05 apply (zenon_L497_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.81/30.05 apply (zenon_L484_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.81/30.05 apply (zenon_L387_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.81/30.05 apply (zenon_L4_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.81/30.05 apply (zenon_L151_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.81/30.05 apply (zenon_L486_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.81/30.05 apply (zenon_L311_); trivial. % 29.81/30.05 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.81/30.05 apply (zenon_L159_); trivial. % 29.81/30.05 apply (zenon_L312_); trivial. % 29.81/30.05 (* end of lemma zenon_L498_ *) % 29.81/30.05 assert (zenon_L499_ : ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.05 do 0 intro. intros zenon_Hb6 zenon_H2d zenon_H108 zenon_H135 zenon_H18c zenon_Hdc zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_Hd0 zenon_Hde zenon_H92 zenon_H69 zenon_H20 zenon_H1e zenon_H174 zenon_H5c zenon_H27 zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hd1 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_Hd9 zenon_H1fd zenon_H125 zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_Hbd zenon_H200 zenon_H8d zenon_H15a zenon_H16a zenon_Had zenon_H16f zenon_H156 zenon_He4 zenon_H83 zenon_H84 zenon_H225 zenon_H17d zenon_H112 zenon_H14b zenon_Hda zenon_He1 zenon_H55 zenon_H18e. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.05 apply (zenon_L4_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.05 apply (zenon_L305_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.05 apply (zenon_L207_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.05 apply (zenon_L165_); trivial. % 29.90/30.05 apply (zenon_L496_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.05 apply (zenon_L126_); trivial. % 29.90/30.05 exact (zenon_H18e zenon_H40). % 29.90/30.05 (* end of lemma zenon_L499_ *) % 29.90/30.05 assert (zenon_L500_ : ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.05 do 0 intro. intros zenon_Hb6 zenon_H2d zenon_H108 zenon_H135 zenon_H18c zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_He1 zenon_H208 zenon_H6f zenon_Hcd zenon_H1d5 zenon_Hd0 zenon_Hde zenon_H92 zenon_H69 zenon_H20 zenon_H174 zenon_H5c zenon_H27 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_Hd9 zenon_H1fd zenon_H125 zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_Hbd zenon_H200 zenon_H8d zenon_H15a zenon_H16a zenon_Had zenon_H16f zenon_H156 zenon_He4 zenon_H83 zenon_H84 zenon_H225 zenon_H17d zenon_H112 zenon_H14b zenon_Hb5 zenon_H100 zenon_H14e zenon_Hc0 zenon_H1a5 zenon_H1b1 zenon_H172 zenon_H23b zenon_Hee zenon_H74 zenon_H10d zenon_H89 zenon_Hc8 zenon_Ha4 zenon_H20d zenon_Hda zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.05 apply (zenon_L241_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.05 apply (zenon_L306_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.05 apply (zenon_L235_); trivial. % 29.90/30.05 apply (zenon_L492_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.05 apply (zenon_L154_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.05 apply (zenon_L499_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.05 apply (zenon_L4_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.05 apply (zenon_L305_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.05 apply (zenon_L207_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.90/30.05 apply (zenon_L483_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.90/30.05 apply (zenon_L264_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.90/30.05 exact (zenon_Hd0 zenon_Hcc). % 29.90/30.05 apply (zenon_L223_); trivial. % 29.90/30.05 apply (zenon_L496_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.05 apply (zenon_L155_); trivial. % 29.90/30.05 exact (zenon_H18e zenon_H40). % 29.90/30.05 (* end of lemma zenon_L500_ *) % 29.90/30.05 assert (zenon_L501_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.05 do 0 intro. intros zenon_Ha4 zenon_Hc8 zenon_Hb6 zenon_H2d zenon_H108 zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_Hde zenon_H92 zenon_H69 zenon_H20 zenon_H1e zenon_H174 zenon_H5c zenon_H27 zenon_H102 zenon_H35 zenon_Hfc zenon_H19a zenon_Hd1 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H3c zenon_H1f zenon_H222 zenon_H42 zenon_Hd9 zenon_H1fd zenon_H125 zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_Hbd zenon_H200 zenon_H8d zenon_H15a zenon_H16a zenon_Had zenon_H16f zenon_H156 zenon_He4 zenon_H83 zenon_H84 zenon_H225 zenon_H17d zenon_H112 zenon_H14b zenon_Hb5 zenon_H100 zenon_H14e zenon_Hc0 zenon_H1a5 zenon_H1b1 zenon_H172 zenon_H23b zenon_Hee zenon_H74 zenon_H10d zenon_H20d zenon_Hda zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.90/30.05 apply (zenon_L500_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.90/30.05 apply (zenon_L4_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.90/30.05 apply (zenon_L151_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.05 apply (zenon_L4_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.05 apply (zenon_L305_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.05 apply (zenon_L207_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.05 apply (zenon_L476_); trivial. % 29.90/30.05 apply (zenon_L496_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.05 apply (zenon_L145_); trivial. % 29.90/30.05 exact (zenon_H18e zenon_H40). % 29.90/30.05 (* end of lemma zenon_L501_ *) % 29.90/30.05 assert (zenon_L502_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.90/30.05 do 0 intro. intros zenon_H17d zenon_H69 zenon_Hc8 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_Hcd zenon_H1d2 zenon_H108 zenon_Hd9 zenon_H1fd zenon_H18c zenon_H101 zenon_Hd1 zenon_H20e zenon_H125 zenon_H14b zenon_H16f zenon_H15a zenon_H74 zenon_He4 zenon_Hee zenon_H23b zenon_H172 zenon_H225 zenon_Had zenon_H8d zenon_H27 zenon_H16a zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_H20 zenon_Hc0 zenon_H35 zenon_H173 zenon_H14e zenon_H100 zenon_Hb5 zenon_H20d zenon_H159 zenon_H42 zenon_H1c7 zenon_H5e zenon_H1ca zenon_H60 zenon_H208 zenon_H6f zenon_H1d5 zenon_H156 zenon_Hd6 zenon_H1af zenon_H1bd zenon_H102 zenon_Hfc zenon_H19e zenon_H3c zenon_H135 zenon_Hde zenon_H222 zenon_Hd0 zenon_H218 zenon_H200 zenon_H18e zenon_H174 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_He1 zenon_H1a5 zenon_H19a zenon_H112 zenon_Ha4. % 29.90/30.05 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.90/30.05 exact (zenon_H84 zenon_H88). % 29.90/30.05 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.90/30.05 exact (zenon_H84 zenon_H88). % 29.90/30.05 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.90/30.05 apply (zenon_L147_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.90/30.05 exact (zenon_H74 zenon_H73). % 29.90/30.05 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.90/30.05 apply (zenon_L498_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.90/30.05 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.90/30.05 exact (zenon_H74 zenon_H73). % 29.90/30.05 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.90/30.05 apply (zenon_L501_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.90/30.05 apply (zenon_L484_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.90/30.05 apply (zenon_L387_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.90/30.05 apply (zenon_L4_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.90/30.05 apply (zenon_L151_); trivial. % 29.90/30.05 apply (zenon_L489_); trivial. % 29.90/30.05 apply (zenon_L494_); trivial. % 29.90/30.05 apply (zenon_L139_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.90/30.05 apply (zenon_L136_); trivial. % 29.90/30.05 apply (zenon_L140_); trivial. % 29.90/30.05 (* end of lemma zenon_L502_ *) % 29.90/30.05 assert (zenon_L503_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.90/30.05 do 0 intro. intros zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H60 zenon_H20d zenon_Hd0 zenon_Hdc zenon_H18c zenon_H135 zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.05 apply (zenon_L194_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.05 apply (zenon_L207_); trivial. % 29.90/30.05 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.05 apply (zenon_L224_); trivial. % 29.90/30.05 apply (zenon_L210_); trivial. % 29.90/30.05 (* end of lemma zenon_L503_ *) % 29.90/30.05 assert (zenon_L504_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.90/30.06 do 0 intro. intros zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H1c7 zenon_H60 zenon_Hd6 zenon_Hb6 zenon_H1dc zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H208 zenon_H6f zenon_H1f zenon_H37 zenon_H1d5 zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.06 apply (zenon_L194_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.06 apply (zenon_L207_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.06 apply (zenon_L480_); trivial. % 29.90/30.06 apply (zenon_L210_); trivial. % 29.90/30.06 (* end of lemma zenon_L504_ *) % 29.90/30.06 assert (zenon_L505_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.06 do 0 intro. intros zenon_H42 zenon_H2d zenon_He9 zenon_H5e zenon_H6c zenon_H1ca zenon_H1d5 zenon_H1f zenon_H6f zenon_H208 zenon_H1dc zenon_Hb6 zenon_Hd6 zenon_H60 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.06 apply (zenon_L4_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.06 apply (zenon_L504_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.06 apply (zenon_L281_); trivial. % 29.90/30.06 exact (zenon_H18e zenon_H40). % 29.90/30.06 (* end of lemma zenon_L505_ *) % 29.90/30.06 assert (zenon_L506_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.06 do 0 intro. intros zenon_H101 zenon_Hb6 zenon_H1dc zenon_H208 zenon_H6f zenon_H159 zenon_H42 zenon_H1c7 zenon_H222 zenon_H5e zenon_H1f zenon_H1ca zenon_H60 zenon_H156 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde zenon_He1 zenon_H135 zenon_H2d zenon_Hd6 zenon_H6c zenon_Hc9 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.06 apply (zenon_L505_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.06 apply (zenon_L93_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.06 apply (zenon_L282_); trivial. % 29.90/30.06 apply (zenon_L334_); trivial. % 29.90/30.06 (* end of lemma zenon_L506_ *) % 29.90/30.06 assert (zenon_L507_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.90/30.06 do 0 intro. intros zenon_H1d5 zenon_Hc9 zenon_He1 zenon_H55 zenon_H1dc zenon_Hb6 zenon_H1af zenon_H16b zenon_H218. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.90/30.06 apply (zenon_L273_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.90/30.06 apply (zenon_L126_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.90/30.06 apply (zenon_L200_); trivial. % 29.90/30.06 apply (zenon_L245_); trivial. % 29.90/30.06 (* end of lemma zenon_L507_ *) % 29.90/30.06 assert (zenon_L508_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.06 do 0 intro. intros zenon_H174 zenon_Hde zenon_Hc8 zenon_H10d zenon_H173 zenon_H18c zenon_Hcd zenon_H101 zenon_H1c7 zenon_Hd6 zenon_H208 zenon_H6f zenon_H1f zenon_H1ca zenon_H6c zenon_H5e zenon_H159 zenon_Hb6 zenon_H1dc zenon_Hc9 zenon_H42 zenon_H2d zenon_H156 zenon_Hd0 zenon_H222 zenon_H1d5 zenon_He1 zenon_H60 zenon_H218 zenon_H135 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.90/30.06 apply (zenon_L142_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.90/30.06 apply (zenon_L272_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.90/30.06 apply (zenon_L159_); trivial. % 29.90/30.06 apply (zenon_L506_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.90/30.06 apply (zenon_L4_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.90/30.06 apply (zenon_L151_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.90/30.06 apply (zenon_L142_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.90/30.06 apply (zenon_L272_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.90/30.06 apply (zenon_L159_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.06 apply (zenon_L505_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.06 apply (zenon_L93_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.06 apply (zenon_L507_); trivial. % 29.90/30.06 apply (zenon_L284_); trivial. % 29.90/30.06 (* end of lemma zenon_L508_ *) % 29.90/30.06 assert (zenon_L509_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.90/30.06 do 0 intro. intros zenon_H14b zenon_H112 zenon_H17d zenon_H225 zenon_H84 zenon_H83 zenon_He4 zenon_H156 zenon_H16f zenon_Had zenon_H16a zenon_H15a zenon_H8d zenon_H200 zenon_Hbd zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_H125 zenon_H1fd zenon_Hd9 zenon_H42 zenon_H222 zenon_H1f zenon_H3c zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_Hd1 zenon_H19a zenon_Hfc zenon_H35 zenon_H102 zenon_H18e zenon_H27 zenon_H5c zenon_H174 zenon_H1e zenon_H2d zenon_H20 zenon_H69 zenon_H92 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H37 zenon_Hdc zenon_H18c zenon_H135 zenon_H1e1 zenon_H108 zenon_Hb5 zenon_H8b. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.90/30.06 apply (zenon_L271_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.90/30.06 apply (zenon_L295_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.90/30.06 apply (zenon_L296_); trivial. % 29.90/30.06 apply (zenon_L297_); trivial. % 29.90/30.06 (* end of lemma zenon_L509_ *) % 29.90/30.06 assert (zenon_L510_ : (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> False). % 29.90/30.06 do 0 intro. intros zenon_H18e zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_H19e zenon_H19a zenon_Hfc zenon_H112 zenon_H102 zenon_H1bd zenon_H1af zenon_H135 zenon_H218 zenon_He1 zenon_H1d5 zenon_H156 zenon_H2d zenon_H42 zenon_H1dc zenon_Hb6 zenon_H159 zenon_H5e zenon_H6c zenon_H1ca zenon_H1f zenon_H6f zenon_H208 zenon_Hd6 zenon_H1c7 zenon_H101 zenon_Hcd zenon_H18c zenon_H173 zenon_H10d zenon_Hc8 zenon_Hde zenon_H174 zenon_H9d zenon_H222 zenon_Hd0 zenon_H20d zenon_H60 zenon_H142. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.90/30.06 apply (zenon_L508_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.90/30.06 apply (zenon_L264_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.90/30.06 exact (zenon_Hd0 zenon_Hcc). % 29.90/30.06 apply (zenon_L223_); trivial. % 29.90/30.06 (* end of lemma zenon_L510_ *) % 29.90/30.06 assert (zenon_L511_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.06 do 0 intro. intros zenon_H156 zenon_H16c zenon_Hb6 zenon_H1dc zenon_H1bd zenon_H101 zenon_Hd1 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H19e zenon_H1d5 zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H1e zenon_Hfc zenon_H112 zenon_H102 zenon_H218 zenon_H2d zenon_H42 zenon_H159 zenon_H6c zenon_H1ca zenon_H1c7 zenon_H173 zenon_H10d zenon_Hc8 zenon_Hde zenon_H174 zenon_H9d zenon_H20d zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.06 apply (zenon_L4_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.06 apply (zenon_L194_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.06 apply (zenon_L207_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.06 apply (zenon_L510_); trivial. % 29.90/30.06 apply (zenon_L491_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.06 apply (zenon_L145_); trivial. % 29.90/30.06 exact (zenon_H18e zenon_H40). % 29.90/30.06 (* end of lemma zenon_L511_ *) % 29.90/30.06 assert (zenon_L512_ : ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (op (op (e1) (e1)) (e1)))) -> False). % 29.90/30.06 do 0 intro. intros zenon_H95 zenon_H37 zenon_H24d. % 29.90/30.06 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 29.90/30.06 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e0) = (op (op (e1) (e1)) (e1)))). % 29.90/30.06 intro zenon_D_pnotp. % 29.90/30.06 apply zenon_H24d. % 29.90/30.06 rewrite <- zenon_D_pnotp. % 29.90/30.06 exact zenon_H13e. % 29.90/30.06 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 29.90/30.06 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H24e]. % 29.90/30.06 congruence. % 29.90/30.06 cut (((op (e3) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 29.90/30.06 intro zenon_D_pnotp. % 29.90/30.06 apply zenon_H24e. % 29.90/30.06 rewrite <- zenon_D_pnotp. % 29.90/30.06 exact zenon_H95. % 29.90/30.06 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 29.90/30.06 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H238]. % 29.90/30.06 congruence. % 29.90/30.06 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 29.90/30.06 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 29.90/30.06 intro zenon_D_pnotp. % 29.90/30.06 apply zenon_H238. % 29.90/30.06 rewrite <- zenon_D_pnotp. % 29.90/30.06 exact zenon_H13e. % 29.90/30.06 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 29.90/30.06 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H235]. % 29.90/30.06 congruence. % 29.90/30.06 apply (zenon_L318_); trivial. % 29.90/30.06 apply zenon_H13f. apply refl_equal. % 29.90/30.06 apply zenon_H13f. apply refl_equal. % 29.90/30.06 apply zenon_H1d. apply refl_equal. % 29.90/30.06 apply zenon_H13f. apply refl_equal. % 29.90/30.06 apply zenon_H13f. apply refl_equal. % 29.90/30.06 (* end of lemma zenon_L512_ *) % 29.90/30.06 assert (zenon_L513_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 29.90/30.06 do 0 intro. intros zenon_Hf4 zenon_H95 zenon_H37. % 29.90/30.06 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H250 | zenon_intro zenon_H24f ]. % 29.90/30.06 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 29.90/30.06 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e2) = (op (op (e1) (e1)) (op (e1) (e1))))). % 29.90/30.06 intro zenon_D_pnotp. % 29.90/30.06 apply zenon_H250. % 29.90/30.06 rewrite <- zenon_D_pnotp. % 29.90/30.06 exact zenon_H145. % 29.90/30.06 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 29.90/30.06 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H251]. % 29.90/30.06 congruence. % 29.90/30.06 cut (((op (e3) (e3)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 29.90/30.06 intro zenon_D_pnotp. % 29.90/30.06 apply zenon_H251. % 29.90/30.06 rewrite <- zenon_D_pnotp. % 29.90/30.06 exact zenon_Hf4. % 29.90/30.06 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.90/30.06 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 29.90/30.06 congruence. % 29.90/30.06 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 29.90/30.06 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))))). % 29.90/30.06 intro zenon_D_pnotp. % 29.90/30.06 apply zenon_H23a. % 29.90/30.06 rewrite <- zenon_D_pnotp. % 29.90/30.06 exact zenon_H145. % 29.90/30.06 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 29.90/30.06 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H234]. % 29.90/30.06 congruence. % 29.90/30.06 apply (zenon_L317_); trivial. % 29.90/30.06 apply zenon_H146. apply refl_equal. % 29.90/30.06 apply zenon_H146. apply refl_equal. % 29.90/30.06 apply zenon_H57. apply refl_equal. % 29.90/30.06 apply zenon_H146. apply refl_equal. % 29.90/30.06 apply zenon_H146. apply refl_equal. % 29.90/30.06 apply (zenon_notand_s _ _ zenon_H24f); [ zenon_intro zenon_H24d | zenon_intro zenon_H38 ]. % 29.90/30.06 apply (zenon_L512_); trivial. % 29.90/30.06 apply zenon_H38. apply sym_equal. exact zenon_H37. % 29.90/30.06 (* end of lemma zenon_L513_ *) % 29.90/30.06 assert (zenon_L514_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 29.90/30.06 do 0 intro. intros zenon_H222 zenon_H5e zenon_Hd5 zenon_H98. % 29.90/30.06 cut (((op (e2) (op (e2) (e1))) = (e1)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 29.90/30.06 intro zenon_D_pnotp. % 29.90/30.06 apply zenon_H222. % 29.90/30.06 rewrite <- zenon_D_pnotp. % 29.90/30.06 exact zenon_H5e. % 29.90/30.06 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 29.90/30.06 cut (((op (e2) (op (e2) (e1))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1bf]. % 29.90/30.06 congruence. % 29.90/30.06 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 29.90/30.06 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (op (e2) (e1))) = (op (e2) (e1)))). % 29.90/30.06 intro zenon_D_pnotp. % 29.90/30.06 apply zenon_H1bf. % 29.90/30.06 rewrite <- zenon_D_pnotp. % 29.90/30.06 exact zenon_H62. % 29.90/30.06 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.90/30.06 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 29.90/30.06 congruence. % 29.90/30.06 apply (zenon_L162_); trivial. % 29.90/30.06 apply zenon_H63. apply refl_equal. % 29.90/30.06 apply zenon_H63. apply refl_equal. % 29.90/30.06 apply zenon_H99. apply sym_equal. exact zenon_H98. % 29.90/30.06 (* end of lemma zenon_L514_ *) % 29.90/30.06 assert (zenon_L515_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.90/30.06 do 0 intro. intros zenon_H208 zenon_H1e1 zenon_H1bd zenon_H1e zenon_H1ca zenon_H98 zenon_H5e zenon_H222 zenon_H3c zenon_He9 zenon_H60 zenon_H1af zenon_H37 zenon_H19e. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.90/30.06 apply (zenon_L210_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.90/30.06 apply (zenon_L514_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.90/30.06 apply (zenon_L219_); trivial. % 29.90/30.06 apply (zenon_L214_); trivial. % 29.90/30.06 (* end of lemma zenon_L515_ *) % 29.90/30.06 assert (zenon_L516_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.06 do 0 intro. intros zenon_Hf9 zenon_H14f zenon_H14e zenon_Hb8 zenon_H100 zenon_H2d zenon_H112 zenon_H6f zenon_Hde zenon_Hbd zenon_Hb6 zenon_He1 zenon_Haa zenon_H19e zenon_H37 zenon_H1af zenon_H60 zenon_H3c zenon_H222 zenon_H5e zenon_H1ca zenon_H1e zenon_H1bd zenon_H1e1 zenon_H208 zenon_He9 zenon_H3f zenon_H18e. % 29.90/30.06 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.90/30.06 apply (zenon_L392_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.90/30.06 apply (zenon_L53_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.90/30.06 apply (zenon_L204_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H95 | zenon_intro zenon_Hab ]. % 29.90/30.06 apply (zenon_L513_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H98 | zenon_intro zenon_Hac ]. % 29.90/30.06 apply (zenon_L515_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9d | zenon_intro zenon_H40 ]. % 29.90/30.06 apply (zenon_L53_); trivial. % 29.90/30.06 exact (zenon_H18e zenon_H40). % 29.90/30.06 (* end of lemma zenon_L516_ *) % 29.90/30.06 assert (zenon_L517_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.06 do 0 intro. intros zenon_H42 zenon_H3f zenon_He9 zenon_H208 zenon_H1bd zenon_H1e zenon_H1ca zenon_H5e zenon_H222 zenon_H3c zenon_H60 zenon_H19e zenon_Haa zenon_Hb6 zenon_Hbd zenon_Hde zenon_H6f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H14f zenon_Hf9 zenon_H20d zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.06 apply (zenon_L4_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.06 apply (zenon_L194_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.06 apply (zenon_L207_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.06 apply (zenon_L224_); trivial. % 29.90/30.06 apply (zenon_L516_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.06 apply (zenon_L145_); trivial. % 29.90/30.06 exact (zenon_H18e zenon_H40). % 29.90/30.06 (* end of lemma zenon_L517_ *) % 29.90/30.06 assert (zenon_L518_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e3)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.06 do 0 intro. intros zenon_H173 zenon_H18c zenon_H14f zenon_Hcd zenon_H101 zenon_Hb6 zenon_H1dc zenon_H208 zenon_H6f zenon_H159 zenon_H42 zenon_H1c7 zenon_H222 zenon_H5e zenon_H1f zenon_H1ca zenon_H60 zenon_H156 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde zenon_He1 zenon_H135 zenon_H2d zenon_Hd6 zenon_H6c zenon_Hc9 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.90/30.06 apply (zenon_L142_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.90/30.06 apply (zenon_L416_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.90/30.06 apply (zenon_L159_); trivial. % 29.90/30.06 apply (zenon_L506_); trivial. % 29.90/30.06 (* end of lemma zenon_L518_ *) % 29.90/30.06 assert (zenon_L519_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 29.90/30.06 do 0 intro. intros zenon_H14b zenon_H174 zenon_H27 zenon_H35 zenon_Hd1 zenon_H20e zenon_H218 zenon_Hd9 zenon_H1fd zenon_H125 zenon_H6b zenon_He7 zenon_Hb8 zenon_H3f zenon_Hbd zenon_H8d zenon_H15a zenon_H16a zenon_Had zenon_H16f zenon_He4 zenon_H83 zenon_H84 zenon_H225 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H37 zenon_H173 zenon_H18c zenon_H14f zenon_H101 zenon_H1dc zenon_H159 zenon_H42 zenon_H222 zenon_H1f zenon_H156 zenon_Hc8 zenon_H89 zenon_H135 zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e zenon_H1e1 zenon_H108 zenon_H2d zenon_Hb6. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.90/30.06 apply (zenon_L270_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.90/30.06 apply (zenon_L518_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.90/30.06 apply (zenon_L217_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.90/30.06 exact (zenon_Hd0 zenon_Hcc). % 29.90/30.06 apply (zenon_L294_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.90/30.06 apply (zenon_L296_); trivial. % 29.90/30.06 apply (zenon_L304_); trivial. % 29.90/30.06 (* end of lemma zenon_L519_ *) % 29.90/30.06 assert (zenon_L520_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.06 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hcd zenon_H101 zenon_H5e zenon_H6c zenon_H1ca zenon_Hfe zenon_H20e zenon_H159 zenon_Hc9 zenon_H42 zenon_H2d zenon_H156 zenon_Hd0 zenon_H222 zenon_H1d5 zenon_He1 zenon_H60 zenon_H16b zenon_H218 zenon_H135 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.90/30.06 apply (zenon_L142_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.90/30.06 apply (zenon_L272_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.90/30.06 apply (zenon_L159_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.06 apply (zenon_L351_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.06 apply (zenon_L93_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.06 apply (zenon_L282_); trivial. % 29.90/30.06 apply (zenon_L284_); trivial. % 29.90/30.06 (* end of lemma zenon_L520_ *) % 29.90/30.06 assert (zenon_L521_ : (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 29.90/30.06 do 0 intro. intros zenon_H18e zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_H19a zenon_Hfc zenon_H112 zenon_H102 zenon_H135 zenon_H218 zenon_H16b zenon_H222 zenon_H156 zenon_H2d zenon_H42 zenon_H159 zenon_H20e zenon_H101 zenon_H18c zenon_H173 zenon_H108 zenon_H37 zenon_Hfe zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_He1 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_Hd0 zenon_Hde zenon_H1e1. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.90/30.06 apply (zenon_L520_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.90/30.06 apply (zenon_L217_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.90/30.06 exact (zenon_Hd0 zenon_Hcc). % 29.90/30.06 apply (zenon_L294_); trivial. % 29.90/30.06 (* end of lemma zenon_L521_ *) % 29.90/30.06 assert (zenon_L522_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 29.90/30.06 do 0 intro. intros zenon_H14b zenon_H17d zenon_H225 zenon_H125 zenon_Hb8 zenon_Had zenon_H8d zenon_H27 zenon_H174 zenon_H35 zenon_Hd1 zenon_H16a zenon_H1fd zenon_Hbd zenon_H3f zenon_H1dc zenon_H15a zenon_H16f zenon_H6b zenon_He7 zenon_H84 zenon_Hd9 zenon_H83 zenon_He4 zenon_H1b1 zenon_H92 zenon_H1a5 zenon_H69 zenon_H20 zenon_Hc0 zenon_Hde zenon_Hd0 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_He1 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_H37 zenon_H173 zenon_H18c zenon_H101 zenon_H20e zenon_H159 zenon_H42 zenon_H156 zenon_H222 zenon_H16b zenon_H218 zenon_H135 zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e zenon_H1e1 zenon_H108 zenon_H2d zenon_Hb6. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.90/30.06 apply (zenon_L400_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.90/30.06 apply (zenon_L521_); trivial. % 29.90/30.06 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.90/30.06 apply (zenon_L296_); trivial. % 29.90/30.06 apply (zenon_L304_); trivial. % 29.90/30.06 (* end of lemma zenon_L522_ *) % 29.90/30.06 assert (zenon_L523_ : ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_Hb6 zenon_H2d zenon_H108 zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_H19a zenon_Hfc zenon_H112 zenon_H102 zenon_H218 zenon_H16b zenon_H222 zenon_H156 zenon_H42 zenon_H159 zenon_H20e zenon_H101 zenon_H173 zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_Hde zenon_Hc0 zenon_H20 zenon_H69 zenon_H1a5 zenon_H92 zenon_H1b1 zenon_He4 zenon_H83 zenon_Hd9 zenon_H84 zenon_He7 zenon_H6b zenon_H16f zenon_H15a zenon_H1dc zenon_H3f zenon_Hbd zenon_H1fd zenon_H16a zenon_Hd1 zenon_H35 zenon_H174 zenon_H27 zenon_H8d zenon_Had zenon_Hb8 zenon_H125 zenon_H225 zenon_H17d zenon_H14b zenon_H1f zenon_H10d zenon_Hc8 zenon_H20d zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_L503_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L272_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L165_); trivial. % 29.90/30.07 apply (zenon_L522_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.07 apply (zenon_L126_); trivial. % 29.90/30.07 exact (zenon_H18e zenon_H40). % 29.90/30.07 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L510_); trivial. % 29.90/30.07 apply (zenon_L522_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.07 apply (zenon_L145_); trivial. % 29.90/30.07 exact (zenon_H18e zenon_H40). % 29.90/30.07 (* end of lemma zenon_L523_ *) % 29.90/30.07 assert (zenon_L524_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_Hd1 zenon_Hde zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_H1ca zenon_Hfe zenon_H108 zenon_H173 zenon_H101 zenon_H20e zenon_H159 zenon_H42 zenon_H2d zenon_H156 zenon_H222 zenon_H16b zenon_H218 zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H1dc zenon_Hb6 zenon_H1f zenon_H10d zenon_Hc8 zenon_H174 zenon_H20d zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_L503_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L154_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_L309_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L510_); trivial. % 29.90/30.07 apply (zenon_L521_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.07 apply (zenon_L145_); trivial. % 29.90/30.07 exact (zenon_H18e zenon_H40). % 29.90/30.07 (* end of lemma zenon_L524_ *) % 29.90/30.07 assert (zenon_L525_ : ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_Hf4 zenon_H155 zenon_H14e. % 29.90/30.07 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 29.90/30.07 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H14e. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_Ha5. % 29.90/30.07 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.90/30.07 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 29.90/30.07 congruence. % 29.90/30.07 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H180. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_Hf4. % 29.90/30.07 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 29.90/30.07 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 29.90/30.07 congruence. % 29.90/30.07 apply zenon_Ha6. apply refl_equal. % 29.90/30.07 apply zenon_H158. apply sym_equal. exact zenon_H155. % 29.90/30.07 apply zenon_Ha6. apply refl_equal. % 29.90/30.07 apply zenon_Ha6. apply refl_equal. % 29.90/30.07 (* end of lemma zenon_L525_ *) % 29.90/30.07 assert (zenon_L526_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_Hf9 zenon_H14f zenon_Hb8 zenon_H100 zenon_H37 zenon_H2d zenon_H112 zenon_H6f zenon_H1e zenon_Hde zenon_Hbd zenon_He9 zenon_H3f zenon_Hb6 zenon_He1 zenon_H155 zenon_H14e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.90/30.07 apply (zenon_L392_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.90/30.07 apply (zenon_L53_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.90/30.07 apply (zenon_L204_); trivial. % 29.90/30.07 apply (zenon_L525_); trivial. % 29.90/30.07 (* end of lemma zenon_L526_ *) % 29.90/30.07 assert (zenon_L527_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H42 zenon_H14e zenon_He1 zenon_Hb6 zenon_H3f zenon_He9 zenon_Hbd zenon_Hde zenon_H6f zenon_H2d zenon_H100 zenon_Hb8 zenon_H14f zenon_Hf9 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.07 apply (zenon_L526_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.07 apply (zenon_L281_); trivial. % 29.90/30.07 exact (zenon_H18e zenon_H40). % 29.90/30.07 (* end of lemma zenon_L527_ *) % 29.90/30.07 assert (zenon_L528_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hcd zenon_H101 zenon_Hf9 zenon_H14f zenon_Hb8 zenon_H100 zenon_H6f zenon_Hde zenon_Hbd zenon_H3f zenon_H14e zenon_H159 zenon_Hb6 zenon_H1dc zenon_Hc9 zenon_H42 zenon_H2d zenon_H156 zenon_Hd0 zenon_H222 zenon_H1d5 zenon_He1 zenon_H60 zenon_H16b zenon_H218 zenon_H135 zenon_H1af zenon_H1bd zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H19e zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.90/30.07 apply (zenon_L142_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.90/30.07 apply (zenon_L416_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.90/30.07 apply (zenon_L159_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_L527_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L93_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_L507_); trivial. % 29.90/30.07 apply (zenon_L284_); trivial. % 29.90/30.07 (* end of lemma zenon_L528_ *) % 29.90/30.07 assert (zenon_L529_ : (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H18e zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_H19a zenon_Hfc zenon_H112 zenon_H102 zenon_H135 zenon_H218 zenon_H16b zenon_H222 zenon_H156 zenon_H2d zenon_H42 zenon_H159 zenon_H14e zenon_H3f zenon_Hbd zenon_Hde zenon_H100 zenon_Hb8 zenon_H14f zenon_Hf9 zenon_H101 zenon_H18c zenon_H173 zenon_H108 zenon_H37 zenon_Hfe zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1af zenon_H1dc zenon_Hb6 zenon_He1. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.90/30.07 apply (zenon_L528_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.90/30.07 apply (zenon_L217_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.90/30.07 exact (zenon_Hd0 zenon_Hcc). % 29.90/30.07 apply (zenon_L301_); trivial. % 29.90/30.07 (* end of lemma zenon_L529_ *) % 29.90/30.07 assert (zenon_L530_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H14b zenon_Hda zenon_He1 zenon_Hb6 zenon_H1dc zenon_H1af zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_H1ca zenon_H37 zenon_H173 zenon_H18c zenon_H101 zenon_Hf9 zenon_H14f zenon_Hb8 zenon_H100 zenon_Hde zenon_Hbd zenon_H3f zenon_H14e zenon_H159 zenon_H42 zenon_H2d zenon_H156 zenon_H222 zenon_H16b zenon_H218 zenon_H135 zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H200 zenon_H18e zenon_H1e1 zenon_H108 zenon_Hb5 zenon_H8b. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.90/30.07 apply (zenon_L192_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.90/30.07 apply (zenon_L529_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.90/30.07 apply (zenon_L296_); trivial. % 29.90/30.07 apply (zenon_L297_); trivial. % 29.90/30.07 (* end of lemma zenon_L530_ *) % 29.90/30.07 assert (zenon_L531_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H14b zenon_H6e zenon_Had zenon_H125 zenon_He1 zenon_Hb6 zenon_H1dc zenon_H1af zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_H1ca zenon_H37 zenon_H173 zenon_H18c zenon_H101 zenon_Hf9 zenon_H14f zenon_Hb8 zenon_H100 zenon_Hde zenon_Hbd zenon_H3f zenon_H14e zenon_H159 zenon_H42 zenon_H2d zenon_H156 zenon_H222 zenon_H16b zenon_H218 zenon_H135 zenon_H102 zenon_H112 zenon_Hfc zenon_H19a zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H200 zenon_H18e zenon_H1e1 zenon_H108 zenon_Hb5 zenon_H8b. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.90/30.07 apply (zenon_L234_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.90/30.07 apply (zenon_L529_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.90/30.07 apply (zenon_L296_); trivial. % 29.90/30.07 apply (zenon_L297_); trivial. % 29.90/30.07 (* end of lemma zenon_L531_ *) % 29.90/30.07 assert (zenon_L532_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_Haa zenon_H8b zenon_Hb5 zenon_H108 zenon_H200 zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_H19a zenon_Hfc zenon_H112 zenon_H102 zenon_H218 zenon_H16b zenon_H222 zenon_H156 zenon_H2d zenon_H42 zenon_H159 zenon_H14e zenon_H3f zenon_Hbd zenon_Hde zenon_H100 zenon_Hb8 zenon_H14f zenon_Hf9 zenon_H101 zenon_H173 zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_H6b zenon_H1dc zenon_Hb6 zenon_H125 zenon_Had zenon_H6e zenon_H14b zenon_H1f zenon_H10d zenon_Hc8 zenon_H174 zenon_H20d zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H18e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_L517_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L416_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L165_); trivial. % 29.90/30.07 apply (zenon_L531_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.07 apply (zenon_L126_); trivial. % 29.90/30.07 exact (zenon_H18e zenon_H40). % 29.90/30.07 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L510_); trivial. % 29.90/30.07 apply (zenon_L531_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.07 apply (zenon_L145_); trivial. % 29.90/30.07 exact (zenon_H18e zenon_H40). % 29.90/30.07 (* end of lemma zenon_L532_ *) % 29.90/30.07 assert (zenon_L533_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H200 zenon_H5c zenon_H1d8 zenon_H14b zenon_H18e zenon_H125 zenon_Hde zenon_H222 zenon_H1f zenon_H3c zenon_H20e zenon_H19a zenon_Hd1 zenon_H101 zenon_Hdc zenon_H18c zenon_H135 zenon_H218 zenon_H17b zenon_H1fd zenon_H89 zenon_Hd9 zenon_Hfc zenon_H1e zenon_H2d zenon_H42 zenon_Hd0 zenon_H37 zenon_H1ca zenon_Hd6 zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H1d2 zenon_H55 zenon_He1 zenon_H208 zenon_H6f zenon_Hcd zenon_H19e zenon_H1d5 zenon_H108 zenon_Hb5 zenon_H8b. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L165_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.90/30.07 apply (zenon_L261_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.90/30.07 apply (zenon_L217_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.90/30.07 apply (zenon_L296_); trivial. % 29.90/30.07 apply (zenon_L297_); trivial. % 29.90/30.07 (* end of lemma zenon_L533_ *) % 29.90/30.07 assert (zenon_L534_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H16f zenon_H15a zenon_Hb5 zenon_H108 zenon_H1d2 zenon_H6c zenon_Hd6 zenon_H1ca zenon_Hd0 zenon_Hfc zenon_Hd9 zenon_H89 zenon_H1fd zenon_H17b zenon_H218 zenon_H135 zenon_H18c zenon_Hde zenon_H125 zenon_H14b zenon_Hee zenon_Hb6 zenon_H42 zenon_H2d zenon_H156 zenon_H1af zenon_H60 zenon_H1c7 zenon_H1bd zenon_H101 zenon_Hdc zenon_Hd1 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H19e zenon_H1d5 zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_He1 zenon_H55 zenon_H18e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L241_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_L533_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L490_); trivial. % 29.90/30.07 apply (zenon_L291_); trivial. % 29.90/30.07 (* end of lemma zenon_L534_ *) % 29.90/30.07 assert (zenon_L535_ : (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H20 zenon_H8b zenon_Hc8 zenon_Had zenon_Hf9 zenon_H100 zenon_H14e zenon_Haa zenon_Hc0 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H16a zenon_H27 zenon_H8d zenon_H225 zenon_H17d zenon_H172 zenon_He4 zenon_H74 zenon_H20d zenon_Hee zenon_H14b zenon_H125 zenon_H1fd zenon_Hd9 zenon_H1d2 zenon_H108 zenon_Hb5 zenon_H20e zenon_Hd1 zenon_H35 zenon_He1 zenon_Hb6 zenon_H10d zenon_H1e zenon_H2d zenon_H173 zenon_H18c zenon_Hcd zenon_H101 zenon_H5c zenon_H1d8 zenon_Hbd zenon_H3f zenon_Hb8 zenon_He7 zenon_H6b zenon_H1dc zenon_H15a zenon_H16f zenon_H159 zenon_H42 zenon_H1c7 zenon_H5e zenon_H1ca zenon_H60 zenon_H208 zenon_H6f zenon_H1d5 zenon_H156 zenon_Hd6 zenon_H1af zenon_H1bd zenon_H102 zenon_Hfc zenon_H19e zenon_H3c zenon_H135 zenon_H222 zenon_Hd0 zenon_H218 zenon_H200 zenon_H18e zenon_H174 zenon_Hde zenon_H1a5 zenon_H19a zenon_H112 zenon_Ha4. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.90/30.07 exact (zenon_H84 zenon_H88). % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.90/30.07 exact (zenon_H84 zenon_H88). % 29.90/30.07 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.90/30.07 apply (zenon_L147_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.90/30.07 exact (zenon_H74 zenon_H73). % 29.90/30.07 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.90/30.07 exact (zenon_H74 zenon_H73). % 29.90/30.07 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.90/30.07 apply (zenon_L503_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.90/30.07 apply (zenon_L508_); trivial. % 29.90/30.07 apply (zenon_L288_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.90/30.07 exact (zenon_H74 zenon_H73). % 29.90/30.07 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_L503_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L272_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L241_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L165_); trivial. % 29.90/30.07 apply (zenon_L509_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L490_); trivial. % 29.90/30.07 apply (zenon_L291_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L241_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L510_); trivial. % 29.90/30.07 apply (zenon_L509_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L235_); trivial. % 29.90/30.07 apply (zenon_L511_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.90/30.07 apply (zenon_L42_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_L351_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L154_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_L309_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L241_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L510_); trivial. % 29.90/30.07 apply (zenon_L295_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L490_); trivial. % 29.90/30.07 apply (zenon_L511_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_L517_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L416_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L241_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L165_); trivial. % 29.90/30.07 apply (zenon_L519_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L235_); trivial. % 29.90/30.07 apply (zenon_L291_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L241_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L510_); trivial. % 29.90/30.07 apply (zenon_L519_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L490_); trivial. % 29.90/30.07 apply (zenon_L511_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.90/30.07 apply (zenon_L151_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.90/30.07 apply (zenon_L523_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.90/30.07 apply (zenon_L42_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.90/30.07 apply (zenon_L524_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_L517_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L416_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L241_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L165_); trivial. % 29.90/30.07 apply (zenon_L530_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L235_); trivial. % 29.90/30.07 apply (zenon_L291_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L532_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L510_); trivial. % 29.90/30.07 apply (zenon_L530_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L490_); trivial. % 29.90/30.07 apply (zenon_L101_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.90/30.07 apply (zenon_L523_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.90/30.07 apply (zenon_L42_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.90/30.07 apply (zenon_L524_); trivial. % 29.90/30.07 apply (zenon_L532_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.90/30.07 apply (zenon_L157_); trivial. % 29.90/30.07 apply (zenon_L461_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.90/30.07 apply (zenon_L508_); trivial. % 29.90/30.07 apply (zenon_L288_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.90/30.07 exact (zenon_H74 zenon_H73). % 29.90/30.07 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_L503_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L272_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_L534_); trivial. % 29.90/30.07 apply (zenon_L266_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.90/30.07 apply (zenon_L151_); trivial. % 29.90/30.07 apply (zenon_L267_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.90/30.07 apply (zenon_L142_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.90/30.07 apply (zenon_L272_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.90/30.07 apply (zenon_L159_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L241_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_L504_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L235_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.07 apply (zenon_L481_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.07 apply (zenon_L281_); trivial. % 29.90/30.07 exact (zenon_H18e zenon_H40). % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L93_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_L282_); trivial. % 29.90/30.07 apply (zenon_L440_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.90/30.07 apply (zenon_L151_); trivial. % 29.90/30.07 apply (zenon_L267_); trivial. % 29.90/30.07 apply (zenon_L288_); trivial. % 29.90/30.07 apply (zenon_L27_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.90/30.07 apply (zenon_L136_); trivial. % 29.90/30.07 apply (zenon_L140_); trivial. % 29.90/30.07 (* end of lemma zenon_L535_ *) % 29.90/30.07 assert (zenon_L536_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_Hde zenon_Hcc zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L89_); trivial. % 29.90/30.07 apply (zenon_L210_); trivial. % 29.90/30.07 (* end of lemma zenon_L536_ *) % 29.90/30.07 assert (zenon_L537_ : ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (op (op (e0) (e0)) (e0)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H90 zenon_H89 zenon_H213. % 29.90/30.07 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 29.90/30.07 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e1) = (op (op (e0) (e0)) (e0)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H213. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H78. % 29.90/30.07 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 29.90/30.07 cut (((op (op (e0) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 29.90/30.07 congruence. % 29.90/30.07 cut (((op (e3) (e0)) = (e1)) = ((op (op (e0) (e0)) (e0)) = (e1))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H214. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H90. % 29.90/30.07 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.90/30.07 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 29.90/30.07 congruence. % 29.90/30.07 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 29.90/30.07 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H21f. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H78. % 29.90/30.07 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 29.90/30.07 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 29.90/30.07 congruence. % 29.90/30.07 apply (zenon_L250_); trivial. % 29.90/30.07 apply zenon_H79. apply refl_equal. % 29.90/30.07 apply zenon_H79. apply refl_equal. % 29.90/30.07 apply zenon_H22. apply refl_equal. % 29.90/30.07 apply zenon_H79. apply refl_equal. % 29.90/30.07 apply zenon_H79. apply refl_equal. % 29.90/30.07 (* end of lemma zenon_L537_ *) % 29.90/30.07 assert (zenon_L538_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 29.90/30.07 do 0 intro. intros zenon_Hf4 zenon_H90 zenon_H89. % 29.90/30.07 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H253 | zenon_intro zenon_H252 ]. % 29.90/30.07 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 29.90/30.07 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e2) = (op (op (e0) (e0)) (op (e0) (e0))))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H253. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H7e. % 29.90/30.07 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 29.90/30.07 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H254]. % 29.90/30.07 congruence. % 29.90/30.07 cut (((op (e3) (e3)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H254. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_Hf4. % 29.90/30.07 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.90/30.07 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 29.90/30.07 congruence. % 29.90/30.07 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 29.90/30.07 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))))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H221. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H7e. % 29.90/30.07 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 29.90/30.07 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 29.90/30.07 congruence. % 29.90/30.07 apply (zenon_L249_); trivial. % 29.90/30.07 apply zenon_H7f. apply refl_equal. % 29.90/30.07 apply zenon_H7f. apply refl_equal. % 29.90/30.07 apply zenon_H57. apply refl_equal. % 29.90/30.07 apply zenon_H7f. apply refl_equal. % 29.90/30.07 apply zenon_H7f. apply refl_equal. % 29.90/30.07 apply (zenon_notand_s _ _ zenon_H252); [ zenon_intro zenon_H213 | zenon_intro zenon_H1f9 ]. % 29.90/30.07 apply (zenon_L537_); trivial. % 29.90/30.07 apply zenon_H1f9. apply sym_equal. exact zenon_H89. % 29.90/30.07 (* end of lemma zenon_L538_ *) % 29.90/30.07 assert (zenon_L539_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 29.90/30.07 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_Hb6 zenon_He1 zenon_H90 zenon_H89. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.90/30.07 apply (zenon_L386_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.90/30.07 apply (zenon_L53_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.90/30.07 apply (zenon_L204_); trivial. % 29.90/30.07 apply (zenon_L538_); trivial. % 29.90/30.07 (* end of lemma zenon_L539_ *) % 29.90/30.07 assert (zenon_L540_ : (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H6f zenon_Hb6 zenon_H1a0. % 29.90/30.07 cut (((op (e3) (e2)) = (e3)) = ((e1) = (e3))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H6f. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_Hb6. % 29.90/30.07 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.90/30.07 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H255]. % 29.90/30.07 congruence. % 29.90/30.07 exact (zenon_H255 zenon_H1a0). % 29.90/30.07 apply zenon_H2f. apply refl_equal. % 29.90/30.07 (* end of lemma zenon_L540_ *) % 29.90/30.07 assert (zenon_L541_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H23b zenon_H89 zenon_He1 zenon_He9 zenon_Hcd zenon_Hf9 zenon_H1f zenon_H3f zenon_Hb6 zenon_H6f zenon_H182 zenon_H14e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 29.90/30.07 apply (zenon_L539_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 29.90/30.07 apply (zenon_L336_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 29.90/30.07 apply (zenon_L540_); trivial. % 29.90/30.07 apply (zenon_L137_); trivial. % 29.90/30.07 (* end of lemma zenon_L541_ *) % 29.90/30.07 assert (zenon_L542_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_Hee zenon_H19a zenon_H1c7 zenon_H222 zenon_H5e zenon_H3c zenon_H1e zenon_H1ca zenon_H256 zenon_Hb1 zenon_H6f zenon_Hb6 zenon_H3f zenon_H1f zenon_Hf9 zenon_Hcd zenon_He9 zenon_He1 zenon_H89 zenon_H23b zenon_H14e zenon_H1af zenon_H1c5 zenon_H156. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.90/30.07 apply (zenon_L387_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.90/30.07 apply (zenon_L265_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.90/30.07 apply (zenon_L204_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 29.90/30.07 apply (zenon_L84_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 29.90/30.07 apply (zenon_L541_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L525_); trivial. % 29.90/30.07 apply (zenon_L290_); trivial. % 29.90/30.07 (* end of lemma zenon_L542_ *) % 29.90/30.07 assert (zenon_L543_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_Hbd zenon_H1bd zenon_H6c zenon_Hcc zenon_Hde zenon_H1d8 zenon_H5c zenon_H200 zenon_H2d zenon_Hee zenon_H19a zenon_H1c7 zenon_H222 zenon_H5e zenon_H3c zenon_H1e zenon_H1ca zenon_H256 zenon_H6f zenon_Hb6 zenon_H3f zenon_H1f zenon_Hf9 zenon_Hcd zenon_He9 zenon_He1 zenon_H89 zenon_H23b zenon_H14e zenon_H1af zenon_H1c5 zenon_H156. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.90/30.07 apply (zenon_L536_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.90/30.07 apply (zenon_L29_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.90/30.07 apply (zenon_L304_); trivial. % 29.90/30.07 apply (zenon_L542_); trivial. % 29.90/30.07 (* end of lemma zenon_L543_ *) % 29.90/30.07 assert (zenon_L544_ : (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> False). % 29.90/30.07 do 0 intro. intros zenon_He1 zenon_H1b9 zenon_Hcc. % 29.90/30.07 cut (((op (e2) (e2)) = (e3)) = ((e2) = (e3))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_He1. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H1b9. % 29.90/30.07 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.90/30.07 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 29.90/30.07 congruence. % 29.90/30.07 exact (zenon_Hd0 zenon_Hcc). % 29.90/30.07 apply zenon_H2f. apply refl_equal. % 29.90/30.07 (* end of lemma zenon_L544_ *) % 29.90/30.07 assert (zenon_L545_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H42 zenon_H2d zenon_H156 zenon_H16c zenon_H1af zenon_He1 zenon_Hcc zenon_H208 zenon_H6f zenon_H1f zenon_H5e zenon_H3c zenon_He9 zenon_H60 zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.90/30.07 apply (zenon_L220_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.90/30.07 apply (zenon_L155_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.90/30.07 apply (zenon_L544_); trivial. % 29.90/30.07 apply (zenon_L290_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.07 apply (zenon_L155_); trivial. % 29.90/30.07 exact (zenon_H18e zenon_H40). % 29.90/30.07 (* end of lemma zenon_L545_ *) % 29.90/30.07 assert (zenon_L546_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H3d. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L194_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L89_); trivial. % 29.90/30.07 apply (zenon_L209_); trivial. % 29.90/30.07 (* end of lemma zenon_L546_ *) % 29.90/30.07 assert (zenon_L547_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H1d5 zenon_H60 zenon_H208 zenon_H20e zenon_Hd1 zenon_Hdc zenon_H101 zenon_H37 zenon_H19e zenon_H1dc zenon_H18e zenon_He7 zenon_Hb8 zenon_H112 zenon_Hdf zenon_Hbd zenon_H1bd zenon_H6c zenon_Hcc zenon_Hde zenon_H1d8 zenon_H5c zenon_H200 zenon_H2d zenon_Hee zenon_H19a zenon_H1c7 zenon_H222 zenon_H5e zenon_H3c zenon_H1e zenon_H1ca zenon_H256 zenon_H6f zenon_Hb6 zenon_H3f zenon_H1f zenon_Hf9 zenon_Hcd zenon_He9 zenon_He1 zenon_H89 zenon_H23b zenon_H14e zenon_H1af zenon_H156. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.90/30.07 apply (zenon_L258_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.90/30.07 apply (zenon_L131_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.90/30.07 apply (zenon_L202_); trivial. % 29.90/30.07 apply (zenon_L543_); trivial. % 29.90/30.07 (* end of lemma zenon_L547_ *) % 29.90/30.07 assert (zenon_L548_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H20d zenon_Hdf zenon_H1e1. % 29.90/30.07 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H20d. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_Hdf. % 29.90/30.07 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 29.90/30.07 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.90/30.07 congruence. % 29.90/30.07 apply zenon_H6d. apply refl_equal. % 29.90/30.07 apply zenon_H1e2. apply sym_equal. exact zenon_H1e1. % 29.90/30.07 (* end of lemma zenon_L548_ *) % 29.90/30.07 assert (zenon_L549_ : (~((op (e2) (e2)) = (op (e2) (op (e2) (e2))))) -> ((op (e2) (e2)) = (e2)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H259 zenon_Hcc. % 29.90/30.07 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 29.90/30.07 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.90/30.07 congruence. % 29.90/30.07 apply zenon_H57. apply refl_equal. % 29.90/30.07 apply zenon_H10c. apply sym_equal. exact zenon_Hcc. % 29.90/30.07 (* end of lemma zenon_L549_ *) % 29.90/30.07 assert (zenon_L550_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H108 zenon_H60 zenon_Hcc zenon_Hf5. % 29.90/30.07 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H108. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H60. % 29.90/30.07 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 29.90/30.07 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 29.90/30.07 congruence. % 29.90/30.07 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.90/30.07 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e2)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H25a. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H28. % 29.90/30.07 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.90/30.07 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 29.90/30.07 congruence. % 29.90/30.07 apply (zenon_L549_); trivial. % 29.90/30.07 apply zenon_H29. apply refl_equal. % 29.90/30.07 apply zenon_H29. apply refl_equal. % 29.90/30.07 apply zenon_Hf8. apply sym_equal. exact zenon_Hf5. % 29.90/30.07 (* end of lemma zenon_L550_ *) % 29.90/30.07 assert (zenon_L551_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H1e6 zenon_Hdf zenon_H20d zenon_H112 zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 29.90/30.07 apply (zenon_L548_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 29.90/30.07 apply (zenon_L187_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 29.90/30.07 apply (zenon_L550_); trivial. % 29.90/30.07 apply (zenon_L245_); trivial. % 29.90/30.07 (* end of lemma zenon_L551_ *) % 29.90/30.07 assert (zenon_L552_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H6b zenon_Hc9 zenon_Hcc. % 29.90/30.07 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H6b. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_Hc9. % 29.90/30.07 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 29.90/30.07 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.90/30.07 congruence. % 29.90/30.07 apply zenon_H6d. apply refl_equal. % 29.90/30.07 apply zenon_H10c. apply sym_equal. exact zenon_Hcc. % 29.90/30.07 (* end of lemma zenon_L552_ *) % 29.90/30.07 assert (zenon_L553_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H174 zenon_He2 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_H1e6 zenon_Hdf zenon_H20d zenon_H112 zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H218. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.90/30.07 apply (zenon_L252_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.90/30.07 apply (zenon_L151_); trivial. % 29.90/30.07 apply (zenon_L551_); trivial. % 29.90/30.07 (* end of lemma zenon_L553_ *) % 29.90/30.07 assert (zenon_L554_ : ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H60 zenon_Hcc zenon_Hda zenon_H27. % 29.90/30.07 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.90/30.07 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H27. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H28. % 29.90/30.07 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.90/30.07 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 29.90/30.07 congruence. % 29.90/30.07 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H2a. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H60. % 29.90/30.07 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 29.90/30.07 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 29.90/30.07 congruence. % 29.90/30.07 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.90/30.07 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e2)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_H25a. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H28. % 29.90/30.07 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.90/30.07 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 29.90/30.07 congruence. % 29.90/30.07 apply (zenon_L549_); trivial. % 29.90/30.07 apply zenon_H29. apply refl_equal. % 29.90/30.07 apply zenon_H29. apply refl_equal. % 29.90/30.07 apply zenon_Hdb. apply sym_equal. exact zenon_Hda. % 29.90/30.07 apply zenon_H29. apply refl_equal. % 29.90/30.07 apply zenon_H29. apply refl_equal. % 29.90/30.07 (* end of lemma zenon_L554_ *) % 29.90/30.07 assert (zenon_L555_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> False). % 29.90/30.07 do 0 intro. intros zenon_Hd6 zenon_H55 zenon_Hcc. % 29.90/30.07 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e2)))). % 29.90/30.07 intro zenon_D_pnotp. % 29.90/30.07 apply zenon_Hd6. % 29.90/30.07 rewrite <- zenon_D_pnotp. % 29.90/30.07 exact zenon_H55. % 29.90/30.07 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 29.90/30.07 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 29.90/30.07 congruence. % 29.90/30.07 apply zenon_H63. apply refl_equal. % 29.90/30.07 apply zenon_H10c. apply sym_equal. exact zenon_Hcc. % 29.90/30.07 (* end of lemma zenon_L555_ *) % 29.90/30.07 assert (zenon_L556_ : (~((op (e1) (e3)) = (op (e2) (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 (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H156 zenon_Hb6 zenon_Hee zenon_Hbd zenon_H1bd zenon_H6c zenon_Hde zenon_H1d8 zenon_H5c zenon_H200 zenon_H256 zenon_H3f zenon_Hf9 zenon_H89 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hcc zenon_Hd6 zenon_H42 zenon_H2d zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_H1ca zenon_H60 zenon_H17b zenon_H218 zenon_H173 zenon_He1 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L241_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.90/30.07 apply (zenon_L258_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.90/30.07 apply (zenon_L131_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.90/30.07 apply (zenon_L259_); trivial. % 29.90/30.07 apply (zenon_L543_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L490_); trivial. % 29.90/30.07 apply (zenon_L545_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.90/30.07 apply (zenon_L154_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.90/30.07 apply (zenon_L555_); trivial. % 29.90/30.07 apply (zenon_L266_); trivial. % 29.90/30.07 (* end of lemma zenon_L556_ *) % 29.90/30.07 assert (zenon_L557_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_Hc0 zenon_H17d zenon_H225 zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H27 zenon_He4 zenon_H74 zenon_H156 zenon_Hee zenon_Hbd zenon_H1bd zenon_H1d8 zenon_H5c zenon_H200 zenon_H256 zenon_H3f zenon_Hf9 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H42 zenon_H1c7 zenon_H222 zenon_H5e zenon_H3c zenon_H1ca zenon_H173 zenon_He1 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H18e zenon_Hde zenon_H174 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H218 zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H19a zenon_H112 zenon_Ha4. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.90/30.07 exact (zenon_H84 zenon_H88). % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.90/30.07 exact (zenon_H84 zenon_H88). % 29.90/30.07 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.90/30.07 apply (zenon_L147_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.90/30.07 exact (zenon_H74 zenon_H73). % 29.90/30.07 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.90/30.07 exact (zenon_H74 zenon_H73). % 29.90/30.07 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.90/30.07 apply (zenon_L241_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.90/30.07 apply (zenon_L547_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.90/30.07 apply (zenon_L490_); trivial. % 29.90/30.07 apply (zenon_L545_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.90/30.07 apply (zenon_L151_); trivial. % 29.90/30.07 apply (zenon_L551_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.90/30.07 apply (zenon_L552_); trivial. % 29.90/30.07 apply (zenon_L553_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.90/30.07 apply (zenon_L554_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.90/30.07 exact (zenon_H74 zenon_H73). % 29.90/30.07 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.90/30.07 apply (zenon_L556_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.90/30.07 apply (zenon_L151_); trivial. % 29.90/30.07 apply (zenon_L551_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.90/30.07 apply (zenon_L49_); trivial. % 29.90/30.07 apply (zenon_L553_); trivial. % 29.90/30.07 apply (zenon_L139_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.90/30.07 apply (zenon_L136_); trivial. % 29.90/30.07 apply (zenon_L140_); trivial. % 29.90/30.07 (* end of lemma zenon_L557_ *) % 29.90/30.07 assert (zenon_L558_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H1d5 zenon_H19e zenon_H37 zenon_H222 zenon_H60 zenon_H5e zenon_H1f zenon_H3c zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H19a zenon_Hd1 zenon_Hdc zenon_H101 zenon_H1e1 zenon_H1bd zenon_Hcc zenon_He1 zenon_H1af zenon_H16b zenon_H218. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.90/30.07 apply (zenon_L258_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.90/30.07 apply (zenon_L209_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.90/30.07 apply (zenon_L544_); trivial. % 29.90/30.07 apply (zenon_L245_); trivial. % 29.90/30.07 (* end of lemma zenon_L558_ *) % 29.90/30.07 assert (zenon_L559_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (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 (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H218 zenon_H16b zenon_H1af zenon_He1 zenon_Hcc zenon_H1bd zenon_H101 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H1d5 zenon_Hde zenon_Hc0 zenon_H17d zenon_H225 zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H27 zenon_He4 zenon_H74 zenon_H156 zenon_Hee zenon_Hbd zenon_H1d8 zenon_H5c zenon_H200 zenon_H256 zenon_H3f zenon_Hf9 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H42 zenon_H1c7 zenon_H1ca zenon_H173 zenon_H159 zenon_H174 zenon_H2d zenon_H10d zenon_Hb6 zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H108 zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_H112 zenon_Ha4 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L557_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L89_); trivial. % 29.90/30.07 apply (zenon_L558_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.07 apply (zenon_L155_); trivial. % 29.90/30.07 exact (zenon_H18e zenon_H40). % 29.90/30.07 (* end of lemma zenon_L559_ *) % 29.90/30.07 assert (zenon_L560_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.90/30.07 do 0 intro. intros zenon_H42 zenon_H2d zenon_He1 zenon_H1af zenon_H1bd zenon_Hfd zenon_H3c zenon_H1e zenon_H1e6 zenon_H20d zenon_H112 zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H16b zenon_H218 zenon_H200 zenon_H18e. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.90/30.07 apply (zenon_L4_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.90/30.07 apply (zenon_L158_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L551_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L79_); trivial. % 29.90/30.07 apply (zenon_L209_); trivial. % 29.90/30.07 exact (zenon_H18e zenon_H40). % 29.90/30.07 (* end of lemma zenon_L560_ *) % 29.90/30.07 assert (zenon_L561_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 29.90/30.07 do 0 intro. intros zenon_H200 zenon_H218 zenon_H16b zenon_H108 zenon_H60 zenon_Hf6 zenon_H112 zenon_H20d zenon_H1e6 zenon_H1e zenon_H3c zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H3d. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.90/30.07 apply (zenon_L551_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.90/30.07 apply (zenon_L207_); trivial. % 29.90/30.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.90/30.07 apply (zenon_L89_); trivial. % 29.90/30.07 apply (zenon_L209_); trivial. % 29.90/30.07 (* end of lemma zenon_L561_ *) % 29.90/30.07 assert (zenon_L562_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.08 do 0 intro. intros zenon_H42 zenon_H2d zenon_H155 zenon_H156 zenon_H101 zenon_H159 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1f zenon_H5e zenon_H222 zenon_H19e zenon_H1d5 zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e zenon_H1e6 zenon_H20d zenon_H112 zenon_Hf6 zenon_H60 zenon_H108 zenon_H16b zenon_H218 zenon_H200 zenon_H18e. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.94/30.08 apply (zenon_L4_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.94/30.08 apply (zenon_L551_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.94/30.08 apply (zenon_L207_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.94/30.08 apply (zenon_L89_); trivial. % 29.94/30.08 apply (zenon_L488_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.94/30.08 apply (zenon_L561_); trivial. % 29.94/30.08 exact (zenon_H18e zenon_H40). % 29.94/30.08 (* end of lemma zenon_L562_ *) % 29.94/30.08 assert (zenon_L563_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.08 do 0 intro. intros zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_Ha4 zenon_H1a5 zenon_H92 zenon_H84 zenon_H1b1 zenon_Hb6 zenon_H10d zenon_H174 zenon_H173 zenon_H1ca zenon_H1c7 zenon_Hd6 zenon_H16f zenon_H15a zenon_H14e zenon_H23b zenon_Hf9 zenon_H3f zenon_H256 zenon_H5c zenon_H1d8 zenon_Hbd zenon_Hee zenon_H74 zenon_He4 zenon_H27 zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_H225 zenon_H17d zenon_Hc0 zenon_He1 zenon_H42 zenon_H2d zenon_H156 zenon_H101 zenon_H159 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1f zenon_H5e zenon_H222 zenon_H19e zenon_H1d5 zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e zenon_H1e6 zenon_H20d zenon_H112 zenon_Hf6 zenon_H60 zenon_H108 zenon_H16b zenon_H218 zenon_H200 zenon_H18e. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.94/30.08 apply (zenon_L559_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.94/30.08 apply (zenon_L560_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.94/30.08 apply (zenon_L159_); trivial. % 29.94/30.08 apply (zenon_L562_); trivial. % 29.94/30.08 (* end of lemma zenon_L563_ *) % 29.94/30.08 assert (zenon_L564_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.08 do 0 intro. intros zenon_H17d zenon_H108 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_Hc0 zenon_H225 zenon_H1dc zenon_He7 zenon_Hb8 zenon_H1b1 zenon_H84 zenon_H92 zenon_H27 zenon_He4 zenon_H74 zenon_H156 zenon_Hee zenon_Hbd zenon_H1bd zenon_Hde zenon_H1d8 zenon_H5c zenon_H200 zenon_H256 zenon_H3f zenon_Hf9 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H42 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H3c zenon_H1ca zenon_H60 zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H18e zenon_Hcc zenon_H6b zenon_H174 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_He1 zenon_H1a5 zenon_H19a zenon_H112 zenon_Ha4. % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.94/30.08 exact (zenon_H84 zenon_H88). % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.94/30.08 exact (zenon_H84 zenon_H88). % 29.94/30.08 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.94/30.08 apply (zenon_L147_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.94/30.08 exact (zenon_H74 zenon_H73). % 29.94/30.08 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.08 exact (zenon_H74 zenon_H73). % 29.94/30.08 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.08 apply (zenon_L241_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.94/30.08 apply (zenon_L547_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.94/30.08 apply (zenon_L207_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.94/30.08 apply (zenon_L89_); trivial. % 29.94/30.08 apply (zenon_L210_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.08 apply (zenon_L235_); trivial. % 29.94/30.08 apply (zenon_L545_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.08 apply (zenon_L4_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.08 apply (zenon_L151_); trivial. % 29.94/30.08 apply (zenon_L559_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.08 apply (zenon_L552_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.08 apply (zenon_L252_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.08 apply (zenon_L4_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.08 apply (zenon_L151_); trivial. % 29.94/30.08 apply (zenon_L563_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.94/30.08 apply (zenon_L554_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.08 exact (zenon_H74 zenon_H73). % 29.94/30.08 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.08 apply (zenon_L556_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.08 apply (zenon_L4_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.08 apply (zenon_L151_); trivial. % 29.94/30.08 apply (zenon_L267_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.08 apply (zenon_L552_); trivial. % 29.94/30.08 apply (zenon_L472_); trivial. % 29.94/30.08 apply (zenon_L139_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.94/30.08 apply (zenon_L136_); trivial. % 29.94/30.08 apply (zenon_L140_); trivial. % 29.94/30.08 (* end of lemma zenon_L564_ *) % 29.94/30.08 assert (zenon_L565_ : ((op (e0) (e2)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> False). % 29.94/30.08 do 0 intro. intros zenon_H117 zenon_H3d zenon_Had zenon_H6e zenon_Ha4 zenon_H112 zenon_H19a zenon_H1a5 zenon_He1 zenon_H10d zenon_H1e zenon_H174 zenon_H6b zenon_Hcc zenon_H18e zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H1d5 zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H60 zenon_H1ca zenon_H3c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H42 zenon_Hd6 zenon_H16f zenon_H15a zenon_H14e zenon_H23b zenon_Hf9 zenon_H3f zenon_H256 zenon_H200 zenon_H5c zenon_H1d8 zenon_Hde zenon_H1bd zenon_Hbd zenon_Hee zenon_H156 zenon_H74 zenon_He4 zenon_H27 zenon_H92 zenon_H84 zenon_H1b1 zenon_Hb8 zenon_He7 zenon_H1dc zenon_H225 zenon_Hc0 zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H108 zenon_H17d zenon_H2d. % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 29.94/30.08 apply (zenon_L546_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 29.94/30.08 apply (zenon_L29_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 29.94/30.08 apply (zenon_L437_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 29.94/30.08 apply (zenon_L34_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 29.94/30.08 exact (zenon_H18e zenon_H40). % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 29.94/30.08 apply (zenon_L564_); trivial. % 29.94/30.08 apply (zenon_L107_); trivial. % 29.94/30.08 (* end of lemma zenon_L565_ *) % 29.94/30.08 assert (zenon_L566_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.08 do 0 intro. intros zenon_H100 zenon_H2d zenon_H17d zenon_H108 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_Hc0 zenon_H225 zenon_H1dc zenon_He7 zenon_Hb8 zenon_H1b1 zenon_H84 zenon_H92 zenon_H27 zenon_He4 zenon_H74 zenon_H156 zenon_Hee zenon_Hbd zenon_H1bd zenon_Hde zenon_H1d8 zenon_H5c zenon_H200 zenon_H256 zenon_H3f zenon_Hf9 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H42 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H3c zenon_H1ca zenon_H60 zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_Hcc zenon_H6b zenon_H174 zenon_H1e zenon_H10d zenon_He1 zenon_H1a5 zenon_H19a zenon_H112 zenon_Ha4 zenon_H6e zenon_Had zenon_H117 zenon_H18e. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.94/30.08 apply (zenon_L4_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.94/30.08 apply (zenon_L153_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.94/30.08 apply (zenon_L565_); trivial. % 29.94/30.08 exact (zenon_H18e zenon_H40). % 29.94/30.08 (* end of lemma zenon_L566_ *) % 29.94/30.08 assert (zenon_L567_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 29.94/30.08 do 0 intro. intros zenon_H1dc zenon_H60 zenon_Hcc zenon_Heb. % 29.94/30.08 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 29.94/30.08 intro zenon_D_pnotp. % 29.94/30.08 apply zenon_H1dc. % 29.94/30.08 rewrite <- zenon_D_pnotp. % 29.94/30.08 exact zenon_H60. % 29.94/30.08 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 29.94/30.08 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 29.94/30.08 congruence. % 29.94/30.08 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.94/30.08 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e2)))). % 29.94/30.08 intro zenon_D_pnotp. % 29.94/30.08 apply zenon_H25a. % 29.94/30.08 rewrite <- zenon_D_pnotp. % 29.94/30.08 exact zenon_H28. % 29.94/30.08 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.94/30.08 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 29.94/30.08 congruence. % 29.94/30.08 apply (zenon_L549_); trivial. % 29.94/30.08 apply zenon_H29. apply refl_equal. % 29.94/30.08 apply zenon_H29. apply refl_equal. % 29.94/30.08 apply zenon_Hec. apply sym_equal. exact zenon_Heb. % 29.94/30.08 (* end of lemma zenon_L567_ *) % 29.94/30.08 assert (zenon_L568_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 29.94/30.08 do 0 intro. intros zenon_Hf9 zenon_H8a zenon_He1 zenon_He9 zenon_H3f zenon_Hcc zenon_H60 zenon_H1dc zenon_H231. % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 29.94/30.08 apply (zenon_L50_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 29.94/30.08 apply (zenon_L53_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 29.94/30.08 apply (zenon_L567_); trivial. % 29.94/30.08 exact (zenon_H231 zenon_Hf4). % 29.94/30.08 (* end of lemma zenon_L568_ *) % 29.94/30.08 assert (zenon_L569_ : ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.94/30.08 do 0 intro. intros zenon_Hdc zenon_H1f zenon_H1fd zenon_H6c zenon_H231 zenon_H1dc zenon_H3f zenon_He9 zenon_He1 zenon_Hf9 zenon_Hb8 zenon_H1d8 zenon_H18e zenon_H10d zenon_H6f zenon_H100 zenon_H2d zenon_H17d zenon_Hc0 zenon_H225 zenon_He7 zenon_H1b1 zenon_H84 zenon_H92 zenon_H27 zenon_He4 zenon_H74 zenon_H156 zenon_Hee zenon_Hbd zenon_H1bd zenon_Hde zenon_H5c zenon_H200 zenon_H256 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H42 zenon_H1c7 zenon_H222 zenon_H5e zenon_H3c zenon_H1ca zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H6b zenon_H174 zenon_H1e zenon_H1a5 zenon_H19a zenon_Ha4 zenon_Had zenon_Hd9 zenon_H8d zenon_H1e6 zenon_Hdf zenon_H20d zenon_H112 zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H218. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.08 apply (zenon_L241_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.94/30.08 apply (zenon_L263_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.94/30.08 apply (zenon_L131_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.94/30.08 apply (zenon_L202_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 29.94/30.08 apply (zenon_L149_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 29.94/30.08 apply (zenon_L235_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 29.94/30.08 apply (zenon_L171_); trivial. % 29.94/30.08 apply (zenon_L543_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.08 apply (zenon_L235_); trivial. % 29.94/30.08 apply (zenon_L545_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.08 apply (zenon_L4_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.08 apply (zenon_L149_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.08 apply (zenon_L566_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.08 apply (zenon_L339_); trivial. % 29.94/30.08 apply (zenon_L568_); trivial. % 29.94/30.08 apply (zenon_L551_); trivial. % 29.94/30.08 (* end of lemma zenon_L569_ *) % 29.94/30.08 assert (zenon_L570_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 29.94/30.08 do 0 intro. intros zenon_H218 zenon_H108 zenon_H60 zenon_Hf6 zenon_H112 zenon_H20d zenon_H1e6 zenon_H8d zenon_Hd9 zenon_Had zenon_Ha4 zenon_H19a zenon_H1a5 zenon_H174 zenon_H6b zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H1d5 zenon_H208 zenon_Hcd zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H222 zenon_H1c7 zenon_H42 zenon_Hd6 zenon_H16f zenon_H15a zenon_H14e zenon_H23b zenon_H256 zenon_H200 zenon_H5c zenon_Hbd zenon_Hee zenon_H156 zenon_H74 zenon_He4 zenon_H27 zenon_H92 zenon_H84 zenon_H1b1 zenon_He7 zenon_H225 zenon_Hc0 zenon_H17d zenon_H2d zenon_H100 zenon_H6f zenon_H10d zenon_H18e zenon_H1d8 zenon_Hb8 zenon_Hf9 zenon_He1 zenon_H3f zenon_H1dc zenon_H231 zenon_H1fd zenon_H1f zenon_Hdc zenon_Hde zenon_Hcc zenon_H1ca zenon_H1e zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1bd zenon_H1af. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.94/30.08 apply (zenon_L569_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.94/30.08 apply (zenon_L207_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.94/30.08 apply (zenon_L89_); trivial. % 29.94/30.08 apply (zenon_L210_); trivial. % 29.94/30.08 (* end of lemma zenon_L570_ *) % 29.94/30.08 assert (zenon_L571_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 29.94/30.08 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hb8 zenon_Had zenon_H6e zenon_H100 zenon_H37 zenon_H10d zenon_H117 zenon_H6f. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 29.94/30.08 apply (zenon_L386_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 29.94/30.08 apply (zenon_L336_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 29.94/30.08 apply (zenon_L337_); trivial. % 29.94/30.08 apply (zenon_L153_); trivial. % 29.94/30.08 (* end of lemma zenon_L571_ *) % 29.94/30.08 assert (zenon_L572_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 29.94/30.08 do 0 intro. intros zenon_H8d zenon_Hd9 zenon_Had zenon_Ha4 zenon_H19a zenon_H1a5 zenon_H1e zenon_H174 zenon_H6b zenon_Hcc zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H1d5 zenon_H208 zenon_Hcd zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H60 zenon_H1ca zenon_H3c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H42 zenon_Hd6 zenon_H16f zenon_H15a zenon_H14e zenon_H23b zenon_Hf9 zenon_H3f zenon_H256 zenon_H200 zenon_H5c zenon_Hde zenon_H1bd zenon_Hbd zenon_Hee zenon_H156 zenon_H74 zenon_He4 zenon_H27 zenon_H92 zenon_H84 zenon_H1b1 zenon_He7 zenon_H1dc zenon_H225 zenon_Hc0 zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H108 zenon_H17d zenon_H2d zenon_H1f zenon_H100 zenon_H6f zenon_H112 zenon_H117 zenon_H10d zenon_H18e zenon_H1d8 zenon_Hb8 zenon_He1 zenon_He2. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.08 apply (zenon_L149_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.94/30.08 apply (zenon_L4_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.94/30.08 apply (zenon_L571_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.94/30.08 apply (zenon_L565_); trivial. % 29.94/30.08 exact (zenon_H18e zenon_H40). % 29.94/30.08 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.08 apply (zenon_L339_); trivial. % 29.94/30.08 apply (zenon_L50_); trivial. % 29.94/30.08 (* end of lemma zenon_L572_ *) % 29.94/30.08 assert (zenon_L573_ : ((op (e0) (e1)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.08 do 0 intro. intros zenon_He9 zenon_H6c zenon_H1ca zenon_H1fd zenon_H231 zenon_H1dc zenon_H3f zenon_Hf9 zenon_Hb8 zenon_H1d8 zenon_H10d zenon_H100 zenon_H17d zenon_Hc0 zenon_H225 zenon_He7 zenon_H1b1 zenon_H84 zenon_H92 zenon_H27 zenon_He4 zenon_H74 zenon_Hee zenon_Hbd zenon_H5c zenon_H256 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H1c7 zenon_H173 zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H6b zenon_H174 zenon_H1a5 zenon_Ha4 zenon_Had zenon_Hd9 zenon_H8d zenon_He1 zenon_H42 zenon_H2d zenon_H156 zenon_H101 zenon_H159 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1f zenon_H5e zenon_H222 zenon_H19e zenon_H1d5 zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e zenon_H1e6 zenon_H20d zenon_H112 zenon_Hf6 zenon_H60 zenon_H108 zenon_H16b zenon_H218 zenon_H200 zenon_H18e. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 29.94/30.08 apply (zenon_L570_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 29.94/30.08 apply (zenon_L560_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 29.94/30.08 apply (zenon_L159_); trivial. % 29.94/30.08 apply (zenon_L562_); trivial. % 29.94/30.08 (* end of lemma zenon_L573_ *) % 29.94/30.08 assert (zenon_L574_ : ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.08 do 0 intro. intros zenon_He2 zenon_He9 zenon_H6c zenon_H1ca zenon_H1fd zenon_H231 zenon_H1dc zenon_H3f zenon_Hf9 zenon_Hb8 zenon_H1d8 zenon_H10d zenon_H100 zenon_H17d zenon_Hc0 zenon_H225 zenon_He7 zenon_H1b1 zenon_H84 zenon_H92 zenon_H27 zenon_He4 zenon_H74 zenon_Hee zenon_Hbd zenon_H5c zenon_H256 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H1c7 zenon_H173 zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H6b zenon_H174 zenon_H1a5 zenon_Ha4 zenon_Had zenon_Hd9 zenon_H8d zenon_He1 zenon_H42 zenon_H2d zenon_H156 zenon_H101 zenon_H159 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1f zenon_H5e zenon_H222 zenon_H19e zenon_H1d5 zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e zenon_H1e6 zenon_H20d zenon_H112 zenon_Hf6 zenon_H60 zenon_H108 zenon_H218 zenon_H200 zenon_H18e. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.08 apply (zenon_L387_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.08 apply (zenon_L4_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.08 apply (zenon_L572_); trivial. % 29.94/30.08 apply (zenon_L573_); trivial. % 29.94/30.08 (* end of lemma zenon_L574_ *) % 29.94/30.08 assert (zenon_L575_ : ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 29.94/30.08 do 0 intro. intros zenon_H60 zenon_Hcc zenon_H55 zenon_Hd6. % 29.94/30.08 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.94/30.08 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 29.94/30.08 intro zenon_D_pnotp. % 29.94/30.08 apply zenon_Hd6. % 29.94/30.08 rewrite <- zenon_D_pnotp. % 29.94/30.08 exact zenon_H28. % 29.94/30.08 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.94/30.08 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 29.94/30.08 congruence. % 29.94/30.08 cut (((op (e2) (op (e2) (e2))) = (e2)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 29.94/30.08 intro zenon_D_pnotp. % 29.94/30.08 apply zenon_Hd7. % 29.94/30.08 rewrite <- zenon_D_pnotp. % 29.94/30.08 exact zenon_H60. % 29.94/30.08 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 29.94/30.08 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 29.94/30.08 congruence. % 29.94/30.08 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 29.94/30.08 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (op (e2) (e2))) = (op (e2) (e2)))). % 29.94/30.08 intro zenon_D_pnotp. % 29.94/30.08 apply zenon_H25a. % 29.94/30.08 rewrite <- zenon_D_pnotp. % 29.94/30.08 exact zenon_H28. % 29.94/30.08 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 29.94/30.08 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 29.94/30.08 congruence. % 29.94/30.08 apply (zenon_L549_); trivial. % 29.94/30.08 apply zenon_H29. apply refl_equal. % 29.94/30.08 apply zenon_H29. apply refl_equal. % 29.94/30.08 apply zenon_H1c2. apply sym_equal. exact zenon_H55. % 29.94/30.08 apply zenon_H29. apply refl_equal. % 29.94/30.08 apply zenon_H29. apply refl_equal. % 29.94/30.08 (* end of lemma zenon_L575_ *) % 29.94/30.08 assert (zenon_L576_ : ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.94/30.08 do 0 intro. intros zenon_He2 zenon_Hb8 zenon_H1d8 zenon_H18e zenon_H10d zenon_H112 zenon_H6f zenon_H100 zenon_H1f zenon_H2d zenon_H17d zenon_H108 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_Hc0 zenon_H225 zenon_H1dc zenon_He7 zenon_H1b1 zenon_H84 zenon_H92 zenon_H27 zenon_He4 zenon_H74 zenon_H156 zenon_Hee zenon_Hbd zenon_H1bd zenon_Hde zenon_H5c zenon_H200 zenon_H256 zenon_H3f zenon_Hf9 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H42 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H3c zenon_H1ca zenon_H60 zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_Hcc zenon_H6b zenon_H174 zenon_H1e zenon_H1a5 zenon_H19a zenon_Ha4 zenon_Had zenon_Hd9 zenon_H8d zenon_H17b zenon_He1. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.08 apply (zenon_L387_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.08 apply (zenon_L4_); trivial. % 29.94/30.08 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.08 apply (zenon_L572_); trivial. % 29.94/30.08 apply (zenon_L267_); trivial. % 29.94/30.08 (* end of lemma zenon_L576_ *) % 29.94/30.08 assert (zenon_L577_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.09 do 0 intro. intros zenon_H17d zenon_H231 zenon_H1fd zenon_Hb8 zenon_H1d8 zenon_H18e zenon_H10d zenon_H6f zenon_H100 zenon_H2d zenon_H108 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_Hc0 zenon_H225 zenon_H1dc zenon_He7 zenon_H1b1 zenon_H84 zenon_H92 zenon_H27 zenon_He4 zenon_H74 zenon_H156 zenon_Hee zenon_Hbd zenon_H1bd zenon_Hde zenon_H5c zenon_H200 zenon_H256 zenon_H3f zenon_Hf9 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H42 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H3c zenon_H1ca zenon_H60 zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_Hcc zenon_H6b zenon_H174 zenon_H1e zenon_Had zenon_Hd9 zenon_H8d zenon_He1 zenon_H1a5 zenon_H19a zenon_H112 zenon_Ha4. % 29.94/30.09 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.94/30.09 exact (zenon_H84 zenon_H88). % 29.94/30.09 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.94/30.09 exact (zenon_H84 zenon_H88). % 29.94/30.09 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.94/30.09 apply (zenon_L147_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.94/30.09 exact (zenon_H74 zenon_H73). % 29.94/30.09 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.94/30.09 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.09 exact (zenon_H74 zenon_H73). % 29.94/30.09 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.09 apply (zenon_L570_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.09 apply (zenon_L552_); trivial. % 29.94/30.09 apply (zenon_L574_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.94/30.09 apply (zenon_L554_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.09 exact (zenon_H74 zenon_H73). % 29.94/30.09 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.94/30.09 apply (zenon_L570_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.94/30.09 apply (zenon_L154_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.94/30.09 apply (zenon_L575_); trivial. % 29.94/30.09 apply (zenon_L266_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.09 apply (zenon_L552_); trivial. % 29.94/30.09 apply (zenon_L576_); trivial. % 29.94/30.09 apply (zenon_L139_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.94/30.09 apply (zenon_L136_); trivial. % 29.94/30.09 apply (zenon_L140_); trivial. % 29.94/30.09 (* end of lemma zenon_L577_ *) % 29.94/30.09 assert (zenon_L578_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 29.94/30.09 do 0 intro. intros zenon_H25b zenon_H84 zenon_H74 zenon_Hf6 zenon_H27 zenon_H1e6 zenon_Hc0 zenon_Ha4 zenon_H1a5 zenon_H225 zenon_Hd6 zenon_H174 zenon_H20d zenon_H218 zenon_H6b zenon_He4 zenon_H17d zenon_H92 zenon_Had zenon_H100 zenon_H10d zenon_H8d zenon_H15a zenon_H1d5 zenon_Hd9 zenon_H108 zenon_H23b zenon_Hee zenon_H1c7 zenon_H256 zenon_H156 zenon_Hf9 zenon_H14e zenon_Hde zenon_Hcc zenon_H1ca zenon_H1bd zenon_H200 zenon_H1fd zenon_H1d8 zenon_H5c zenon_H3f zenon_H1e zenon_H112 zenon_Hb8 zenon_H2d zenon_H1dc zenon_H18e zenon_He7 zenon_Hbd zenon_H101 zenon_H222 zenon_Hcd zenon_H20e zenon_Hd1 zenon_H6f zenon_H3c zenon_H5e zenon_H60 zenon_H19e zenon_H1af zenon_H208 zenon_He1 zenon_H159 zenon_H173 zenon_H42 zenon_H102 zenon_Hfc zenon_H35 zenon_H16f zenon_H19a zenon_H1b1. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 29.94/30.09 apply (zenon_L577_); trivial. % 29.94/30.09 apply (zenon_L564_); trivial. % 29.94/30.09 (* end of lemma zenon_L578_ *) % 29.94/30.09 assert (zenon_L579_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 29.94/30.09 do 0 intro. intros zenon_H25c zenon_H256 zenon_H84 zenon_H74 zenon_H2d zenon_H1e zenon_H8d zenon_H135 zenon_H3c zenon_H18c zenon_He1 zenon_Hcd zenon_H14b zenon_H1dc zenon_H6b zenon_H156 zenon_H1d8 zenon_H27 zenon_H1d2 zenon_H108 zenon_Hd6 zenon_H1bd zenon_H5e zenon_H60 zenon_H1c7 zenon_H1af zenon_H1ca zenon_H1d5 zenon_H173 zenon_H1e6 zenon_Hf6 zenon_Hb8 zenon_H112 zenon_H6f zenon_H10d zenon_H100 zenon_Had zenon_H102 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H18e zenon_H42 zenon_Hd9 zenon_H11e zenon_H1a5 zenon_Hc8 zenon_H23b zenon_Hee zenon_Hb5 zenon_Hf9 zenon_H20 zenon_H225 zenon_H222 zenon_H101 zenon_H159 zenon_H83 zenon_H218 zenon_He4 zenon_H15a zenon_H16f zenon_H16a zenon_H174 zenon_H17d zenon_H92 zenon_H14e zenon_H172 zenon_H200 zenon_H5c zenon_H125 zenon_Hbd zenon_He7 zenon_H3f zenon_H1fd zenon_Hde zenon_H208 zenon_H20d zenon_H20e zenon_H246 zenon_Hc0 zenon_H19a zenon_H1b1 zenon_Ha4 zenon_Haa zenon_H25b. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 29.94/30.09 apply (zenon_L452_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 29.94/30.09 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.94/30.09 exact (zenon_H84 zenon_H88). % 29.94/30.09 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.94/30.09 exact (zenon_H84 zenon_H88). % 29.94/30.09 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.94/30.09 apply (zenon_L147_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.94/30.09 apply (zenon_L495_); trivial. % 29.94/30.09 apply (zenon_L139_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.94/30.09 apply (zenon_L136_); trivial. % 29.94/30.09 apply (zenon_L140_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 29.94/30.09 apply (zenon_L502_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 29.94/30.09 apply (zenon_L479_); trivial. % 29.94/30.09 apply (zenon_L535_); trivial. % 29.94/30.09 apply (zenon_L578_); trivial. % 29.94/30.09 (* end of lemma zenon_L579_ *) % 29.94/30.09 assert (zenon_L580_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.09 do 0 intro. intros zenon_H1a8 zenon_H6c zenon_Hc9 zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_Hde zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H200 zenon_H172 zenon_H92 zenon_H17d zenon_H174 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H222 zenon_H225 zenon_H20 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_Hd9 zenon_H42 zenon_H18e zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H102 zenon_Had zenon_H100 zenon_H10d zenon_H6f zenon_Hb8 zenon_Hf6 zenon_H1e6 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H1af zenon_H1c7 zenon_H60 zenon_H5e zenon_H1bd zenon_Hd6 zenon_H108 zenon_H1d2 zenon_H27 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_He1 zenon_H18c zenon_H3c zenon_H135 zenon_H8d zenon_H1e zenon_H2d zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H112 zenon_H14e. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.09 apply (zenon_L120_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.09 apply (zenon_L458_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.09 apply (zenon_L579_); trivial. % 29.94/30.09 apply (zenon_L137_); trivial. % 29.94/30.09 (* end of lemma zenon_L580_ *) % 29.94/30.09 assert (zenon_L581_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.94/30.09 do 0 intro. intros zenon_H14e zenon_H112 zenon_H25c zenon_H256 zenon_H84 zenon_H74 zenon_H2d zenon_H1e zenon_H8d zenon_H135 zenon_H18c zenon_He1 zenon_Hcd zenon_H14b zenon_H1dc zenon_H6b zenon_H156 zenon_H1d8 zenon_H27 zenon_H1d2 zenon_H108 zenon_Hd6 zenon_H1bd zenon_H1c7 zenon_H1ca zenon_H1d5 zenon_H173 zenon_H1e6 zenon_Hf6 zenon_Hb8 zenon_H6f zenon_H10d zenon_H100 zenon_Had zenon_H102 zenon_Hd1 zenon_Hfc zenon_H35 zenon_H18e zenon_H42 zenon_Hd9 zenon_H11e zenon_H1a5 zenon_Hc8 zenon_H23b zenon_Hee zenon_Hb5 zenon_Hf9 zenon_H20 zenon_H225 zenon_H101 zenon_H159 zenon_H83 zenon_H218 zenon_He4 zenon_H15a zenon_H16f zenon_H16a zenon_H174 zenon_H17d zenon_H92 zenon_H172 zenon_H200 zenon_H5c zenon_H125 zenon_Hbd zenon_He7 zenon_H3f zenon_H1fd zenon_Hde zenon_H208 zenon_H20d zenon_H20e zenon_H246 zenon_Hc0 zenon_H1b1 zenon_Ha4 zenon_Haa zenon_H25b zenon_Hc9 zenon_H1a8 zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.94/30.09 apply (zenon_L580_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.94/30.09 apply (zenon_L218_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.94/30.09 apply (zenon_L256_); trivial. % 29.94/30.09 apply (zenon_L214_); trivial. % 29.94/30.09 (* end of lemma zenon_L581_ *) % 29.94/30.09 assert (zenon_L582_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.09 do 0 intro. intros zenon_H19e zenon_H222 zenon_H60 zenon_H9d zenon_H5e zenon_H1f zenon_H1a8 zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H172 zenon_H92 zenon_H17d zenon_H174 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H225 zenon_H20 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_Hd9 zenon_H42 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H102 zenon_Had zenon_H100 zenon_H10d zenon_H6f zenon_Hb8 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H1d2 zenon_H27 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_He1 zenon_H18c zenon_H135 zenon_H8d zenon_H2d zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H14e zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.94/30.09 apply (zenon_L4_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.94/30.09 apply (zenon_L581_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.94/30.09 apply (zenon_L456_); trivial. % 29.94/30.09 exact (zenon_H18e zenon_H40). % 29.94/30.09 (* end of lemma zenon_L582_ *) % 29.94/30.09 assert (zenon_L583_ : ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.09 do 0 intro. intros zenon_H68 zenon_H13b zenon_H19e zenon_H222 zenon_H60 zenon_H5e zenon_H1f zenon_H1a8 zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H172 zenon_H92 zenon_H17d zenon_H174 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H225 zenon_H20 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_Hd9 zenon_H42 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H102 zenon_Had zenon_H100 zenon_H10d zenon_H6f zenon_Hb8 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H1d2 zenon_H27 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_He1 zenon_H18c zenon_H135 zenon_H8d zenon_H2d zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H14e zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.94/30.09 apply (zenon_L457_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.94/30.09 exact (zenon_H13b zenon_Hfd). % 29.94/30.09 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.94/30.09 apply (zenon_L282_); trivial. % 29.94/30.09 apply (zenon_L582_); trivial. % 29.94/30.09 (* end of lemma zenon_L583_ *) % 29.94/30.09 assert (zenon_L584_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 29.94/30.09 do 0 intro. intros zenon_H8d zenon_H68 zenon_H6f zenon_H112 zenon_H117 zenon_H10d zenon_H18e zenon_H1d8 zenon_Hb8 zenon_He1 zenon_He2. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.09 apply (zenon_L252_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.09 apply (zenon_L18_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.09 apply (zenon_L339_); trivial. % 29.94/30.09 apply (zenon_L50_); trivial. % 29.94/30.09 (* end of lemma zenon_L584_ *) % 29.94/30.09 assert (zenon_L585_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.09 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_Hd2 zenon_H6f zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.94/30.09 apply (zenon_L4_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.94/30.09 apply (zenon_L125_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.94/30.09 apply (zenon_L308_); trivial. % 29.94/30.09 exact (zenon_H18e zenon_H40). % 29.94/30.09 (* end of lemma zenon_L585_ *) % 29.94/30.09 assert (zenon_L586_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 29.94/30.09 do 0 intro. intros zenon_H14e zenon_H112 zenon_H172 zenon_H92 zenon_H20 zenon_He7 zenon_H8d zenon_H16a zenon_H83 zenon_H84 zenon_H17d zenon_H218 zenon_H16b zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H108 zenon_H1ca zenon_H5e zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H159 zenon_H3c zenon_H101 zenon_Had zenon_H173 zenon_H1dc zenon_H6b zenon_Hd1 zenon_H18c zenon_H20d zenon_H14b zenon_H200 zenon_Hf9 zenon_He9 zenon_H10d zenon_H231 zenon_H5c zenon_H27 zenon_H174 zenon_H102 zenon_H35 zenon_Hfc zenon_H20e zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_H125 zenon_He4 zenon_H225 zenon_Hb5 zenon_H42 zenon_Hb8 zenon_H100 zenon_H2d zenon_H3f zenon_H1e zenon_Hde zenon_Hbd zenon_Hd6 zenon_H1af zenon_Hd0 zenon_H1d8 zenon_H135 zenon_H18e zenon_H1a8 zenon_H6f zenon_H6c zenon_He1 zenon_He2. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.09 apply (zenon_L252_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.09 apply (zenon_L120_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.09 apply (zenon_L585_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.09 apply (zenon_L394_); trivial. % 29.94/30.09 apply (zenon_L137_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.09 apply (zenon_L157_); trivial. % 29.94/30.09 apply (zenon_L50_); trivial. % 29.94/30.09 (* end of lemma zenon_L586_ *) % 29.94/30.09 assert (zenon_L587_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> False). % 29.94/30.09 do 0 intro. intros zenon_H25c zenon_H256 zenon_H74 zenon_H1e6 zenon_Hf6 zenon_H11e zenon_H1a5 zenon_Hc8 zenon_H23b zenon_Hee zenon_H246 zenon_Hc0 zenon_H1b1 zenon_Ha4 zenon_Haa zenon_H25b zenon_H14e zenon_H112 zenon_H172 zenon_H92 zenon_H20 zenon_He7 zenon_H8d zenon_H16a zenon_H83 zenon_H84 zenon_H17d zenon_H218 zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H108 zenon_H1ca zenon_H5e zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H159 zenon_H3c zenon_H101 zenon_Had zenon_H173 zenon_H1dc zenon_H6b zenon_Hd1 zenon_H18c zenon_H20d zenon_H14b zenon_H200 zenon_Hf9 zenon_He9 zenon_H10d zenon_H231 zenon_H5c zenon_H27 zenon_H174 zenon_H102 zenon_H35 zenon_Hfc zenon_H20e zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_H125 zenon_He4 zenon_H225 zenon_Hb5 zenon_H42 zenon_Hb8 zenon_H100 zenon_H2d zenon_H3f zenon_H1e zenon_Hde zenon_Hbd zenon_Hd6 zenon_H1af zenon_Hd0 zenon_H1d8 zenon_H135 zenon_H18e zenon_H1a8 zenon_H6f zenon_H6c zenon_He1. % 29.94/30.09 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.09 exact (zenon_H74 zenon_H73). % 29.94/30.09 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.09 apply (zenon_L453_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.09 apply (zenon_L580_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.09 apply (zenon_L252_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.09 apply (zenon_L4_); trivial. % 29.94/30.09 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.09 apply (zenon_L385_); trivial. % 29.94/30.09 apply (zenon_L586_); trivial. % 29.94/30.09 (* end of lemma zenon_L587_ *) % 29.94/30.09 assert (zenon_L588_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H1a8 zenon_H18e zenon_H135 zenon_He2 zenon_H1d8 zenon_He1 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H218 zenon_H16b zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H1e zenon_H2d zenon_H42 zenon_H6f zenon_H100 zenon_Hb8 zenon_H1bd zenon_Hcd zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H5e zenon_H6c zenon_H1ca zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_H159 zenon_H3c zenon_H101 zenon_H6e zenon_H92 zenon_H69 zenon_H16a zenon_H83 zenon_H84 zenon_H17d zenon_H20d zenon_H5c zenon_H27 zenon_H174 zenon_H20e zenon_H173 zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H200 zenon_He4 zenon_H225 zenon_H18c zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_Hc8 zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H3f zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H112 zenon_H14e. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.10 apply (zenon_L18_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.10 apply (zenon_L585_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.10 apply (zenon_L429_); trivial. % 29.94/30.10 apply (zenon_L137_); trivial. % 29.94/30.10 (* end of lemma zenon_L588_ *) % 29.94/30.10 assert (zenon_L589_ : (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H231 zenon_H14e zenon_H25c zenon_H256 zenon_H84 zenon_H74 zenon_H3c zenon_H18c zenon_Hcd zenon_H14b zenon_H1dc zenon_H6b zenon_H156 zenon_H27 zenon_H1d2 zenon_H108 zenon_H1bd zenon_H5e zenon_H60 zenon_H1c7 zenon_H1ca zenon_H1d5 zenon_H173 zenon_H1e6 zenon_Hf6 zenon_H102 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H11e zenon_H1a5 zenon_Hc8 zenon_H23b zenon_Hee zenon_Hb5 zenon_Hf9 zenon_H20 zenon_H225 zenon_H222 zenon_H101 zenon_H159 zenon_H83 zenon_H218 zenon_He4 zenon_H15a zenon_H16f zenon_H16a zenon_H17d zenon_H92 zenon_H172 zenon_H200 zenon_H5c zenon_H125 zenon_Hbd zenon_He7 zenon_H3f zenon_H1fd zenon_Hde zenon_H208 zenon_H20d zenon_H20e zenon_H246 zenon_Hc0 zenon_H1b1 zenon_Ha4 zenon_Haa zenon_H25b zenon_H1a8 zenon_H174 zenon_H6c zenon_H6f zenon_H42 zenon_H2d zenon_H1e zenon_H112 zenon_H10d zenon_H100 zenon_Had zenon_Hb8 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_H1d8 zenon_H135 zenon_H18e zenon_Hd9 zenon_H8d zenon_H17b zenon_He1. % 29.94/30.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.10 exact (zenon_H74 zenon_H73). % 29.94/30.10 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.10 apply (zenon_L453_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.10 apply (zenon_L580_); trivial. % 29.94/30.10 apply (zenon_L441_); trivial. % 29.94/30.10 (* end of lemma zenon_L589_ *) % 29.94/30.10 assert (zenon_L590_ : (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.94/30.10 do 0 intro. intros zenon_He1 zenon_H8d zenon_Hd9 zenon_H18e zenon_H135 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H1e zenon_H2d zenon_H42 zenon_H6f zenon_H174 zenon_H1a8 zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_Hde zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H200 zenon_H172 zenon_H92 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H222 zenon_H225 zenon_H20 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H102 zenon_Hf6 zenon_H1e6 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H1c7 zenon_H60 zenon_H5e zenon_H1bd zenon_H108 zenon_H1d2 zenon_H27 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_H18c zenon_H3c zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H14e zenon_H231 zenon_H1f zenon_H69 zenon_H17d zenon_H112. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.94/30.10 exact (zenon_H84 zenon_H88). % 29.94/30.10 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.94/30.10 apply (zenon_L16_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 29.94/30.10 exact (zenon_H74 zenon_H73). % 29.94/30.10 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 29.94/30.10 apply (zenon_L587_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 29.94/30.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.10 exact (zenon_H74 zenon_H73). % 29.94/30.10 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.10 apply (zenon_L453_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.10 apply (zenon_L580_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.10 apply (zenon_L252_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.10 apply (zenon_L4_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.10 apply (zenon_L385_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.10 apply (zenon_L252_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.10 apply (zenon_L588_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.10 apply (zenon_L157_); trivial. % 29.94/30.10 apply (zenon_L50_); trivial. % 29.94/30.10 apply (zenon_L589_); trivial. % 29.94/30.10 apply (zenon_L139_); trivial. % 29.94/30.10 (* end of lemma zenon_L590_ *) % 29.94/30.10 assert (zenon_L591_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H135 zenon_He2 zenon_H1d8 zenon_H3c zenon_He9 zenon_Hd0 zenon_H1af zenon_H15e zenon_H20e. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.94/30.10 apply (zenon_L307_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.94/30.10 apply (zenon_L88_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.94/30.10 exact (zenon_Hd0 zenon_Hcc). % 29.94/30.10 apply (zenon_L358_); trivial. % 29.94/30.10 (* end of lemma zenon_L591_ *) % 29.94/30.10 assert (zenon_L592_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H135 zenon_He2 zenon_H1d8 zenon_He1 zenon_H3d zenon_Hd0 zenon_H1af zenon_H15e zenon_H20e. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.94/30.10 apply (zenon_L307_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.94/30.10 apply (zenon_L126_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.94/30.10 exact (zenon_Hd0 zenon_Hcc). % 29.94/30.10 apply (zenon_L358_); trivial. % 29.94/30.10 (* end of lemma zenon_L592_ *) % 29.94/30.10 assert (zenon_L593_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_Hfc zenon_H20e zenon_H15e zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.94/30.10 apply (zenon_L4_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.94/30.10 apply (zenon_L203_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.94/30.10 apply (zenon_L592_); trivial. % 29.94/30.10 exact (zenon_H18e zenon_H40). % 29.94/30.10 (* end of lemma zenon_L593_ *) % 29.94/30.10 assert (zenon_L594_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.94/30.10 do 0 intro. intros zenon_H16f zenon_H68 zenon_H19e zenon_Hfe zenon_Hcd zenon_H55 zenon_H76 zenon_H6f zenon_H208 zenon_H18e zenon_H135 zenon_He2 zenon_H1d8 zenon_He1 zenon_Hd0 zenon_H1af zenon_H20e zenon_Hfc zenon_H1e zenon_H2d zenon_H42 zenon_H16a zenon_H16b. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.10 apply (zenon_L18_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.10 apply (zenon_L215_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.10 apply (zenon_L593_); trivial. % 29.94/30.10 apply (zenon_L101_); trivial. % 29.94/30.10 (* end of lemma zenon_L594_ *) % 29.94/30.10 assert (zenon_L595_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H135 zenon_He1 zenon_H9d zenon_H222 zenon_Hd0 zenon_H1af zenon_H76 zenon_H6b. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.94/30.10 apply (zenon_L273_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.94/30.10 apply (zenon_L264_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.94/30.10 exact (zenon_Hd0 zenon_Hcc). % 29.94/30.10 apply (zenon_L193_); trivial. % 29.94/30.10 (* end of lemma zenon_L595_ *) % 29.94/30.10 assert (zenon_L596_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H101 zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H13b zenon_H16b zenon_H16a zenon_H42 zenon_H2d zenon_H1e zenon_Hfc zenon_H20e zenon_H1d8 zenon_He2 zenon_H18e zenon_H208 zenon_H6f zenon_Hcd zenon_Hfe zenon_H19e zenon_H68 zenon_H16f zenon_H135 zenon_He1 zenon_H222 zenon_Hd0 zenon_H1af zenon_H76 zenon_H6b. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.10 apply (zenon_L18_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.10 apply (zenon_L220_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.10 apply (zenon_L591_); trivial. % 29.94/30.10 apply (zenon_L101_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.94/30.10 exact (zenon_H13b zenon_Hfd). % 29.94/30.10 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.94/30.10 apply (zenon_L594_); trivial. % 29.94/30.10 apply (zenon_L595_); trivial. % 29.94/30.10 (* end of lemma zenon_L596_ *) % 29.94/30.10 assert (zenon_L597_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H1a8 zenon_H6e zenon_H18e zenon_H135 zenon_He2 zenon_H1d8 zenon_He1 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H218 zenon_H16b zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H1e zenon_H2d zenon_H42 zenon_H108 zenon_Hfe zenon_H1ca zenon_H6c zenon_H5e zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_H159 zenon_H3c zenon_H101 zenon_Hda zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H20d zenon_H14b zenon_H5c zenon_H27 zenon_H174 zenon_H20e zenon_H173 zenon_H1f zenon_H16f zenon_H15a zenon_Hd9 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H231 zenon_H125 zenon_H200 zenon_He4 zenon_H225 zenon_Hde zenon_H18c zenon_Hb5 zenon_H8d zenon_H23b zenon_H20 zenon_Hee zenon_Had zenon_H100 zenon_Hb8 zenon_Hc8 zenon_H6b zenon_H1dc zenon_He7 zenon_Hbd zenon_H3f zenon_H112 zenon_H14e. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.10 apply (zenon_L18_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.10 apply (zenon_L585_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.10 apply (zenon_L432_); trivial. % 29.94/30.10 apply (zenon_L137_); trivial. % 29.94/30.10 (* end of lemma zenon_L597_ *) % 29.94/30.10 assert (zenon_L598_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H26 zenon_H117 zenon_H6f. % 29.94/30.10 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 29.94/30.10 cut (((e3) = (e3)) = ((e1) = (e3))). % 29.94/30.10 intro zenon_D_pnotp. % 29.94/30.10 apply zenon_H6f. % 29.94/30.10 rewrite <- zenon_D_pnotp. % 29.94/30.10 exact zenon_H2e. % 29.94/30.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.94/30.10 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 29.94/30.10 congruence. % 29.94/30.10 cut (((op (e0) (e2)) = (e1)) = ((e3) = (e1))). % 29.94/30.10 intro zenon_D_pnotp. % 29.94/30.10 apply zenon_H70. % 29.94/30.10 rewrite <- zenon_D_pnotp. % 29.94/30.10 exact zenon_H26. % 29.94/30.10 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.94/30.10 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 29.94/30.10 congruence. % 29.94/30.10 exact (zenon_H151 zenon_H117). % 29.94/30.10 apply zenon_H22. apply refl_equal. % 29.94/30.10 apply zenon_H2f. apply refl_equal. % 29.94/30.10 apply zenon_H2f. apply refl_equal. % 29.94/30.10 (* end of lemma zenon_L598_ *) % 29.94/30.10 assert (zenon_L599_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H1a8 zenon_H6c zenon_H18e zenon_H135 zenon_H18c zenon_Hdc zenon_He1 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H6f zenon_H1e zenon_H2d zenon_H42 zenon_H1a5 zenon_H26 zenon_H112 zenon_H14e. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.10 apply (zenon_L120_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.10 apply (zenon_L146_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.10 apply (zenon_L136_); trivial. % 29.94/30.10 apply (zenon_L137_); trivial. % 29.94/30.10 (* end of lemma zenon_L599_ *) % 29.94/30.10 assert (zenon_L600_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H1a8 zenon_H6e zenon_H18e zenon_H135 zenon_He2 zenon_H1d8 zenon_He1 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H6f zenon_H1e zenon_H2d zenon_H42 zenon_H1a5 zenon_H26 zenon_H112 zenon_H14e. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.10 apply (zenon_L18_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.10 apply (zenon_L585_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.10 apply (zenon_L136_); trivial. % 29.94/30.10 apply (zenon_L137_); trivial. % 29.94/30.10 (* end of lemma zenon_L600_ *) % 29.94/30.10 assert (zenon_L601_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H25c zenon_H256 zenon_H84 zenon_H74 zenon_H3c zenon_H18c zenon_Hcd zenon_H14b zenon_H1dc zenon_H6b zenon_H156 zenon_H27 zenon_H1d2 zenon_H108 zenon_H1bd zenon_H5e zenon_H60 zenon_H1c7 zenon_H1ca zenon_H1d5 zenon_H173 zenon_H1e6 zenon_Hf6 zenon_Hb8 zenon_H10d zenon_H100 zenon_Had zenon_H102 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_Hd9 zenon_H11e zenon_Hc8 zenon_H23b zenon_Hee zenon_Hb5 zenon_Hf9 zenon_H20 zenon_H225 zenon_H222 zenon_H101 zenon_H159 zenon_H83 zenon_H218 zenon_He4 zenon_H15a zenon_H16f zenon_H16a zenon_H174 zenon_H17d zenon_H92 zenon_H172 zenon_H200 zenon_H5c zenon_H125 zenon_Hbd zenon_He7 zenon_H3f zenon_H1fd zenon_Hde zenon_H208 zenon_H20d zenon_H20e zenon_H246 zenon_Hc0 zenon_H1b1 zenon_Ha4 zenon_Haa zenon_H25b zenon_H8d zenon_H14e zenon_H112 zenon_H26 zenon_H1a5 zenon_H42 zenon_H2d zenon_H1e zenon_Hd6 zenon_H1af zenon_Hd0 zenon_H1d8 zenon_H135 zenon_H18e zenon_H1a8 zenon_H6f zenon_H6c zenon_He1. % 29.94/30.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.10 exact (zenon_H74 zenon_H73). % 29.94/30.10 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.10 apply (zenon_L599_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.10 apply (zenon_L580_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.10 apply (zenon_L252_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.10 apply (zenon_L600_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.10 apply (zenon_L157_); trivial. % 29.94/30.10 apply (zenon_L50_); trivial. % 29.94/30.10 (* end of lemma zenon_L601_ *) % 29.94/30.10 assert (zenon_L602_ : ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.94/30.10 do 0 intro. intros zenon_H69 zenon_He1 zenon_H6f zenon_H1a8 zenon_H18e zenon_H135 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_H1e zenon_H2d zenon_H42 zenon_H1a5 zenon_H26 zenon_H14e zenon_H8d zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_Hde zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H200 zenon_H172 zenon_H92 zenon_H174 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H222 zenon_H225 zenon_H20 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H11e zenon_Hd9 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H102 zenon_Had zenon_H100 zenon_H10d zenon_Hb8 zenon_Hf6 zenon_H1e6 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H1c7 zenon_H60 zenon_H5e zenon_H1bd zenon_H108 zenon_H1d2 zenon_H27 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_H18c zenon_H3c zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H17d zenon_H112. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.94/30.10 exact (zenon_H84 zenon_H88). % 29.94/30.10 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.94/30.10 apply (zenon_L16_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.94/30.10 apply (zenon_L601_); trivial. % 29.94/30.10 apply (zenon_L139_); trivial. % 29.94/30.10 (* end of lemma zenon_L602_ *) % 29.94/30.10 assert (zenon_L603_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H55 zenon_Hcd zenon_Hfe zenon_H1af zenon_H37 zenon_H19e. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.94/30.10 apply (zenon_L120_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.94/30.10 apply (zenon_L212_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.94/30.10 apply (zenon_L170_); trivial. % 29.94/30.10 apply (zenon_L214_); trivial. % 29.94/30.10 (* end of lemma zenon_L603_ *) % 29.94/30.10 assert (zenon_L604_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H19e zenon_H37 zenon_Hfe zenon_Hcd zenon_H18c zenon_H68 zenon_H208 zenon_Hd0 zenon_H1af zenon_H76 zenon_H6b. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.94/30.10 apply (zenon_L49_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.94/30.10 apply (zenon_L603_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.94/30.10 exact (zenon_Hd0 zenon_Hcc). % 29.94/30.10 apply (zenon_L193_); trivial. % 29.94/30.10 (* end of lemma zenon_L604_ *) % 29.94/30.10 assert (zenon_L605_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.94/30.10 do 0 intro. intros zenon_H16f zenon_H6f zenon_H6b zenon_H76 zenon_H208 zenon_H68 zenon_H18c zenon_Hcd zenon_Hfe zenon_H19e zenon_H20e zenon_H1af zenon_Hd0 zenon_He9 zenon_H3c zenon_Hde zenon_Hdf zenon_H135 zenon_H16a zenon_H16b. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.10 apply (zenon_L18_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.10 apply (zenon_L604_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.10 apply (zenon_L363_); trivial. % 29.94/30.10 apply (zenon_L101_); trivial. % 29.94/30.10 (* end of lemma zenon_L605_ *) % 29.94/30.10 assert (zenon_L606_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.10 do 0 intro. intros zenon_H172 zenon_H20 zenon_H35 zenon_H6b zenon_H76 zenon_H222 zenon_H16f zenon_H68 zenon_H19e zenon_Hcd zenon_H208 zenon_H20e zenon_Hfc zenon_H16a zenon_H16b zenon_H13b zenon_H18c zenon_H3c zenon_Hdf zenon_H101 zenon_H42 zenon_H14e zenon_Hb8 zenon_H100 zenon_H2d zenon_H112 zenon_H6f zenon_H3f zenon_H1e zenon_Hde zenon_Hbd zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_He2 zenon_H135 zenon_H18e. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.94/30.10 apply (zenon_L16_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.94/30.10 apply (zenon_L42_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.94/30.10 apply (zenon_L605_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.94/30.10 exact (zenon_H13b zenon_Hfd). % 29.94/30.10 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.94/30.10 apply (zenon_L594_); trivial. % 29.94/30.10 apply (zenon_L595_); trivial. % 29.94/30.10 apply (zenon_L393_); trivial. % 29.94/30.10 (* end of lemma zenon_L606_ *) % 29.94/30.10 assert (zenon_L607_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 29.94/30.10 do 0 intro. intros zenon_He4 zenon_H74 zenon_H174 zenon_H27 zenon_He9 zenon_H8d zenon_H26 zenon_H1a5 zenon_H1a8 zenon_H18e zenon_H135 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_Hbd zenon_Hde zenon_H1e zenon_H3f zenon_H6f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H42 zenon_H101 zenon_Hdf zenon_H3c zenon_H18c zenon_H13b zenon_H16a zenon_Hfc zenon_H20e zenon_H208 zenon_Hcd zenon_H19e zenon_H68 zenon_H16f zenon_H222 zenon_H6b zenon_H35 zenon_H20 zenon_H172 zenon_He1. % 29.94/30.10 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.10 exact (zenon_H74 zenon_H73). % 29.94/30.10 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.10 apply (zenon_L48_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.10 apply (zenon_L49_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.10 apply (zenon_L252_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.10 apply (zenon_L4_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.10 apply (zenon_L378_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.10 apply (zenon_L252_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.10 apply (zenon_L600_); trivial. % 29.94/30.10 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.10 apply (zenon_L606_); trivial. % 29.94/30.10 apply (zenon_L50_); trivial. % 29.94/30.10 (* end of lemma zenon_L607_ *) % 29.94/30.10 assert (zenon_L608_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> False). % 29.94/30.10 do 0 intro. intros zenon_H1bd zenon_H5e zenon_H1ba zenon_Hd5. % 29.94/30.10 cut (((op (e2) (op (e2) (e1))) = (e1)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 29.94/30.10 intro zenon_D_pnotp. % 29.94/30.10 apply zenon_H1bd. % 29.94/30.10 rewrite <- zenon_D_pnotp. % 29.94/30.10 exact zenon_H5e. % 29.94/30.10 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 29.94/30.10 cut (((op (e2) (op (e2) (e1))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H25d]. % 29.94/30.10 congruence. % 29.94/30.10 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H6d ]. % 29.94/30.10 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e2) (op (e2) (e1))) = (op (e2) (e0)))). % 29.94/30.10 intro zenon_D_pnotp. % 29.94/30.10 apply zenon_H25d. % 29.94/30.10 rewrite <- zenon_D_pnotp. % 29.94/30.10 exact zenon_H1ac. % 29.94/30.10 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.94/30.10 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 29.94/30.10 congruence. % 29.94/30.10 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 29.94/30.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.94/30.10 congruence. % 29.94/30.10 apply zenon_H57. apply refl_equal. % 29.94/30.10 apply zenon_H1bb. apply sym_equal. exact zenon_H1ba. % 29.94/30.10 apply zenon_H6d. apply refl_equal. % 29.94/30.10 apply zenon_H6d. apply refl_equal. % 29.94/30.10 apply zenon_Hd8. apply sym_equal. exact zenon_Hd5. % 29.94/30.10 (* end of lemma zenon_L608_ *) % 29.94/30.10 assert (zenon_L609_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H19e zenon_H26 zenon_H27 zenon_H222 zenon_H5e zenon_H98 zenon_H1a8 zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H172 zenon_H92 zenon_H17d zenon_H174 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H225 zenon_H20 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_Hd9 zenon_H42 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H102 zenon_Had zenon_H100 zenon_H10d zenon_H6f zenon_Hb8 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H60 zenon_H1d2 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_He1 zenon_H18c zenon_H135 zenon_H8d zenon_H2d zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H14e zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.94/30.11 apply (zenon_L4_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.94/30.11 apply (zenon_L580_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.94/30.11 apply (zenon_L514_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.94/30.11 apply (zenon_L3_); trivial. % 29.94/30.11 apply (zenon_L214_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.94/30.11 apply (zenon_L456_); trivial. % 29.94/30.11 exact (zenon_H18e zenon_H40). % 29.94/30.11 (* end of lemma zenon_L609_ *) % 29.94/30.11 assert (zenon_L610_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H42 zenon_H2d zenon_H15e zenon_Hfc zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.94/30.11 apply (zenon_L4_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.94/30.11 apply (zenon_L203_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.94/30.11 apply (zenon_L456_); trivial. % 29.94/30.11 exact (zenon_H18e zenon_H40). % 29.94/30.11 (* end of lemma zenon_L610_ *) % 29.94/30.11 assert (zenon_L611_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H16f zenon_H6f zenon_H19e zenon_H60 zenon_He9 zenon_H5e zenon_H1f zenon_H18c zenon_H68 zenon_H208 zenon_H18e zenon_H200 zenon_Hc9 zenon_Hde zenon_H1e zenon_H3c zenon_H1c7 zenon_Hd6 zenon_Hf6 zenon_H112 zenon_H108 zenon_H1e6 zenon_H1bd zenon_H1af zenon_Hfc zenon_H2d zenon_H42 zenon_H16a zenon_H16b. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.11 apply (zenon_L18_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.11 apply (zenon_L454_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.11 apply (zenon_L610_); trivial. % 29.94/30.11 apply (zenon_L101_); trivial. % 29.94/30.11 (* end of lemma zenon_L611_ *) % 29.94/30.11 assert (zenon_L612_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H98 zenon_H5e zenon_H222 zenon_Hfe zenon_H1af zenon_H37 zenon_H19e. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.94/30.11 apply (zenon_L120_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.94/30.11 apply (zenon_L514_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.94/30.11 apply (zenon_L170_); trivial. % 29.94/30.11 apply (zenon_L214_); trivial. % 29.94/30.11 (* end of lemma zenon_L612_ *) % 29.94/30.11 assert (zenon_L613_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H16f zenon_H14e zenon_H112 zenon_H26 zenon_H1a5 zenon_H6f zenon_Hd6 zenon_H1a8 zenon_H19e zenon_Hfe zenon_H222 zenon_H5e zenon_H98 zenon_H18c zenon_H68 zenon_H208 zenon_H18e zenon_H135 zenon_He2 zenon_H1d8 zenon_He1 zenon_Hd0 zenon_H1af zenon_H20e zenon_Hfc zenon_H1e zenon_H2d zenon_H42 zenon_H16a zenon_H16b. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.11 apply (zenon_L600_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.11 apply (zenon_L612_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.11 apply (zenon_L593_); trivial. % 29.94/30.11 apply (zenon_L101_); trivial. % 29.94/30.11 (* end of lemma zenon_L613_ *) % 29.94/30.11 assert (zenon_L614_ : (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H18e zenon_H135 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_Hbd zenon_Hde zenon_H1e zenon_H3f zenon_H6f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H42 zenon_H124 zenon_H13b zenon_H60 zenon_H3c zenon_H101 zenon_Hd1 zenon_H200 zenon_H6b zenon_H1bd zenon_Hcd zenon_H16f zenon_H26 zenon_H1a5 zenon_H1a8 zenon_H19e zenon_H222 zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_H20e zenon_Hfc zenon_H16a zenon_H35 zenon_H8d zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20d zenon_H1fd zenon_He7 zenon_H125 zenon_H5c zenon_H172 zenon_H92 zenon_H174 zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H225 zenon_H20 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H11e zenon_Hd9 zenon_H102 zenon_Had zenon_H10d zenon_Hf6 zenon_H1e6 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H1c7 zenon_H108 zenon_H1d2 zenon_H27 zenon_H156 zenon_H1dc zenon_H14b zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H17d zenon_He1 zenon_He2. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.11 apply (zenon_L252_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.11 apply (zenon_L4_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.11 apply (zenon_L584_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.11 apply (zenon_L252_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.11 apply (zenon_L18_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.94/30.11 apply (zenon_L602_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.94/30.11 apply (zenon_L42_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 29.94/30.11 apply (zenon_L596_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 29.94/30.11 apply (zenon_L45_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.11 apply (zenon_L600_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.94/30.11 apply (zenon_L604_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.94/30.11 apply (zenon_L608_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.94/30.11 apply (zenon_L350_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.94/30.11 apply (zenon_L273_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.94/30.11 apply (zenon_L215_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.94/30.11 exact (zenon_Hd0 zenon_Hcc). % 29.94/30.11 apply (zenon_L294_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.11 apply (zenon_L593_); trivial. % 29.94/30.11 apply (zenon_L101_); trivial. % 29.94/30.11 apply (zenon_L613_); trivial. % 29.94/30.11 apply (zenon_L393_); trivial. % 29.94/30.11 apply (zenon_L50_); trivial. % 29.94/30.11 (* end of lemma zenon_L614_ *) % 29.94/30.11 assert (zenon_L615_ : (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H231 zenon_H17d zenon_H25c zenon_H256 zenon_H84 zenon_H74 zenon_H3c zenon_H18c zenon_Hcd zenon_H14b zenon_H1dc zenon_H6b zenon_H156 zenon_H27 zenon_H1d2 zenon_H108 zenon_H1bd zenon_H5e zenon_H60 zenon_H1c7 zenon_H1ca zenon_H1d5 zenon_H173 zenon_H1e6 zenon_Hf6 zenon_Hb8 zenon_H10d zenon_H100 zenon_Had zenon_H102 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_Hd9 zenon_H11e zenon_Hc8 zenon_H23b zenon_Hee zenon_Hb5 zenon_Hf9 zenon_H20 zenon_H225 zenon_H222 zenon_H101 zenon_H159 zenon_H83 zenon_H218 zenon_He4 zenon_H15a zenon_H16f zenon_H16a zenon_H174 zenon_H92 zenon_H172 zenon_H200 zenon_H5c zenon_H125 zenon_Hbd zenon_He7 zenon_H3f zenon_H1fd zenon_Hde zenon_H208 zenon_H20d zenon_H20e zenon_H246 zenon_Hc0 zenon_H1b1 zenon_Haa zenon_H25b zenon_H8d zenon_H14e zenon_H1a5 zenon_H42 zenon_H2d zenon_H1e zenon_Hd6 zenon_H1af zenon_Hd0 zenon_H1d8 zenon_H135 zenon_H18e zenon_H1a8 zenon_H6f zenon_He1 zenon_H69 zenon_H112 zenon_Ha4. % 29.94/30.11 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 29.94/30.11 exact (zenon_H84 zenon_H88). % 29.94/30.11 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 29.94/30.11 apply (zenon_L590_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 29.94/30.11 apply (zenon_L602_); trivial. % 29.94/30.11 apply (zenon_L140_); trivial. % 29.94/30.11 (* end of lemma zenon_L615_ *) % 29.94/30.11 assert (zenon_L616_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H8d zenon_H18e zenon_H135 zenon_He2 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_Hbd zenon_H1e zenon_H3f zenon_H6f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H42 zenon_H101 zenon_H3c zenon_H18c zenon_H13b zenon_H16b zenon_H16a zenon_Hfc zenon_H20e zenon_H208 zenon_H19e zenon_H16f zenon_H222 zenon_H6b zenon_H35 zenon_H20 zenon_H172 zenon_He4 zenon_Hda zenon_Hd9 zenon_Hcd zenon_H68 zenon_Hdf zenon_Hde zenon_He1. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.11 apply (zenon_L252_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.11 apply (zenon_L18_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.11 apply (zenon_L606_); trivial. % 29.94/30.11 apply (zenon_L51_); trivial. % 29.94/30.11 (* end of lemma zenon_L616_ *) % 29.94/30.11 assert (zenon_L617_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (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 (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> False). % 29.94/30.11 do 0 intro. intros zenon_Hf6 zenon_H1e6 zenon_H246 zenon_H83 zenon_H11e zenon_H17d zenon_Hc0 zenon_H74 zenon_Hd1 zenon_H20d zenon_H14b zenon_H27 zenon_H1fd zenon_Hf9 zenon_H231 zenon_H125 zenon_H225 zenon_H1d2 zenon_H108 zenon_Hb5 zenon_H200 zenon_H5c zenon_H102 zenon_H1bd zenon_H218 zenon_H60 zenon_H1d5 zenon_H156 zenon_H159 zenon_H173 zenon_H23b zenon_Hee zenon_Had zenon_He7 zenon_H1dc zenon_H15a zenon_H1c7 zenon_H5e zenon_H1ca zenon_Hc8 zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_Ha4 zenon_H1a8 zenon_H174 zenon_H10d zenon_H8d zenon_H18e zenon_H135 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_Hbd zenon_H1e zenon_H3f zenon_H6f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H42 zenon_H101 zenon_H3c zenon_H18c zenon_H13b zenon_H16a zenon_Hfc zenon_H20e zenon_H208 zenon_H19e zenon_H16f zenon_H222 zenon_H6b zenon_H35 zenon_H20 zenon_H172 zenon_He4 zenon_Hda zenon_Hd9 zenon_Hcd zenon_H68 zenon_Hdf zenon_Hde zenon_He1. % 29.94/30.11 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.11 exact (zenon_H74 zenon_H73). % 29.94/30.11 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.11 apply (zenon_L453_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.11 apply (zenon_L49_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.11 apply (zenon_L252_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.11 apply (zenon_L4_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.11 apply (zenon_L584_); trivial. % 29.94/30.11 apply (zenon_L616_); trivial. % 29.94/30.11 (* end of lemma zenon_L617_ *) % 29.94/30.11 assert (zenon_L618_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H1ba zenon_H5e zenon_H1bd zenon_H9d zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.94/30.11 apply (zenon_L120_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.94/30.11 apply (zenon_L608_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.94/30.11 apply (zenon_L256_); trivial. % 29.94/30.11 apply (zenon_L214_); trivial. % 29.94/30.11 (* end of lemma zenon_L618_ *) % 29.94/30.11 assert (zenon_L619_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H9d zenon_H222 zenon_Hd0 zenon_H1d5 zenon_H1d8 zenon_Hd6 zenon_H1af zenon_H14f zenon_H14e zenon_H112 zenon_H3f zenon_H1e zenon_H2d zenon_H8a zenon_Hbd zenon_He1. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.94/30.11 apply (zenon_L49_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.94/30.11 apply (zenon_L264_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.94/30.11 exact (zenon_Hd0 zenon_Hcc). % 29.94/30.11 apply (zenon_L371_); trivial. % 29.94/30.11 (* end of lemma zenon_L619_ *) % 29.94/30.11 assert (zenon_L620_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H174 zenon_H64 zenon_H2d zenon_H1e zenon_H6f zenon_H26 zenon_H17b zenon_He1. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.11 apply (zenon_L148_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.11 apply (zenon_L4_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.11 apply (zenon_L598_); trivial. % 29.94/30.11 apply (zenon_L267_); trivial. % 29.94/30.11 (* end of lemma zenon_L620_ *) % 29.94/30.11 assert (zenon_L621_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H174 zenon_H2d zenon_H1e zenon_He2 zenon_Hb8 zenon_H1d8 zenon_H18e zenon_H10d zenon_H112 zenon_H6f zenon_H68 zenon_H8d zenon_H17b zenon_He1. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.11 apply (zenon_L252_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.11 apply (zenon_L4_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.11 apply (zenon_L584_); trivial. % 29.94/30.11 apply (zenon_L267_); trivial. % 29.94/30.11 (* end of lemma zenon_L621_ *) % 29.94/30.11 assert (zenon_L622_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.94/30.11 do 0 intro. intros zenon_He4 zenon_H74 zenon_Hcd zenon_Hdf zenon_Hde zenon_H174 zenon_H2d zenon_H1e zenon_Hb8 zenon_H1d8 zenon_H18e zenon_H10d zenon_H112 zenon_H6f zenon_H68 zenon_H8d zenon_H17b zenon_He1. % 29.94/30.11 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.11 exact (zenon_H74 zenon_H73). % 29.94/30.11 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.11 apply (zenon_L48_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.11 apply (zenon_L49_); trivial. % 29.94/30.11 apply (zenon_L621_); trivial. % 29.94/30.11 (* end of lemma zenon_L622_ *) % 29.94/30.11 assert (zenon_L623_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))) -> ((op (e2) (e2)) = (e0)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H25f zenon_H142. % 29.94/30.11 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H260]. % 29.94/30.11 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H260]. % 29.94/30.11 congruence. % 29.94/30.11 exact (zenon_H260 zenon_H142). % 29.94/30.11 exact (zenon_H260 zenon_H142). % 29.94/30.11 (* end of lemma zenon_L623_ *) % 29.94/30.11 assert (zenon_L624_ : (~((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e0)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H261 zenon_H142. % 29.94/30.11 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 29.94/30.11 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H260]. % 29.94/30.11 congruence. % 29.94/30.11 exact (zenon_H260 zenon_H142). % 29.94/30.11 apply zenon_H57. apply refl_equal. % 29.94/30.11 (* end of lemma zenon_L624_ *) % 29.94/30.11 assert (zenon_L625_ : ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (op (op (e2) (e2)) (e2)))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H26 zenon_H142 zenon_H262. % 29.94/30.11 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 29.94/30.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e1) = (op (op (e2) (e2)) (e2)))). % 29.94/30.11 intro zenon_D_pnotp. % 29.94/30.11 apply zenon_H262. % 29.94/30.11 rewrite <- zenon_D_pnotp. % 29.94/30.11 exact zenon_H160. % 29.94/30.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 29.94/30.11 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H263]. % 29.94/30.11 congruence. % 29.94/30.11 cut (((op (e0) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 29.94/30.11 intro zenon_D_pnotp. % 29.94/30.11 apply zenon_H263. % 29.94/30.11 rewrite <- zenon_D_pnotp. % 29.94/30.11 exact zenon_H26. % 29.94/30.11 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.94/30.11 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 29.94/30.11 congruence. % 29.94/30.11 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 29.94/30.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 29.94/30.11 intro zenon_D_pnotp. % 29.94/30.11 apply zenon_H264. % 29.94/30.11 rewrite <- zenon_D_pnotp. % 29.94/30.11 exact zenon_H160. % 29.94/30.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 29.94/30.11 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H261]. % 29.94/30.11 congruence. % 29.94/30.11 apply (zenon_L624_); trivial. % 29.94/30.11 apply zenon_H161. apply refl_equal. % 29.94/30.11 apply zenon_H161. apply refl_equal. % 29.94/30.11 apply zenon_H22. apply refl_equal. % 29.94/30.11 apply zenon_H161. apply refl_equal. % 29.94/30.11 apply zenon_H161. apply refl_equal. % 29.94/30.11 (* end of lemma zenon_L625_ *) % 29.94/30.11 assert (zenon_L626_ : ((op (e0) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H89 zenon_H26 zenon_H142. % 29.94/30.11 apply (zenon_notand_s _ _ ax23); [ zenon_intro zenon_H1d0 | zenon_intro zenon_H265 ]. % 29.94/30.11 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 29.94/30.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e3) = (op (op (e2) (e2)) (op (e2) (e2))))). % 29.94/30.11 intro zenon_D_pnotp. % 29.94/30.11 apply zenon_H1d0. % 29.94/30.11 rewrite <- zenon_D_pnotp. % 29.94/30.11 exact zenon_H166. % 29.94/30.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 29.94/30.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 29.94/30.11 congruence. % 29.94/30.11 cut (((op (e0) (e0)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))). % 29.94/30.11 intro zenon_D_pnotp. % 29.94/30.11 apply zenon_H1d1. % 29.94/30.11 rewrite <- zenon_D_pnotp. % 29.94/30.11 exact zenon_H89. % 29.94/30.11 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 29.94/30.11 cut (((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H266]. % 29.94/30.11 congruence. % 29.94/30.11 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 29.94/30.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 29.94/30.11 intro zenon_D_pnotp. % 29.94/30.11 apply zenon_H266. % 29.94/30.11 rewrite <- zenon_D_pnotp. % 29.94/30.11 exact zenon_H166. % 29.94/30.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 29.94/30.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H25f]. % 29.94/30.11 congruence. % 29.94/30.11 apply (zenon_L623_); trivial. % 29.94/30.11 apply zenon_H167. apply refl_equal. % 29.94/30.11 apply zenon_H167. apply refl_equal. % 29.94/30.11 apply zenon_H2f. apply refl_equal. % 29.94/30.11 apply zenon_H167. apply refl_equal. % 29.94/30.11 apply zenon_H167. apply refl_equal. % 29.94/30.11 apply (zenon_notand_s _ _ zenon_H265); [ zenon_intro zenon_H262 | zenon_intro zenon_H1c1 ]. % 29.94/30.11 apply (zenon_L625_); trivial. % 29.94/30.11 apply zenon_H1c1. apply sym_equal. exact zenon_H142. % 29.94/30.11 (* end of lemma zenon_L626_ *) % 29.94/30.11 assert (zenon_L627_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H20d zenon_Hc9 zenon_Hf5. % 29.94/30.11 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 29.94/30.11 intro zenon_D_pnotp. % 29.94/30.11 apply zenon_H20d. % 29.94/30.11 rewrite <- zenon_D_pnotp. % 29.94/30.11 exact zenon_Hc9. % 29.94/30.11 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 29.94/30.11 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 29.94/30.11 congruence. % 29.94/30.11 apply zenon_H6d. apply refl_equal. % 29.94/30.11 apply zenon_Hf8. apply sym_equal. exact zenon_Hf5. % 29.94/30.11 (* end of lemma zenon_L627_ *) % 29.94/30.11 assert (zenon_L628_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H267 zenon_H218 zenon_H156 zenon_H1b9 zenon_H60 zenon_Hc9 zenon_H20d zenon_H231. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 29.94/30.11 apply (zenon_L259_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 29.94/30.11 apply (zenon_L179_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 29.94/30.11 apply (zenon_L627_); trivial. % 29.94/30.11 exact (zenon_H231 zenon_Hf4). % 29.94/30.11 (* end of lemma zenon_L628_ *) % 29.94/30.11 assert (zenon_L629_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H1d2 zenon_H1e1 zenon_Hfe zenon_H37 zenon_Hd0 zenon_H108 zenon_H1c5. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 29.94/30.11 apply (zenon_L296_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 29.94/30.11 apply (zenon_L170_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 29.94/30.11 exact (zenon_Hd0 zenon_Hcc). % 29.94/30.11 apply (zenon_L171_); trivial. % 29.94/30.11 (* end of lemma zenon_L629_ *) % 29.94/30.11 assert (zenon_L630_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H1af zenon_H1bd zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H1d2 zenon_H1e1 zenon_Hfe zenon_H37 zenon_Hd0 zenon_H108. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.94/30.11 apply (zenon_L332_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.94/30.11 apply (zenon_L209_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.94/30.11 apply (zenon_L628_); trivial. % 29.94/30.11 apply (zenon_L629_); trivial. % 29.94/30.11 (* end of lemma zenon_L630_ *) % 29.94/30.11 assert (zenon_L631_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H200 zenon_Hde zenon_Hd5 zenon_H5e zenon_H26 zenon_H14b zenon_H27 zenon_H5c zenon_Hd0 zenon_H37 zenon_H1d2 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hc9 zenon_H20d zenon_H231 zenon_H1bd zenon_H1af zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H108 zenon_Hb5 zenon_H8b. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.94/30.11 apply (zenon_L49_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.94/30.11 apply (zenon_L608_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.94/30.11 apply (zenon_L626_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.94/30.11 apply (zenon_L191_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.94/30.11 apply (zenon_L630_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.94/30.11 apply (zenon_L296_); trivial. % 29.94/30.11 apply (zenon_L297_); trivial. % 29.94/30.11 (* end of lemma zenon_L631_ *) % 29.94/30.11 assert (zenon_L632_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H14b zenon_Hde zenon_Hda zenon_Hd0 zenon_H37 zenon_H1d2 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hc9 zenon_H20d zenon_H231 zenon_H1bd zenon_H1af zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H1e1 zenon_H108 zenon_Hb5 zenon_H8b. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.94/30.11 apply (zenon_L192_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.94/30.11 apply (zenon_L630_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.94/30.11 apply (zenon_L296_); trivial. % 29.94/30.11 apply (zenon_L297_); trivial. % 29.94/30.11 (* end of lemma zenon_L632_ *) % 29.94/30.11 assert (zenon_L633_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H200 zenon_H5c zenon_H1d8 zenon_H1e zenon_H3c zenon_H26 zenon_H14b zenon_Hde zenon_Hda zenon_Hd0 zenon_H37 zenon_H1d2 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hc9 zenon_H20d zenon_H231 zenon_H1bd zenon_H1af zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H108 zenon_Hb5 zenon_H8b. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.94/30.11 apply (zenon_L194_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.94/30.11 apply (zenon_L207_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.94/30.11 apply (zenon_L626_); trivial. % 29.94/30.11 apply (zenon_L632_); trivial. % 29.94/30.11 (* end of lemma zenon_L633_ *) % 29.94/30.11 assert (zenon_L634_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H1d2 zenon_H55 zenon_H60 zenon_H1bd zenon_H27 zenon_H26 zenon_Hd0 zenon_H108 zenon_H1c5. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 29.94/30.11 apply (zenon_L165_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 29.94/30.11 apply (zenon_L3_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 29.94/30.11 exact (zenon_Hd0 zenon_Hcc). % 29.94/30.11 apply (zenon_L171_); trivial. % 29.94/30.11 (* end of lemma zenon_L634_ *) % 29.94/30.11 assert (zenon_L635_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_He1 zenon_H218 zenon_H17b zenon_H1d2 zenon_H55 zenon_H60 zenon_H1bd zenon_H27 zenon_H26 zenon_Hd0 zenon_H108. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.94/30.11 apply (zenon_L332_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.94/30.11 apply (zenon_L126_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.94/30.11 apply (zenon_L259_); trivial. % 29.94/30.11 apply (zenon_L634_); trivial. % 29.94/30.11 (* end of lemma zenon_L635_ *) % 29.94/30.11 assert (zenon_L636_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H135 zenon_H10e zenon_H5c zenon_H108 zenon_H26 zenon_H27 zenon_H1bd zenon_H60 zenon_H1d2 zenon_He1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hd0 zenon_H17b zenon_H218. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.94/30.11 apply (zenon_L191_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.94/30.11 apply (zenon_L635_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.94/30.11 exact (zenon_Hd0 zenon_Hcc). % 29.94/30.11 apply (zenon_L405_); trivial. % 29.94/30.11 (* end of lemma zenon_L636_ *) % 29.94/30.11 assert (zenon_L637_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 29.94/30.11 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H1af zenon_H1bd zenon_H218 zenon_H17b zenon_H60 zenon_H1d2 zenon_H1e1 zenon_Hfe zenon_H37 zenon_Hd0 zenon_H108. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.94/30.11 apply (zenon_L273_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.94/30.11 apply (zenon_L209_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.94/30.11 apply (zenon_L259_); trivial. % 29.94/30.11 apply (zenon_L629_); trivial. % 29.94/30.11 (* end of lemma zenon_L637_ *) % 29.94/30.11 assert (zenon_L638_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.94/30.11 do 0 intro. intros zenon_H14b zenon_H89 zenon_Hc8 zenon_H27 zenon_H26 zenon_H5c zenon_H135 zenon_Hd0 zenon_H37 zenon_H1d2 zenon_H60 zenon_H17b zenon_H218 zenon_H1bd zenon_H1af zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H1e1 zenon_H108 zenon_Hb5 zenon_H8b. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.94/30.11 apply (zenon_L636_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.94/30.11 apply (zenon_L637_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.94/30.11 apply (zenon_L296_); trivial. % 29.94/30.11 apply (zenon_L297_); trivial. % 29.94/30.11 (* end of lemma zenon_L638_ *) % 29.94/30.11 assert (zenon_L639_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 29.94/30.11 do 0 intro. intros zenon_Had zenon_H68 zenon_H90. % 29.94/30.11 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 29.94/30.11 intro zenon_D_pnotp. % 29.94/30.11 apply zenon_Had. % 29.94/30.11 rewrite <- zenon_D_pnotp. % 29.94/30.11 exact zenon_H68. % 29.94/30.11 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H26a]. % 29.94/30.11 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 29.94/30.11 congruence. % 29.94/30.11 apply zenon_Hd4. apply refl_equal. % 29.94/30.11 apply zenon_H26a. apply sym_equal. exact zenon_H90. % 29.94/30.11 (* end of lemma zenon_L639_ *) % 29.94/30.11 assert (zenon_L640_ : (((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). % 29.94/30.11 do 0 intro. intros zenon_H23b zenon_H68 zenon_Had zenon_H1f zenon_H3f zenon_Hb6 zenon_H6f zenon_Hf6 zenon_H1e5. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 29.94/30.11 apply (zenon_L639_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 29.94/30.11 apply (zenon_L336_); trivial. % 29.94/30.11 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 29.94/30.11 apply (zenon_L540_); trivial. % 29.94/30.11 apply (zenon_L187_); trivial. % 29.94/30.12 (* end of lemma zenon_L640_ *) % 29.94/30.12 assert (zenon_L641_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (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). % 29.94/30.12 do 0 intro. intros zenon_H208 zenon_H18c zenon_H5e zenon_H3c zenon_He9 zenon_H60 zenon_H23b zenon_H68 zenon_Had zenon_H1f zenon_H3f zenon_Hb6 zenon_H6f zenon_Hf6. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.94/30.12 apply (zenon_L120_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.94/30.12 apply (zenon_L218_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.94/30.12 apply (zenon_L219_); trivial. % 29.94/30.12 apply (zenon_L640_); trivial. % 29.94/30.12 (* end of lemma zenon_L641_ *) % 29.94/30.12 assert (zenon_L642_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.12 do 0 intro. intros zenon_Hb6 zenon_H68 zenon_H13b zenon_H19e zenon_H222 zenon_H60 zenon_H5e zenon_H1f zenon_H1a8 zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H172 zenon_H92 zenon_H17d zenon_H174 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H225 zenon_H20 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_Hd9 zenon_H42 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H102 zenon_Had zenon_H100 zenon_H10d zenon_H6f zenon_Hb8 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H1d2 zenon_H27 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_He1 zenon_H18c zenon_H135 zenon_H8d zenon_H2d zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H14e zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.94/30.12 apply (zenon_L641_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.94/30.12 exact (zenon_H13b zenon_Hfd). % 29.94/30.12 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.94/30.12 apply (zenon_L282_); trivial. % 29.94/30.12 apply (zenon_L582_); trivial. % 29.94/30.12 (* end of lemma zenon_L642_ *) % 29.94/30.12 assert (zenon_L643_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (((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). % 29.94/30.12 do 0 intro. intros zenon_H208 zenon_H18c zenon_H55 zenon_Hcd zenon_Hfe zenon_H37 zenon_H23b zenon_H68 zenon_Had zenon_H1f zenon_H3f zenon_Hb6 zenon_H6f zenon_Hf6. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 29.94/30.12 apply (zenon_L120_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 29.94/30.12 apply (zenon_L212_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 29.94/30.12 apply (zenon_L170_); trivial. % 29.94/30.12 apply (zenon_L640_); trivial. % 29.94/30.12 (* end of lemma zenon_L643_ *) % 29.94/30.12 assert (zenon_L644_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (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 (e1) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.94/30.12 do 0 intro. intros zenon_H16f zenon_Hf6 zenon_H6f zenon_H3f zenon_H1f zenon_Had zenon_H68 zenon_H23b zenon_Hfe zenon_Hcd zenon_H55 zenon_H18c zenon_H208 zenon_Hee zenon_Hb6 zenon_H16a zenon_H16b. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.12 apply (zenon_L18_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.12 apply (zenon_L643_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.12 apply (zenon_L490_); trivial. % 29.94/30.12 apply (zenon_L101_); trivial. % 29.94/30.12 (* end of lemma zenon_L644_ *) % 29.94/30.12 assert (zenon_L645_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (((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)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.94/30.12 do 0 intro. intros zenon_H101 zenon_H60 zenon_H3c zenon_H5e zenon_H13b zenon_H16b zenon_H16a zenon_Hee zenon_H208 zenon_H18c zenon_Hcd zenon_Hfe zenon_H23b zenon_H68 zenon_Had zenon_H1f zenon_H3f zenon_H6f zenon_Hf6 zenon_H16f zenon_H135 zenon_He2 zenon_H1d8 zenon_H222 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1af zenon_H1dc zenon_Hb6 zenon_He1. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.94/30.12 apply (zenon_L641_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.94/30.12 exact (zenon_H13b zenon_Hfd). % 29.94/30.12 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.94/30.12 apply (zenon_L644_); trivial. % 29.94/30.12 apply (zenon_L310_); trivial. % 29.94/30.12 (* end of lemma zenon_L645_ *) % 29.94/30.12 assert (zenon_L646_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.12 do 0 intro. intros zenon_H1a8 zenon_Hdc zenon_He1 zenon_Hb6 zenon_H10d zenon_H1e zenon_H2d zenon_H174 zenon_H18e zenon_H200 zenon_H218 zenon_Hd0 zenon_H222 zenon_Hde zenon_H135 zenon_H3c zenon_H19e zenon_Hfc zenon_H102 zenon_H1bd zenon_H1af zenon_H6c zenon_Hd6 zenon_H156 zenon_H1d5 zenon_H6f zenon_H208 zenon_H60 zenon_H1ca zenon_H1f zenon_H5e zenon_H1c7 zenon_H42 zenon_H159 zenon_H17d zenon_H20d zenon_Hb5 zenon_H100 zenon_H173 zenon_H35 zenon_Hc0 zenon_H20 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H16a zenon_H27 zenon_H8d zenon_Had zenon_H225 zenon_H172 zenon_H23b zenon_Hee zenon_He4 zenon_H74 zenon_H15a zenon_H16f zenon_H14b zenon_H125 zenon_H20e zenon_Hd1 zenon_H101 zenon_H18c zenon_H1fd zenon_Hd9 zenon_H108 zenon_H1d2 zenon_Hcd zenon_H1a5 zenon_Ha4 zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_H64 zenon_Hc8 zenon_H112 zenon_H14e. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.12 apply (zenon_L120_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.12 apply (zenon_L146_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.12 apply (zenon_L495_); trivial. % 29.94/30.12 apply (zenon_L137_); trivial. % 29.94/30.12 (* end of lemma zenon_L646_ *) % 29.94/30.12 assert (zenon_L647_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.12 do 0 intro. intros zenon_H1a8 zenon_H6c zenon_He2 zenon_Ha4 zenon_H1a5 zenon_He1 zenon_Hb6 zenon_H10d zenon_H1e zenon_H2d zenon_H174 zenon_H18e zenon_H200 zenon_H218 zenon_Hd0 zenon_H222 zenon_Hde zenon_H135 zenon_H3c zenon_H19e zenon_Hfc zenon_H102 zenon_H1bd zenon_H1af zenon_Hd6 zenon_H156 zenon_H1d5 zenon_H6f zenon_H208 zenon_H60 zenon_H1ca zenon_H5e zenon_H1c7 zenon_H42 zenon_H159 zenon_H20d zenon_Hb5 zenon_H100 zenon_H173 zenon_H35 zenon_Hc0 zenon_H20 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H16a zenon_H27 zenon_H8d zenon_Had zenon_H225 zenon_H172 zenon_H23b zenon_Hee zenon_He4 zenon_H74 zenon_H15a zenon_H16f zenon_H14b zenon_H125 zenon_H20e zenon_Hd1 zenon_H101 zenon_H18c zenon_H1fd zenon_Hd9 zenon_H108 zenon_H1d2 zenon_Hcd zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hc8 zenon_H69 zenon_H17d zenon_H112 zenon_H14e. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.12 apply (zenon_L120_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.12 apply (zenon_L585_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.12 apply (zenon_L502_); trivial. % 29.94/30.12 apply (zenon_L137_); trivial. % 29.94/30.12 (* end of lemma zenon_L647_ *) % 29.94/30.12 assert (zenon_L648_ : (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 29.94/30.12 do 0 intro. intros zenon_H18e zenon_H135 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_Hbd zenon_Hde zenon_H1e zenon_H3f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H42 zenon_H1a8 zenon_H218 zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H108 zenon_H1ca zenon_H5e zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H159 zenon_H3c zenon_H101 zenon_H200 zenon_Hda zenon_H14b zenon_H20d zenon_H18c zenon_Hd1 zenon_H6b zenon_H1dc zenon_Hb6 zenon_H173 zenon_H35 zenon_Ha4 zenon_H1a5 zenon_H10d zenon_H174 zenon_Hfc zenon_H102 zenon_Hb5 zenon_Hc0 zenon_H20 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H16a zenon_H27 zenon_H8d zenon_Had zenon_H225 zenon_H172 zenon_H23b zenon_Hee zenon_He4 zenon_H74 zenon_H15a zenon_H16f zenon_H125 zenon_H20e zenon_H1fd zenon_Hd9 zenon_He7 zenon_H5c zenon_Hc8 zenon_H17d zenon_H6f zenon_H6c zenon_He1 zenon_He2. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.12 apply (zenon_L252_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.12 apply (zenon_L4_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.12 apply (zenon_L385_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.12 apply (zenon_L252_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.94/30.12 apply (zenon_L647_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.94/30.12 apply (zenon_L42_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.12 apply (zenon_L18_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.12 apply (zenon_L585_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.12 apply (zenon_L315_); trivial. % 29.94/30.12 apply (zenon_L137_); trivial. % 29.94/30.12 apply (zenon_L393_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.12 apply (zenon_L157_); trivial. % 29.94/30.12 apply (zenon_L50_); trivial. % 29.94/30.12 (* end of lemma zenon_L648_ *) % 29.94/30.12 assert (zenon_L649_ : ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.94/30.12 do 0 intro. intros zenon_H1f zenon_Hb6 zenon_H14e zenon_H25c zenon_H256 zenon_H84 zenon_H74 zenon_H3c zenon_H18c zenon_Hcd zenon_H14b zenon_H1dc zenon_H6b zenon_H156 zenon_H27 zenon_H1d2 zenon_H108 zenon_H1bd zenon_H5e zenon_H60 zenon_H1c7 zenon_H1ca zenon_H1d5 zenon_H173 zenon_H1e6 zenon_Hf6 zenon_H102 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H11e zenon_H1a5 zenon_Hc8 zenon_H23b zenon_Hee zenon_Hb5 zenon_Hf9 zenon_H20 zenon_H225 zenon_H222 zenon_H101 zenon_H159 zenon_H83 zenon_H218 zenon_He4 zenon_H15a zenon_H16f zenon_H16a zenon_H17d zenon_H92 zenon_H172 zenon_H200 zenon_H5c zenon_H125 zenon_Hbd zenon_He7 zenon_H3f zenon_H1fd zenon_Hde zenon_H208 zenon_H20d zenon_H20e zenon_H246 zenon_Hc0 zenon_H1b1 zenon_Ha4 zenon_Haa zenon_H25b zenon_H1a8 zenon_H174 zenon_H6c zenon_H6f zenon_H42 zenon_H2d zenon_H1e zenon_H112 zenon_H10d zenon_H100 zenon_Had zenon_Hb8 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_H1d8 zenon_H135 zenon_H18e zenon_Hd9 zenon_H8d zenon_H17b zenon_He1. % 29.94/30.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.12 exact (zenon_H74 zenon_H73). % 29.94/30.12 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.12 apply (zenon_L48_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.12 apply (zenon_L146_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.12 apply (zenon_L493_); trivial. % 29.94/30.12 apply (zenon_L137_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.12 apply (zenon_L580_); trivial. % 29.94/30.12 apply (zenon_L441_); trivial. % 29.94/30.12 (* end of lemma zenon_L649_ *) % 29.94/30.12 assert (zenon_L650_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 29.94/30.12 do 0 intro. intros zenon_H8d zenon_H64 zenon_H2d zenon_H6f zenon_H68 zenon_He1 zenon_Hc9 zenon_Hb6 zenon_Hb5. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.12 apply (zenon_L148_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.12 apply (zenon_L18_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.12 apply (zenon_L273_); trivial. % 29.94/30.12 apply (zenon_L461_); trivial. % 29.94/30.12 (* end of lemma zenon_L650_ *) % 29.94/30.12 assert (zenon_L651_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 29.94/30.12 do 0 intro. intros zenon_H14e zenon_H69 zenon_Hc8 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_Hcd zenon_H1d2 zenon_H108 zenon_Hd9 zenon_H1fd zenon_H18c zenon_H101 zenon_Hd1 zenon_H20e zenon_H125 zenon_H14b zenon_H16f zenon_H15a zenon_H74 zenon_He4 zenon_Hee zenon_H23b zenon_H172 zenon_H225 zenon_Had zenon_H8d zenon_H27 zenon_H16a zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_H20 zenon_Hc0 zenon_H35 zenon_H173 zenon_H100 zenon_Hb5 zenon_H20d zenon_H159 zenon_H42 zenon_H1c7 zenon_H5e zenon_H1ca zenon_H60 zenon_H208 zenon_H6f zenon_H1d5 zenon_H156 zenon_Hd6 zenon_H1af zenon_H1bd zenon_H102 zenon_Hfc zenon_H19e zenon_H3c zenon_H135 zenon_Hde zenon_H222 zenon_Hd0 zenon_H218 zenon_H200 zenon_H18e zenon_H174 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_He1 zenon_H1a5 zenon_Ha4 zenon_H1a8 zenon_H25b zenon_Haa zenon_H246 zenon_Hf9 zenon_H11e zenon_Hf6 zenon_H1e6 zenon_H256 zenon_H25c zenon_H26 zenon_H17d zenon_H112. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 29.94/30.12 exact (zenon_H84 zenon_H88). % 29.94/30.12 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 29.94/30.12 apply (zenon_L16_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 29.94/30.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.12 exact (zenon_H74 zenon_H73). % 29.94/30.12 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.12 apply (zenon_L599_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.12 apply (zenon_L580_); trivial. % 29.94/30.12 apply (zenon_L647_); trivial. % 29.94/30.12 apply (zenon_L139_); trivial. % 29.94/30.12 (* end of lemma zenon_L651_ *) % 29.94/30.12 assert (zenon_L652_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 29.94/30.12 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_Hd5 zenon_Hcd zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1af zenon_H1dc zenon_Hb6 zenon_He1. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 29.94/30.12 apply (zenon_L49_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 29.94/30.12 apply (zenon_L212_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 29.94/30.12 exact (zenon_Hd0 zenon_Hcc). % 29.94/30.12 apply (zenon_L301_); trivial. % 29.94/30.12 (* end of lemma zenon_L652_ *) % 29.94/30.12 assert (zenon_L653_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 29.94/30.12 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H1af zenon_H1bd zenon_H1dc zenon_Hb6 zenon_H1d2 zenon_H1e1 zenon_Hfe zenon_H37 zenon_Hd0 zenon_H108. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 29.94/30.12 apply (zenon_L273_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 29.94/30.12 apply (zenon_L209_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 29.94/30.12 apply (zenon_L200_); trivial. % 29.94/30.12 apply (zenon_L629_); trivial. % 29.94/30.12 (* end of lemma zenon_L653_ *) % 29.94/30.12 assert (zenon_L654_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 29.94/30.12 do 0 intro. intros zenon_H16f zenon_H6f zenon_H19e zenon_H1af zenon_Hfe zenon_H222 zenon_H5e zenon_H98 zenon_H18c zenon_H68 zenon_H208 zenon_Hee zenon_Hb6 zenon_H16a zenon_H16b. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.12 apply (zenon_L18_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.12 apply (zenon_L612_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.12 apply (zenon_L490_); trivial. % 29.94/30.12 apply (zenon_L101_); trivial. % 29.94/30.12 (* end of lemma zenon_L654_ *) % 29.94/30.12 assert (zenon_L655_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.12 do 0 intro. intros zenon_He4 zenon_H74 zenon_H174 zenon_H10d zenon_H8d zenon_H172 zenon_H20 zenon_H35 zenon_H16a zenon_Hb6 zenon_Hee zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_H19e zenon_H16f zenon_Hdf zenon_Hcd zenon_H1d5 zenon_H6b zenon_H1dc zenon_H101 zenon_H60 zenon_H3c zenon_H13b zenon_H23b zenon_Had zenon_Hf6 zenon_H124 zenon_H42 zenon_H14e zenon_Hb8 zenon_H100 zenon_H2d zenon_H112 zenon_H6f zenon_H3f zenon_H1e zenon_Hde zenon_Hbd zenon_Hd6 zenon_H1af zenon_Hd0 zenon_He1 zenon_H1d8 zenon_H135 zenon_H18e. % 29.94/30.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.12 exact (zenon_H74 zenon_H73). % 29.94/30.12 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.12 apply (zenon_L48_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.12 apply (zenon_L49_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.12 apply (zenon_L252_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.12 apply (zenon_L4_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.12 apply (zenon_L584_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.94/30.12 apply (zenon_L16_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.94/30.12 apply (zenon_L42_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 29.94/30.12 apply (zenon_L645_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 29.94/30.12 apply (zenon_L585_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 29.94/30.12 apply (zenon_L652_); trivial. % 29.94/30.12 apply (zenon_L654_); trivial. % 29.94/30.12 apply (zenon_L393_); trivial. % 29.94/30.12 (* end of lemma zenon_L655_ *) % 29.94/30.12 assert (zenon_L656_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.12 do 0 intro. intros zenon_H1a8 zenon_H124 zenon_Hf6 zenon_H13b zenon_Hdf zenon_Hdc zenon_Ha4 zenon_H1a5 zenon_He1 zenon_Hb6 zenon_H10d zenon_H1e zenon_H2d zenon_H174 zenon_H18e zenon_H200 zenon_H218 zenon_Hd0 zenon_H222 zenon_Hde zenon_H135 zenon_H3c zenon_H19e zenon_Hfc zenon_H102 zenon_H1bd zenon_H1af zenon_Hd6 zenon_H156 zenon_H1d5 zenon_H6f zenon_H208 zenon_H60 zenon_H1ca zenon_H5e zenon_H1c7 zenon_H42 zenon_H159 zenon_H20d zenon_Hb5 zenon_H100 zenon_H173 zenon_H35 zenon_Hc0 zenon_H20 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H16a zenon_H27 zenon_H8d zenon_Had zenon_H225 zenon_H172 zenon_H23b zenon_Hee zenon_He4 zenon_H74 zenon_H15a zenon_H16f zenon_H14b zenon_H125 zenon_H20e zenon_Hd1 zenon_H101 zenon_H18c zenon_H1fd zenon_Hd9 zenon_H108 zenon_H1d2 zenon_Hcd zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H3f zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hc8 zenon_H69 zenon_H17d zenon_H112 zenon_H14e. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.12 apply (zenon_L655_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.12 apply (zenon_L146_); trivial. % 29.94/30.12 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.12 apply (zenon_L502_); trivial. % 29.94/30.12 apply (zenon_L137_); trivial. % 29.94/30.12 (* end of lemma zenon_L656_ *) % 29.94/30.12 assert (zenon_L657_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.13 do 0 intro. intros zenon_H1a8 zenon_H1d8 zenon_Hbd zenon_H3f zenon_H100 zenon_Hb8 zenon_H124 zenon_Hf6 zenon_Had zenon_H23b zenon_H13b zenon_H3c zenon_H101 zenon_H16f zenon_H222 zenon_Hee zenon_H16a zenon_H20 zenon_H172 zenon_H8d zenon_H10d zenon_H174 zenon_H74 zenon_He4 zenon_H18c zenon_H18e zenon_H102 zenon_H35 zenon_H1e zenon_Hfc zenon_Hdc zenon_Hd1 zenon_H19e zenon_H135 zenon_Hdf zenon_Hde zenon_H108 zenon_Hfe zenon_H1ca zenon_H6c zenon_H5e zenon_H60 zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_H6f zenon_Hcd zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1af zenon_H1dc zenon_Hb6 zenon_He1 zenon_H2d zenon_H42 zenon_H112 zenon_H14e. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.13 apply (zenon_L655_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.13 apply (zenon_L146_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.13 apply (zenon_L464_); trivial. % 29.94/30.13 apply (zenon_L137_); trivial. % 29.94/30.13 (* end of lemma zenon_L657_ *) % 29.94/30.13 assert (zenon_L658_ : (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> False). % 29.94/30.13 do 0 intro. intros zenon_H20 zenon_H182 zenon_H14f. % 29.94/30.13 cut (((op (e1) (e3)) = (e1)) = ((e0) = (e1))). % 29.94/30.13 intro zenon_D_pnotp. % 29.94/30.13 apply zenon_H20. % 29.94/30.13 rewrite <- zenon_D_pnotp. % 29.94/30.13 exact zenon_H182. % 29.94/30.13 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 29.94/30.13 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H26b]. % 29.94/30.13 congruence. % 29.94/30.13 exact (zenon_H26b zenon_H14f). % 29.94/30.13 apply zenon_H22. apply refl_equal. % 29.94/30.13 (* end of lemma zenon_L658_ *) % 29.94/30.13 assert (zenon_L659_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 29.94/30.13 do 0 intro. intros zenon_H1a8 zenon_H6e zenon_Hdc zenon_Hd0 zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_Hde zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H200 zenon_H172 zenon_H14e zenon_H92 zenon_H17d zenon_H174 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H222 zenon_H225 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_Hd9 zenon_H42 zenon_H18e zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H102 zenon_Had zenon_H100 zenon_H10d zenon_H6f zenon_H112 zenon_Hb8 zenon_Hf6 zenon_H1e6 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H1af zenon_H1c7 zenon_H60 zenon_H5e zenon_H1bd zenon_Hd6 zenon_H108 zenon_H1d2 zenon_H27 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_He1 zenon_H18c zenon_H3c zenon_H135 zenon_H8d zenon_H1e zenon_H2d zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H20 zenon_H14f. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.13 apply (zenon_L18_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.13 apply (zenon_L146_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.13 apply (zenon_L579_); trivial. % 29.94/30.13 apply (zenon_L658_); trivial. % 29.94/30.13 (* end of lemma zenon_L659_ *) % 29.94/30.13 assert (zenon_L660_ : (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e0) = (e1))) -> False). % 29.94/30.13 do 0 intro. intros zenon_H13b zenon_H124 zenon_Hb6 zenon_H6c zenon_Hdf zenon_H1a8 zenon_H6e zenon_Hdc zenon_Hd0 zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_Hde zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H200 zenon_H172 zenon_H14e zenon_H92 zenon_H17d zenon_H174 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H222 zenon_H225 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_Hd9 zenon_H42 zenon_H18e zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H102 zenon_Had zenon_H100 zenon_H10d zenon_H6f zenon_H112 zenon_Hb8 zenon_Hf6 zenon_H1e6 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H1af zenon_H1c7 zenon_H60 zenon_H5e zenon_H1bd zenon_Hd6 zenon_H108 zenon_H1d2 zenon_H27 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_He1 zenon_H18c zenon_H3c zenon_H135 zenon_H8d zenon_H1e zenon_H2d zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H20. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.94/30.13 apply (zenon_L656_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.94/30.13 apply (zenon_L42_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.13 apply (zenon_L18_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.13 apply (zenon_L146_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.13 apply (zenon_L464_); trivial. % 29.94/30.13 apply (zenon_L137_); trivial. % 29.94/30.13 apply (zenon_L659_); trivial. % 29.94/30.13 (* end of lemma zenon_L660_ *) % 29.94/30.13 assert (zenon_L661_ : ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 29.94/30.13 do 0 intro. intros zenon_He9 zenon_H18e zenon_H135 zenon_He2 zenon_H1d8 zenon_He1 zenon_Hd0 zenon_H1af zenon_Hd6 zenon_Hbd zenon_Hde zenon_H1e zenon_H3f zenon_H112 zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H42 zenon_H1a8 zenon_H218 zenon_H60 zenon_H19e zenon_H1d5 zenon_H222 zenon_H156 zenon_H108 zenon_H1ca zenon_H5e zenon_H1bd zenon_H1c7 zenon_H1d2 zenon_H208 zenon_Hcd zenon_H159 zenon_H3c zenon_H101 zenon_H1dc zenon_H6b zenon_Hdf zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H173 zenon_Ha4 zenon_H1a5 zenon_H10d zenon_H174 zenon_H200 zenon_H20d zenon_Hc0 zenon_H20 zenon_H92 zenon_H1b1 zenon_H83 zenon_H84 zenon_H16a zenon_H27 zenon_H8d zenon_Had zenon_H225 zenon_H172 zenon_H23b zenon_Hee zenon_He4 zenon_H74 zenon_H15a zenon_H16f zenon_H14b zenon_H125 zenon_H20e zenon_H18c zenon_H1fd zenon_Hd9 zenon_He7 zenon_H5c zenon_Hc8 zenon_H17d zenon_H6f zenon_H6c zenon_Hb6 zenon_Hb5. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 29.94/30.13 apply (zenon_L252_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 29.94/30.13 apply (zenon_L4_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 29.94/30.13 apply (zenon_L378_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 29.94/30.13 apply (zenon_L252_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 29.94/30.13 apply (zenon_L647_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 29.94/30.13 apply (zenon_L42_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.13 apply (zenon_L18_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.13 apply (zenon_L585_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.13 apply (zenon_L465_); trivial. % 29.94/30.13 apply (zenon_L137_); trivial. % 29.94/30.13 apply (zenon_L393_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 29.94/30.13 apply (zenon_L157_); trivial. % 29.94/30.13 apply (zenon_L461_); trivial. % 29.94/30.13 (* end of lemma zenon_L661_ *) % 29.94/30.13 assert (zenon_L662_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (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)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 29.94/30.13 do 0 intro. intros zenon_H1a8 zenon_H1d8 zenon_Hbd zenon_H3f zenon_H112 zenon_H100 zenon_Hb8 zenon_H14e zenon_H124 zenon_Hf6 zenon_Had zenon_H23b zenon_H13b zenon_H3c zenon_H101 zenon_H16f zenon_H222 zenon_Hee zenon_H16a zenon_H172 zenon_H8d zenon_H10d zenon_H174 zenon_H74 zenon_He4 zenon_H18c zenon_H18e zenon_H102 zenon_H35 zenon_H1e zenon_Hfc zenon_Hdc zenon_Hd1 zenon_H19e zenon_H14b zenon_Hda zenon_He1 zenon_H1dc zenon_H1af zenon_Hd6 zenon_H1d5 zenon_Hd0 zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_H1ca zenon_H108 zenon_Hde zenon_H135 zenon_H6b zenon_Hdf zenon_H2d zenon_Hb6 zenon_H42 zenon_H20 zenon_H14f. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.13 apply (zenon_L655_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.13 apply (zenon_L146_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.13 apply (zenon_L467_); trivial. % 29.94/30.13 apply (zenon_L658_); trivial. % 29.94/30.13 (* end of lemma zenon_L662_ *) % 29.94/30.13 assert (zenon_L663_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 29.94/30.13 do 0 intro. intros zenon_H101 zenon_H3c zenon_H18c zenon_Hdc zenon_Hd1 zenon_H18e zenon_He1 zenon_H1d5 zenon_H19e zenon_Hcd zenon_H6f zenon_H208 zenon_H1d2 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H5e zenon_H6c zenon_Hd6 zenon_H1ca zenon_Hfe zenon_H108 zenon_H1e zenon_H2d zenon_H42 zenon_H135 zenon_Hdf zenon_Hde zenon_H222 zenon_Hd0 zenon_H17b zenon_H218. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.94/30.13 apply (zenon_L433_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.94/30.13 apply (zenon_L154_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.94/30.13 apply (zenon_L309_); trivial. % 29.94/30.13 apply (zenon_L406_); trivial. % 29.94/30.13 (* end of lemma zenon_L663_ *) % 29.94/30.13 assert (zenon_L664_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.13 do 0 intro. intros zenon_H156 zenon_Hbd zenon_Hdf zenon_H5c zenon_H1d8 zenon_H3f zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_H15a zenon_H16f zenon_H112 zenon_H14f zenon_H14b zenon_H125 zenon_Hde zenon_H18c zenon_H135 zenon_H1fd zenon_H89 zenon_Hd9 zenon_H108 zenon_Hd0 zenon_Hd6 zenon_H6c zenon_H1d2 zenon_H1bd zenon_Hb6 zenon_H42 zenon_H2d zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_H1ca zenon_H60 zenon_H17b zenon_H218 zenon_H173 zenon_He1 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 29.94/30.13 apply (zenon_L470_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 29.94/30.13 apply (zenon_L416_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 29.94/30.13 apply (zenon_L471_); trivial. % 29.94/30.13 apply (zenon_L266_); trivial. % 29.94/30.13 (* end of lemma zenon_L664_ *) % 29.94/30.13 assert (zenon_L665_ : ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 29.94/30.13 do 0 intro. intros zenon_H26 zenon_H14e zenon_H25c zenon_H256 zenon_H84 zenon_H74 zenon_H3c zenon_H18c zenon_Hcd zenon_H14b zenon_H1dc zenon_H6b zenon_H156 zenon_H27 zenon_H1d2 zenon_H108 zenon_H1bd zenon_H5e zenon_H60 zenon_H1c7 zenon_H1ca zenon_H1d5 zenon_H173 zenon_H1e6 zenon_Hf6 zenon_H102 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H11e zenon_H1a5 zenon_Hc8 zenon_H23b zenon_Hee zenon_Hb5 zenon_Hf9 zenon_H20 zenon_H225 zenon_H222 zenon_H101 zenon_H159 zenon_H83 zenon_H218 zenon_He4 zenon_H15a zenon_H16f zenon_H16a zenon_H17d zenon_H92 zenon_H172 zenon_H200 zenon_H5c zenon_H125 zenon_Hbd zenon_He7 zenon_H3f zenon_H1fd zenon_Hde zenon_H208 zenon_H20d zenon_H20e zenon_H246 zenon_Hc0 zenon_H1b1 zenon_Ha4 zenon_Haa zenon_H25b zenon_H1a8 zenon_H174 zenon_H6c zenon_H6f zenon_H42 zenon_H2d zenon_H1e zenon_H112 zenon_H10d zenon_H100 zenon_Had zenon_Hb8 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_H1d8 zenon_H135 zenon_H18e zenon_Hd9 zenon_H8d zenon_H17b zenon_He1. % 29.94/30.13 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 29.94/30.13 exact (zenon_H74 zenon_H73). % 29.94/30.13 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 29.94/30.13 apply (zenon_L599_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 29.94/30.13 apply (zenon_L580_); trivial. % 29.94/30.13 apply (zenon_L441_); trivial. % 29.94/30.13 (* end of lemma zenon_L665_ *) % 29.94/30.13 assert (zenon_L666_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 29.94/30.13 do 0 intro. intros zenon_H1a8 zenon_Hdc zenon_Ha4 zenon_H1a5 zenon_Hde zenon_H174 zenon_H18e zenon_H200 zenon_H218 zenon_Hd0 zenon_H222 zenon_H135 zenon_H3c zenon_H19e zenon_Hfc zenon_H102 zenon_H1bd zenon_H1af zenon_Hd6 zenon_H156 zenon_H1d5 zenon_H6f zenon_H208 zenon_H60 zenon_H1ca zenon_H5e zenon_H1c7 zenon_H42 zenon_H159 zenon_H16f zenon_H15a zenon_H1dc zenon_H6b zenon_He7 zenon_Hb8 zenon_H3f zenon_Hbd zenon_H1d8 zenon_H5c zenon_H101 zenon_Hcd zenon_H18c zenon_H173 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_He1 zenon_H35 zenon_Hd1 zenon_H20e zenon_Hb5 zenon_H108 zenon_H1d2 zenon_Hd9 zenon_H1fd zenon_H125 zenon_H14b zenon_Hee zenon_H20d zenon_H74 zenon_He4 zenon_H172 zenon_H17d zenon_H225 zenon_H8d zenon_H27 zenon_H16a zenon_H84 zenon_H83 zenon_H1b1 zenon_H92 zenon_Hc0 zenon_Haa zenon_H100 zenon_Hf9 zenon_Had zenon_Hc8 zenon_H8b zenon_H20 zenon_H112 zenon_H14e. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 29.94/30.13 apply (zenon_L48_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 29.94/30.13 apply (zenon_L146_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 29.94/30.13 apply (zenon_L535_); trivial. % 29.94/30.13 apply (zenon_L137_); trivial. % 29.94/30.13 (* end of lemma zenon_L666_ *) % 29.94/30.13 assert (zenon_L667_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 29.94/30.13 do 0 intro. intros zenon_H200 zenon_Hd6 zenon_H6b zenon_Hcd zenon_Hde zenon_H135 zenon_Hd5 zenon_H5e zenon_H26 zenon_H89 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H1af zenon_H1bd zenon_H1dc zenon_Hb6 zenon_H1d2 zenon_Hfe zenon_H37 zenon_Hd0 zenon_H108. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.94/30.13 apply (zenon_L652_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.94/30.13 apply (zenon_L608_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.94/30.13 apply (zenon_L626_); trivial. % 29.94/30.13 apply (zenon_L653_); trivial. % 29.94/30.13 (* end of lemma zenon_L667_ *) % 29.94/30.13 assert (zenon_L668_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.13 do 0 intro. intros zenon_H42 zenon_H3f zenon_He9 zenon_H208 zenon_H1ca zenon_H5e zenon_H222 zenon_H60 zenon_H19e zenon_Haa zenon_He1 zenon_Hb6 zenon_Hbd zenon_H6f zenon_H2d zenon_H100 zenon_Hb8 zenon_H14e zenon_H14f zenon_Hf9 zenon_H89 zenon_H26 zenon_H135 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_H1dc zenon_He7 zenon_H1d8 zenon_H5c zenon_H16c zenon_H156 zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.94/30.13 apply (zenon_L4_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.94/30.13 apply (zenon_L326_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.94/30.13 apply (zenon_L207_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.94/30.13 apply (zenon_L626_); trivial. % 29.94/30.13 apply (zenon_L516_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.94/30.13 apply (zenon_L456_); trivial. % 29.94/30.13 exact (zenon_H18e zenon_H40). % 29.94/30.13 (* end of lemma zenon_L668_ *) % 29.94/30.13 assert (zenon_L669_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.13 do 0 intro. intros zenon_H124 zenon_H68 zenon_Hd0 zenon_H89 zenon_H14f zenon_Hb6 zenon_He9 zenon_H19e zenon_H26 zenon_H27 zenon_H222 zenon_H5e zenon_H1a8 zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H172 zenon_H92 zenon_H17d zenon_H174 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H225 zenon_H20 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_Hd9 zenon_H42 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H102 zenon_Had zenon_H100 zenon_H10d zenon_H6f zenon_Hb8 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H60 zenon_H1d2 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_He1 zenon_H18c zenon_H135 zenon_H8d zenon_H2d zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H14e zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 29.94/30.13 apply (zenon_L641_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 29.94/30.13 apply (zenon_L458_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 29.94/30.13 apply (zenon_L241_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.94/30.13 apply (zenon_L652_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.94/30.13 apply (zenon_L608_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.94/30.13 apply (zenon_L626_); trivial. % 29.94/30.13 apply (zenon_L516_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 29.94/30.13 apply (zenon_L490_); trivial. % 29.94/30.13 apply (zenon_L668_); trivial. % 29.94/30.13 apply (zenon_L609_); trivial. % 29.94/30.13 (* end of lemma zenon_L669_ *) % 29.94/30.13 assert (zenon_L670_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.94/30.13 do 0 intro. intros zenon_H14b zenon_Hde zenon_Hda zenon_Hd0 zenon_H37 zenon_H1d2 zenon_Hb6 zenon_H1dc zenon_H1bd zenon_H1af zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H1e1 zenon_H108 zenon_Hb5 zenon_H8b. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 29.94/30.13 apply (zenon_L192_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 29.94/30.13 apply (zenon_L653_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 29.94/30.13 apply (zenon_L296_); trivial. % 29.94/30.13 apply (zenon_L297_); trivial. % 29.94/30.13 (* end of lemma zenon_L670_ *) % 29.94/30.13 assert (zenon_L671_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 29.94/30.13 do 0 intro. intros zenon_H200 zenon_H19e zenon_H222 zenon_H60 zenon_H9d zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_H26 zenon_H89 zenon_H14b zenon_Hde zenon_Hda zenon_Hd0 zenon_H37 zenon_H1d2 zenon_Hb6 zenon_H1dc zenon_H1bd zenon_H1af zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H108 zenon_Hb5 zenon_H8b. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 29.94/30.13 apply (zenon_L49_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 29.94/30.13 apply (zenon_L618_); trivial. % 29.94/30.13 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 29.94/30.13 apply (zenon_L626_); trivial. % 29.94/30.13 apply (zenon_L670_); trivial. % 29.94/30.13 (* end of lemma zenon_L671_ *) % 29.94/30.13 assert (zenon_L672_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 29.94/30.14 do 0 intro. intros zenon_H42 zenon_H2d zenon_H8b zenon_Hb5 zenon_H1d5 zenon_He1 zenon_H1dc zenon_Hb6 zenon_H1d2 zenon_Hd0 zenon_Hda zenon_H14b zenon_H89 zenon_H26 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H9d zenon_H60 zenon_H222 zenon_H19e zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 29.94/30.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 29.94/30.14 apply (zenon_L4_); trivial. % 29.94/30.14 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 29.94/30.14 apply (zenon_L671_); trivial. % 29.94/30.14 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 29.94/30.14 apply (zenon_L456_); trivial. % 29.94/30.14 exact (zenon_H18e zenon_H40). % 29.94/30.14 (* end of lemma zenon_L672_ *) % 29.94/30.14 assert (zenon_L673_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H101 zenon_H6f zenon_H3f zenon_H1f zenon_Had zenon_H23b zenon_H13b zenon_H42 zenon_H2d zenon_H8b zenon_Hb5 zenon_H1d5 zenon_He1 zenon_H1dc zenon_Hb6 zenon_H1d2 zenon_Hd0 zenon_Hda zenon_H14b zenon_H89 zenon_H26 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H60 zenon_H222 zenon_H19e zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H18e. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.00/30.14 apply (zenon_L641_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.00/30.14 exact (zenon_H13b zenon_Hfd). % 30.00/30.14 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.00/30.14 apply (zenon_L282_); trivial. % 30.00/30.14 apply (zenon_L672_); trivial. % 30.00/30.14 (* end of lemma zenon_L673_ *) % 30.00/30.14 assert (zenon_L674_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.00/30.14 do 0 intro. intros zenon_H200 zenon_Hd6 zenon_H6b zenon_Hcd zenon_H135 zenon_Hd5 zenon_H5e zenon_H26 zenon_H89 zenon_H14b zenon_Hde zenon_Hda zenon_Hd0 zenon_H37 zenon_H1d2 zenon_Hb6 zenon_H1dc zenon_H1bd zenon_H1af zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H108 zenon_Hb5 zenon_H8b. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.00/30.14 apply (zenon_L652_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.00/30.14 apply (zenon_L608_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.00/30.14 apply (zenon_L626_); trivial. % 30.00/30.14 apply (zenon_L670_); trivial. % 30.00/30.14 (* end of lemma zenon_L674_ *) % 30.00/30.14 assert (zenon_L675_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.00/30.14 do 0 intro. intros zenon_H14b zenon_H89 zenon_Hc8 zenon_H27 zenon_H26 zenon_H5c zenon_H135 zenon_Hd0 zenon_H37 zenon_H1d2 zenon_H60 zenon_H17b zenon_H218 zenon_H1bd zenon_H1af zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H1e1 zenon_H108 zenon_H2d zenon_Hb6. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.00/30.14 apply (zenon_L636_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.00/30.14 apply (zenon_L637_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.00/30.14 apply (zenon_L296_); trivial. % 30.00/30.14 apply (zenon_L304_); trivial. % 30.00/30.14 (* end of lemma zenon_L675_ *) % 30.00/30.14 assert (zenon_L676_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 30.00/30.14 do 0 intro. intros zenon_H200 zenon_H218 zenon_H17b zenon_Hd0 zenon_H222 zenon_H9d zenon_Hde zenon_H135 zenon_H1e zenon_H3c zenon_H1c7 zenon_Hd6 zenon_Hf6 zenon_H112 zenon_H108 zenon_H1e6 zenon_H1bd zenon_H1af zenon_H3d. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.00/30.14 apply (zenon_L406_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.00/30.14 apply (zenon_L207_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.00/30.14 apply (zenon_L455_); trivial. % 30.00/30.14 apply (zenon_L209_); trivial. % 30.00/30.14 (* end of lemma zenon_L676_ *) % 30.00/30.14 assert (zenon_L677_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_H135 zenon_Hde zenon_H9d zenon_H222 zenon_Hd0 zenon_H200 zenon_H218 zenon_H17b zenon_H60 zenon_H1af zenon_H16c zenon_H156. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.00/30.14 apply (zenon_L273_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.00/30.14 apply (zenon_L676_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.00/30.14 apply (zenon_L259_); trivial. % 30.00/30.14 apply (zenon_L290_); trivial. % 30.00/30.14 (* end of lemma zenon_L677_ *) % 30.00/30.14 assert (zenon_L678_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H16f zenon_H15a zenon_H2d zenon_H1d2 zenon_H5c zenon_H26 zenon_H27 zenon_Hc8 zenon_H89 zenon_H14b zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H19e zenon_Hee zenon_Hb6 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_H135 zenon_Hde zenon_H9d zenon_H222 zenon_Hd0 zenon_H200 zenon_H218 zenon_H17b zenon_H60 zenon_H1af zenon_H156. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.00/30.14 apply (zenon_L241_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.00/30.14 apply (zenon_L406_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.00/30.14 apply (zenon_L618_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.00/30.14 apply (zenon_L626_); trivial. % 30.00/30.14 apply (zenon_L675_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.00/30.14 apply (zenon_L490_); trivial. % 30.00/30.14 apply (zenon_L677_); trivial. % 30.00/30.14 (* end of lemma zenon_L678_ *) % 30.00/30.14 assert (zenon_L679_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H101 zenon_H6f zenon_H3f zenon_H1f zenon_Had zenon_H23b zenon_H13b zenon_H16f zenon_H15a zenon_H2d zenon_H1d2 zenon_H5c zenon_H26 zenon_H27 zenon_Hc8 zenon_H89 zenon_H14b zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H19e zenon_Hee zenon_Hb6 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H1bd zenon_H1e6 zenon_H108 zenon_H112 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_H1e zenon_H135 zenon_Hde zenon_H222 zenon_Hd0 zenon_H200 zenon_H218 zenon_H17b zenon_H60 zenon_H1af zenon_H156. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.00/30.14 apply (zenon_L641_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.00/30.14 exact (zenon_H13b zenon_Hfd). % 30.00/30.14 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.00/30.14 apply (zenon_L282_); trivial. % 30.00/30.14 apply (zenon_L678_); trivial. % 30.00/30.14 (* end of lemma zenon_L679_ *) % 30.00/30.14 assert (zenon_L680_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.00/30.14 do 0 intro. intros zenon_H200 zenon_H1dc zenon_Hd6 zenon_H6b zenon_Hcd zenon_Hde zenon_Hd5 zenon_H5e zenon_H14b zenon_H89 zenon_Hc8 zenon_H27 zenon_H26 zenon_H5c zenon_H135 zenon_Hd0 zenon_H37 zenon_H1d2 zenon_H60 zenon_H17b zenon_H218 zenon_H1bd zenon_H1af zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H108 zenon_H2d zenon_Hb6. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.00/30.14 apply (zenon_L652_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.00/30.14 apply (zenon_L608_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.00/30.14 apply (zenon_L626_); trivial. % 30.00/30.14 apply (zenon_L675_); trivial. % 30.00/30.14 (* end of lemma zenon_L680_ *) % 30.00/30.14 assert (zenon_L681_ : ((op (e0) (e2)) = (e1)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H26 zenon_H124 zenon_H13b zenon_Hd0 zenon_Hb6 zenon_H19e zenon_H27 zenon_H222 zenon_H5e zenon_H1a8 zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_H1fd zenon_H3f zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H172 zenon_H92 zenon_H17d zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H225 zenon_H20 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_Hd9 zenon_H42 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H102 zenon_Had zenon_H100 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H60 zenon_H1d2 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_H18c zenon_H135 zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H14e zenon_H1af zenon_H1bd zenon_H1e6 zenon_H108 zenon_Hf6 zenon_Hd6 zenon_H1c7 zenon_H3c zenon_Hde zenon_H200 zenon_H174 zenon_H2d zenon_H1e zenon_Hb8 zenon_H1d8 zenon_H18e zenon_H10d zenon_H112 zenon_H6f zenon_H68 zenon_H8d zenon_H17b zenon_He1. % 30.00/30.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.00/30.14 exact (zenon_H74 zenon_H73). % 30.00/30.14 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.00/30.14 apply (zenon_L48_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.00/30.14 apply (zenon_L679_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.00/30.14 apply (zenon_L45_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.00/30.14 apply (zenon_L4_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.00/30.14 apply (zenon_L680_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.00/30.14 apply (zenon_L456_); trivial. % 30.00/30.14 exact (zenon_H18e zenon_H40). % 30.00/30.14 apply (zenon_L609_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.00/30.14 apply (zenon_L4_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.00/30.14 apply (zenon_L598_); trivial. % 30.00/30.14 apply (zenon_L267_); trivial. % 30.00/30.14 apply (zenon_L621_); trivial. % 30.00/30.14 (* end of lemma zenon_L681_ *) % 30.00/30.14 assert (zenon_L682_ : ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H26 zenon_Hd0 zenon_H14e zenon_H112 zenon_H25c zenon_H256 zenon_H84 zenon_H74 zenon_H2d zenon_H1e zenon_H8d zenon_H135 zenon_H3c zenon_H18c zenon_He1 zenon_Hcd zenon_H14b zenon_H1dc zenon_H6b zenon_H156 zenon_H1d8 zenon_H27 zenon_H1d2 zenon_H108 zenon_Hd6 zenon_H1bd zenon_H5e zenon_H60 zenon_H1c7 zenon_H1af zenon_H1ca zenon_H1d5 zenon_H173 zenon_H1e6 zenon_Hf6 zenon_Hb8 zenon_H6f zenon_H10d zenon_H100 zenon_Had zenon_H102 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H18e zenon_H42 zenon_Hd9 zenon_H11e zenon_H1a5 zenon_Hc8 zenon_H23b zenon_Hee zenon_Hb5 zenon_Hf9 zenon_H20 zenon_H225 zenon_H222 zenon_H101 zenon_H159 zenon_H83 zenon_H218 zenon_He4 zenon_H15a zenon_H16f zenon_H16a zenon_H174 zenon_H17d zenon_H92 zenon_H172 zenon_H200 zenon_H5c zenon_H125 zenon_Hbd zenon_He7 zenon_H3f zenon_H1fd zenon_H208 zenon_H20d zenon_H20e zenon_H246 zenon_Hc0 zenon_H1b1 zenon_Ha4 zenon_Haa zenon_H25b zenon_H6c zenon_H1a8 zenon_H8b zenon_Hde. % 30.00/30.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.00/30.14 exact (zenon_H74 zenon_H73). % 30.00/30.14 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.00/30.14 apply (zenon_L599_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.00/30.14 apply (zenon_L580_); trivial. % 30.00/30.14 apply (zenon_L288_); trivial. % 30.00/30.14 (* end of lemma zenon_L682_ *) % 30.00/30.14 assert (zenon_L683_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H42 zenon_H2d zenon_Hd2 zenon_H6f zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e zenon_H1e6 zenon_H20d zenon_H112 zenon_Hf6 zenon_H60 zenon_H108 zenon_H16b zenon_H218 zenon_H200 zenon_H18e. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.00/30.14 apply (zenon_L4_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.00/30.14 apply (zenon_L125_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.00/30.14 apply (zenon_L561_); trivial. % 30.00/30.14 exact (zenon_H18e zenon_H40). % 30.00/30.14 (* end of lemma zenon_L683_ *) % 30.00/30.14 assert (zenon_L684_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H1a8 zenon_H6e zenon_H16b zenon_Ha4 zenon_H1a5 zenon_He1 zenon_H8d zenon_Hd9 zenon_Had zenon_H1e zenon_H174 zenon_H6b zenon_Hcc zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H1d5 zenon_H208 zenon_Hcd zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H60 zenon_H1ca zenon_H3c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H42 zenon_Hd6 zenon_H16f zenon_H15a zenon_H23b zenon_Hf9 zenon_H3f zenon_H256 zenon_H200 zenon_H5c zenon_Hde zenon_H1bd zenon_Hbd zenon_Hee zenon_H156 zenon_H74 zenon_He4 zenon_H27 zenon_H92 zenon_H84 zenon_H1b1 zenon_He7 zenon_H1dc zenon_H225 zenon_Hc0 zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H108 zenon_H2d zenon_H100 zenon_H6f zenon_H10d zenon_H18e zenon_H1d8 zenon_Hb8 zenon_H1fd zenon_H231 zenon_H17d zenon_H112 zenon_H14e. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.00/30.14 apply (zenon_L18_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.00/30.14 apply (zenon_L683_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.00/30.14 apply (zenon_L577_); trivial. % 30.00/30.14 apply (zenon_L137_); trivial. % 30.00/30.14 (* end of lemma zenon_L684_ *) % 30.00/30.14 assert (zenon_L685_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H42 zenon_H2d zenon_H15e zenon_Hfc zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e zenon_H1e6 zenon_H20d zenon_H112 zenon_Hf6 zenon_H60 zenon_H108 zenon_H16b zenon_H218 zenon_H200 zenon_H18e. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.00/30.14 apply (zenon_L4_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.00/30.14 apply (zenon_L203_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.00/30.14 apply (zenon_L561_); trivial. % 30.00/30.14 exact (zenon_H18e zenon_H40). % 30.00/30.14 (* end of lemma zenon_L685_ *) % 30.00/30.14 assert (zenon_L686_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 30.00/30.14 do 0 intro. intros zenon_H16f zenon_H68 zenon_H19e zenon_He9 zenon_H5e zenon_H1f zenon_H76 zenon_H6f zenon_H208 zenon_H18e zenon_H200 zenon_H218 zenon_H108 zenon_H60 zenon_Hf6 zenon_H112 zenon_H20d zenon_H1e6 zenon_H1e zenon_H3c zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_Hfc zenon_H2d zenon_H42 zenon_H16a zenon_H16b. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.00/30.14 apply (zenon_L18_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.00/30.14 apply (zenon_L220_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.00/30.14 apply (zenon_L685_); trivial. % 30.00/30.14 apply (zenon_L101_); trivial. % 30.00/30.14 (* end of lemma zenon_L686_ *) % 30.00/30.14 assert (zenon_L687_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.00/30.14 do 0 intro. intros zenon_He4 zenon_H74 zenon_Hcd zenon_Hcc zenon_H6b zenon_H174 zenon_H2d zenon_H1e zenon_Hb8 zenon_H1d8 zenon_H18e zenon_H10d zenon_H112 zenon_H6f zenon_H68 zenon_H8d zenon_H17b zenon_He1. % 30.00/30.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.00/30.14 exact (zenon_H74 zenon_H73). % 30.00/30.14 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.00/30.14 apply (zenon_L48_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.00/30.14 apply (zenon_L552_); trivial. % 30.00/30.14 apply (zenon_L621_); trivial. % 30.00/30.14 (* end of lemma zenon_L687_ *) % 30.00/30.14 assert (zenon_L688_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.00/30.14 do 0 intro. intros zenon_He4 zenon_H74 zenon_Hcd zenon_H68 zenon_Hcc zenon_H6b zenon_H174 zenon_H112 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_H17b zenon_He1. % 30.00/30.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.00/30.14 exact (zenon_H74 zenon_H73). % 30.00/30.14 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.00/30.14 apply (zenon_L48_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.00/30.14 apply (zenon_L552_); trivial. % 30.00/30.14 apply (zenon_L472_); trivial. % 30.00/30.14 (* end of lemma zenon_L688_ *) % 30.00/30.14 assert (zenon_L689_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H225 zenon_Hf6 zenon_H6f zenon_H3f zenon_H1f zenon_Had zenon_H23b zenon_H3c zenon_H5e zenon_H18c zenon_H208 zenon_H27 zenon_H60 zenon_He4 zenon_H74 zenon_Hcd zenon_H68 zenon_Hcc zenon_H6b zenon_H174 zenon_H112 zenon_H2d zenon_H1e zenon_H10d zenon_Hb6 zenon_He1. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.00/30.14 exact (zenon_H74 zenon_H73). % 30.00/30.14 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.00/30.14 apply (zenon_L641_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.00/30.14 apply (zenon_L554_); trivial. % 30.00/30.14 apply (zenon_L688_); trivial. % 30.00/30.14 (* end of lemma zenon_L689_ *) % 30.00/30.14 assert (zenon_L690_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 30.00/30.14 do 0 intro. intros zenon_Hf6 zenon_H1e1 zenon_Hb1. % 30.00/30.14 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 30.00/30.14 intro zenon_D_pnotp. % 30.00/30.14 apply zenon_Hf6. % 30.00/30.14 rewrite <- zenon_D_pnotp. % 30.00/30.14 exact zenon_H1e1. % 30.00/30.14 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 30.00/30.14 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 30.00/30.14 congruence. % 30.00/30.14 apply zenon_H10a. apply refl_equal. % 30.00/30.14 apply zenon_Hb2. apply sym_equal. exact zenon_Hb1. % 30.00/30.14 (* end of lemma zenon_L690_ *) % 30.00/30.14 assert (zenon_L691_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H16f zenon_H89 zenon_H15a zenon_Hee zenon_H42 zenon_Hd2 zenon_H6f zenon_H156 zenon_H1af zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1dc zenon_Hb6 zenon_He1 zenon_Hf6 zenon_H112 zenon_H1e6 zenon_H2d zenon_H3f zenon_H1e zenon_H200 zenon_H5c zenon_H1d8 zenon_H3c zenon_Hde zenon_Hcc zenon_H1bd zenon_Hbd zenon_H18e. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.00/30.14 apply (zenon_L241_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.00/30.14 apply (zenon_L125_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.00/30.14 apply (zenon_L490_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.00/30.14 apply (zenon_L4_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.00/30.14 apply (zenon_L125_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.00/30.14 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.00/30.14 apply (zenon_L546_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.00/30.14 apply (zenon_L29_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.00/30.14 apply (zenon_L304_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.00/30.14 apply (zenon_L690_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.00/30.14 apply (zenon_L187_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.00/30.14 apply (zenon_L301_); trivial. % 30.00/30.14 apply (zenon_L290_); trivial. % 30.00/30.14 exact (zenon_H18e zenon_H40). % 30.00/30.14 (* end of lemma zenon_L691_ *) % 30.00/30.14 assert (zenon_L692_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H1a8 zenon_H6c zenon_H18c zenon_Hb6 zenon_H89 zenon_H1b1 zenon_H16f zenon_H35 zenon_Hfc zenon_H102 zenon_H42 zenon_H173 zenon_H159 zenon_He1 zenon_H208 zenon_H1af zenon_H19e zenon_H60 zenon_H5e zenon_H3c zenon_H6f zenon_Hd1 zenon_H20e zenon_Hcd zenon_H222 zenon_H101 zenon_Hbd zenon_He7 zenon_H18e zenon_H1dc zenon_H2d zenon_Hb8 zenon_H1e zenon_H3f zenon_H5c zenon_H1d8 zenon_H1fd zenon_H200 zenon_H1bd zenon_H1ca zenon_Hcc zenon_Hde zenon_Hf9 zenon_H156 zenon_H256 zenon_H1c7 zenon_Hee zenon_H23b zenon_H108 zenon_Hd9 zenon_H1d5 zenon_H15a zenon_H8d zenon_H10d zenon_H100 zenon_Had zenon_H92 zenon_H17d zenon_He4 zenon_H6b zenon_H218 zenon_H20d zenon_H174 zenon_Hd6 zenon_H225 zenon_H1a5 zenon_Ha4 zenon_Hc0 zenon_H1e6 zenon_H27 zenon_Hf6 zenon_H74 zenon_H84 zenon_H25b zenon_H112 zenon_H14e. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.00/30.14 apply (zenon_L120_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.00/30.14 apply (zenon_L691_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.00/30.14 apply (zenon_L578_); trivial. % 30.00/30.14 apply (zenon_L137_); trivial. % 30.00/30.14 (* end of lemma zenon_L692_ *) % 30.00/30.14 assert (zenon_L693_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.00/30.14 do 0 intro. intros zenon_H1a8 zenon_H6c zenon_H18c zenon_H18e zenon_H200 zenon_H218 zenon_H16b zenon_H108 zenon_H60 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_H1e zenon_H3c zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H1d5 zenon_H19e zenon_H222 zenon_H5e zenon_H1f zenon_H6f zenon_H208 zenon_Hcd zenon_H20e zenon_H159 zenon_H101 zenon_H156 zenon_H2d zenon_H42 zenon_He1 zenon_Hc0 zenon_H17d zenon_H225 zenon_H6b zenon_H1dc zenon_He7 zenon_Hb8 zenon_H27 zenon_He4 zenon_H74 zenon_Hee zenon_Hbd zenon_H1d8 zenon_H5c zenon_H256 zenon_H3f zenon_Hf9 zenon_H23b zenon_H15a zenon_H16f zenon_Hd6 zenon_H1c7 zenon_H1ca zenon_H173 zenon_H174 zenon_H10d zenon_Hb6 zenon_H1b1 zenon_H84 zenon_H92 zenon_H1a5 zenon_Ha4 zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H112 zenon_H14e. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.00/30.14 apply (zenon_L120_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.00/30.14 apply (zenon_L683_); trivial. % 30.00/30.14 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.00/30.14 apply (zenon_L563_); trivial. % 30.00/30.14 apply (zenon_L137_); trivial. % 30.00/30.15 (* end of lemma zenon_L693_ *) % 30.00/30.15 assert (zenon_L694_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 30.00/30.15 do 0 intro. intros zenon_H14e zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_Ha4 zenon_H1a5 zenon_H92 zenon_H84 zenon_H1b1 zenon_Hb6 zenon_H10d zenon_H174 zenon_H173 zenon_H1ca zenon_H1c7 zenon_Hd6 zenon_H16f zenon_H15a zenon_H23b zenon_Hf9 zenon_H3f zenon_H256 zenon_H5c zenon_H1d8 zenon_Hbd zenon_Hee zenon_H74 zenon_He4 zenon_H27 zenon_Hb8 zenon_He7 zenon_H1dc zenon_H6b zenon_H225 zenon_Hc0 zenon_He1 zenon_H42 zenon_H2d zenon_H156 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1f zenon_H5e zenon_H222 zenon_H19e zenon_H1d5 zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H60 zenon_H108 zenon_H218 zenon_H200 zenon_H18e zenon_H18c zenon_H1a8 zenon_H1fd zenon_Hd9 zenon_H8d zenon_H100 zenon_Had zenon_H25b zenon_H17d zenon_H112. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.00/30.15 exact (zenon_H84 zenon_H88). % 30.00/30.15 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.00/30.15 apply (zenon_L689_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.00/30.15 apply (zenon_L692_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.00/30.15 apply (zenon_L4_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.00/30.15 apply (zenon_L151_); trivial. % 30.00/30.15 apply (zenon_L693_); trivial. % 30.00/30.15 apply (zenon_L139_); trivial. % 30.00/30.15 (* end of lemma zenon_L694_ *) % 30.00/30.15 assert (zenon_L695_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.00/30.15 do 0 intro. intros zenon_H1a8 zenon_Hcd zenon_Hdc zenon_H18e zenon_Hbd zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1d8 zenon_H5c zenon_H200 zenon_H1e zenon_H3f zenon_H2d zenon_H1e6 zenon_Hf6 zenon_He1 zenon_Hb6 zenon_H1dc zenon_Hd6 zenon_H6b zenon_H1d5 zenon_H1af zenon_H156 zenon_H6f zenon_H42 zenon_Hee zenon_H15a zenon_H89 zenon_H16f zenon_H1a5 zenon_H26 zenon_H112 zenon_H14e. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.00/30.15 apply (zenon_L48_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.00/30.15 apply (zenon_L691_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.00/30.15 apply (zenon_L136_); trivial. % 30.00/30.15 apply (zenon_L137_); trivial. % 30.00/30.15 (* end of lemma zenon_L695_ *) % 30.00/30.15 assert (zenon_L696_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.00/30.15 do 0 intro. intros zenon_H1a8 zenon_H6e zenon_H18e zenon_H200 zenon_H218 zenon_H16b zenon_H108 zenon_H60 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_H1e zenon_H3c zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H6f zenon_H2d zenon_H42 zenon_H1a5 zenon_H26 zenon_H112 zenon_H14e. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.00/30.15 apply (zenon_L18_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.00/30.15 apply (zenon_L683_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.00/30.15 apply (zenon_L136_); trivial. % 30.00/30.15 apply (zenon_L137_); trivial. % 30.00/30.15 (* end of lemma zenon_L696_ *) % 30.00/30.15 assert (zenon_L697_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> False). % 30.00/30.15 do 0 intro. intros zenon_Hb5 zenon_H25b zenon_H84 zenon_H74 zenon_H27 zenon_Hc0 zenon_Ha4 zenon_H225 zenon_Hd6 zenon_H174 zenon_H6b zenon_He4 zenon_H17d zenon_H92 zenon_Had zenon_H100 zenon_H10d zenon_H8d zenon_H15a zenon_H1d5 zenon_Hd9 zenon_H23b zenon_Hee zenon_H1c7 zenon_H256 zenon_H156 zenon_Hf9 zenon_H1ca zenon_H1fd zenon_H1d8 zenon_H5c zenon_H3f zenon_Hb8 zenon_H1dc zenon_He7 zenon_Hbd zenon_H101 zenon_H222 zenon_Hcd zenon_H20e zenon_Hd1 zenon_H5e zenon_H19e zenon_H208 zenon_H159 zenon_H173 zenon_H102 zenon_Hfc zenon_H35 zenon_H16f zenon_H1b1 zenon_Hb6 zenon_H18c zenon_H14e zenon_H112 zenon_H26 zenon_H1a5 zenon_H42 zenon_H2d zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H60 zenon_H108 zenon_H218 zenon_H200 zenon_H18e zenon_H1a8 zenon_H6f zenon_H6c zenon_He1. % 30.00/30.15 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.00/30.15 exact (zenon_H74 zenon_H73). % 30.00/30.15 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.00/30.15 apply (zenon_L695_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.00/30.15 apply (zenon_L4_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.00/30.15 apply (zenon_L151_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.00/30.15 apply (zenon_L695_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.00/30.15 apply (zenon_L696_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.00/30.15 apply (zenon_L157_); trivial. % 30.00/30.15 apply (zenon_L461_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.00/30.15 apply (zenon_L552_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.00/30.15 apply (zenon_L692_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.00/30.15 apply (zenon_L4_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.00/30.15 apply (zenon_L598_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.00/30.15 apply (zenon_L692_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.00/30.15 apply (zenon_L696_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.00/30.15 apply (zenon_L157_); trivial. % 30.00/30.15 apply (zenon_L50_); trivial. % 30.00/30.15 (* end of lemma zenon_L697_ *) % 30.00/30.15 assert (zenon_L698_ : ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 30.00/30.15 do 0 intro. intros zenon_H69 zenon_H20 zenon_He1 zenon_H6f zenon_H1a8 zenon_H18e zenon_H200 zenon_H218 zenon_H108 zenon_H60 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_H1e zenon_H3c zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H2d zenon_H42 zenon_H1a5 zenon_H26 zenon_H14e zenon_H18c zenon_Hb6 zenon_H1b1 zenon_H16f zenon_H35 zenon_Hfc zenon_H102 zenon_H173 zenon_H159 zenon_H208 zenon_H19e zenon_H5e zenon_Hd1 zenon_H20e zenon_Hcd zenon_H222 zenon_H101 zenon_Hbd zenon_He7 zenon_H1dc zenon_Hb8 zenon_H3f zenon_H5c zenon_H1d8 zenon_H1fd zenon_H1ca zenon_Hf9 zenon_H156 zenon_H256 zenon_H1c7 zenon_Hee zenon_H23b zenon_Hd9 zenon_H1d5 zenon_H15a zenon_H8d zenon_H10d zenon_H100 zenon_Had zenon_H92 zenon_He4 zenon_H6b zenon_H174 zenon_Hd6 zenon_H225 zenon_Ha4 zenon_Hc0 zenon_H27 zenon_H74 zenon_H84 zenon_H25b zenon_Hb5 zenon_H17d zenon_H112. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.00/30.15 exact (zenon_H84 zenon_H88). % 30.00/30.15 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.00/30.15 apply (zenon_L16_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.00/30.15 apply (zenon_L697_); trivial. % 30.00/30.15 apply (zenon_L139_); trivial. % 30.00/30.15 (* end of lemma zenon_L698_ *) % 30.00/30.15 assert (zenon_L699_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 30.00/30.15 do 0 intro. intros zenon_H10d zenon_H26 zenon_H1a0. % 30.00/30.15 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 30.00/30.15 intro zenon_D_pnotp. % 30.00/30.15 apply zenon_H10d. % 30.00/30.15 rewrite <- zenon_D_pnotp. % 30.00/30.15 exact zenon_H26. % 30.00/30.15 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 30.00/30.15 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.00/30.15 congruence. % 30.00/30.15 apply zenon_H10f. apply refl_equal. % 30.00/30.15 apply zenon_H1a1. apply sym_equal. exact zenon_H1a0. % 30.00/30.15 (* end of lemma zenon_L699_ *) % 30.00/30.15 assert (zenon_L700_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.00/30.15 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_Hd5 zenon_H5e zenon_H222 zenon_H26 zenon_H10d zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.00/30.15 apply (zenon_L386_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.00/30.15 apply (zenon_L514_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.00/30.15 apply (zenon_L699_); trivial. % 30.00/30.15 apply (zenon_L551_); trivial. % 30.00/30.15 (* end of lemma zenon_L700_ *) % 30.00/30.15 assert (zenon_L701_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.00/30.15 do 0 intro. intros zenon_He4 zenon_H74 zenon_Hcd zenon_H68 zenon_Hcc zenon_H6b zenon_H8b zenon_Hde. % 30.00/30.15 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.00/30.15 exact (zenon_H74 zenon_H73). % 30.00/30.15 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.00/30.15 apply (zenon_L48_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.00/30.15 apply (zenon_L552_); trivial. % 30.00/30.15 apply (zenon_L288_); trivial. % 30.00/30.15 (* end of lemma zenon_L701_ *) % 30.00/30.15 assert (zenon_L702_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.00/30.15 do 0 intro. intros zenon_He4 zenon_He1 zenon_H17b zenon_H26 zenon_H6f zenon_H1e zenon_H2d zenon_H174 zenon_Hcd zenon_H68 zenon_Hcc zenon_H6b zenon_H8b zenon_Hde. % 30.00/30.15 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.00/30.15 apply (zenon_L232_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.00/30.15 apply (zenon_L4_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.00/30.15 apply (zenon_L598_); trivial. % 30.00/30.15 apply (zenon_L267_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.00/30.15 apply (zenon_L48_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.00/30.15 apply (zenon_L552_); trivial. % 30.00/30.15 apply (zenon_L288_); trivial. % 30.00/30.15 (* end of lemma zenon_L702_ *) % 30.00/30.15 assert (zenon_L703_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.00/30.15 do 0 intro. intros zenon_H42 zenon_H2d zenon_Hd2 zenon_H6f zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H18e. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.00/30.15 apply (zenon_L4_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.00/30.15 apply (zenon_L125_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.00/30.15 apply (zenon_L546_); trivial. % 30.00/30.15 exact (zenon_H18e zenon_H40). % 30.00/30.15 (* end of lemma zenon_L703_ *) % 30.00/30.15 assert (zenon_L704_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.00/30.15 do 0 intro. intros zenon_H14e zenon_H112 zenon_H25c zenon_H256 zenon_H84 zenon_H74 zenon_H2d zenon_H1e zenon_H8d zenon_H135 zenon_H3c zenon_H18c zenon_He1 zenon_Hcd zenon_H14b zenon_H1dc zenon_H6b zenon_H156 zenon_H1d8 zenon_H27 zenon_H1d2 zenon_H108 zenon_Hd6 zenon_H1bd zenon_H5e zenon_H60 zenon_H1c7 zenon_H1af zenon_H1ca zenon_H1d5 zenon_H173 zenon_H1e6 zenon_Hf6 zenon_Hb8 zenon_H6f zenon_H10d zenon_H100 zenon_Had zenon_H102 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H18e zenon_H42 zenon_Hd9 zenon_H11e zenon_H1a5 zenon_Hc8 zenon_H23b zenon_Hee zenon_Hb5 zenon_Hf9 zenon_H225 zenon_H222 zenon_H101 zenon_H159 zenon_H83 zenon_H218 zenon_He4 zenon_H15a zenon_H16f zenon_H16a zenon_H174 zenon_H17d zenon_H92 zenon_H172 zenon_H200 zenon_H5c zenon_H125 zenon_Hbd zenon_He7 zenon_H3f zenon_H1fd zenon_Hde zenon_H208 zenon_H20d zenon_H20e zenon_H246 zenon_Hc0 zenon_H1b1 zenon_Ha4 zenon_Haa zenon_H25b zenon_Hcc zenon_H26 zenon_H1a8 zenon_H8b zenon_H20. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.00/30.15 exact (zenon_H84 zenon_H88). % 30.00/30.15 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.00/30.15 apply (zenon_L701_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.00/30.15 exact (zenon_H74 zenon_H73). % 30.00/30.15 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.00/30.15 apply (zenon_L536_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.00/30.15 apply (zenon_L554_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.00/30.15 apply (zenon_L702_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.00/30.15 apply (zenon_L703_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.00/30.15 apply (zenon_L579_); trivial. % 30.00/30.15 apply (zenon_L137_); trivial. % 30.00/30.15 apply (zenon_L27_); trivial. % 30.00/30.15 (* end of lemma zenon_L704_ *) % 30.00/30.15 assert (zenon_L705_ : ((op (e0) (e3)) = (e3)) -> ((op (e2) (e1)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.00/30.15 do 0 intro. intros zenon_H16b zenon_Hd5 zenon_Hfe zenon_H20 zenon_H1a8 zenon_H26 zenon_Hcc zenon_H25b zenon_Haa zenon_Ha4 zenon_H1b1 zenon_Hc0 zenon_H246 zenon_H20e zenon_H20d zenon_H208 zenon_Hde zenon_H1fd zenon_He7 zenon_Hbd zenon_H125 zenon_H5c zenon_H200 zenon_H172 zenon_H92 zenon_H17d zenon_H174 zenon_H16a zenon_H16f zenon_H15a zenon_He4 zenon_H218 zenon_H83 zenon_H159 zenon_H101 zenon_H222 zenon_H225 zenon_Hf9 zenon_Hb5 zenon_Hee zenon_H23b zenon_Hc8 zenon_H1a5 zenon_H11e zenon_Hd9 zenon_H42 zenon_H18e zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H102 zenon_Had zenon_H10d zenon_H1e6 zenon_H173 zenon_H1d5 zenon_H1ca zenon_H1af zenon_H1c7 zenon_H60 zenon_H5e zenon_H1bd zenon_Hd6 zenon_H108 zenon_H1d2 zenon_H27 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_H18c zenon_H3c zenon_H135 zenon_H8d zenon_H74 zenon_H84 zenon_H256 zenon_H25c zenon_H14e zenon_H1e zenon_H3f zenon_H6f zenon_H112 zenon_H2d zenon_H37 zenon_H100 zenon_He1 zenon_He2 zenon_Hb8 zenon_Hf6. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.00/30.15 apply (zenon_L700_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.00/30.15 apply (zenon_L608_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.00/30.15 apply (zenon_L350_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.00/30.15 apply (zenon_L704_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.00/30.15 apply (zenon_L29_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.00/30.15 apply (zenon_L355_); trivial. % 30.00/30.15 apply (zenon_L690_); trivial. % 30.00/30.15 (* end of lemma zenon_L705_ *) % 30.00/30.15 assert (zenon_L706_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.00/30.15 do 0 intro. intros zenon_H17d zenon_Hb5 zenon_H25b zenon_H84 zenon_H74 zenon_H27 zenon_Hc0 zenon_H225 zenon_Hd6 zenon_H174 zenon_H6b zenon_He4 zenon_H92 zenon_Had zenon_H100 zenon_H10d zenon_H8d zenon_H15a zenon_H1d5 zenon_Hd9 zenon_H23b zenon_Hee zenon_H1c7 zenon_H256 zenon_H156 zenon_Hf9 zenon_H1ca zenon_H1fd zenon_H1d8 zenon_H5c zenon_H3f zenon_Hb8 zenon_H1dc zenon_He7 zenon_Hbd zenon_H101 zenon_H222 zenon_Hcd zenon_H20e zenon_Hd1 zenon_H5e zenon_H19e zenon_H208 zenon_H159 zenon_H173 zenon_H102 zenon_Hfc zenon_H35 zenon_H16f zenon_H1b1 zenon_Hb6 zenon_H18c zenon_H14e zenon_H1a5 zenon_H42 zenon_H2d zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H60 zenon_H108 zenon_H218 zenon_H200 zenon_H18e zenon_H1a8 zenon_H6f zenon_He1 zenon_H16a zenon_H124 zenon_H20 zenon_Haa zenon_H246 zenon_H125 zenon_H172 zenon_H83 zenon_Hc8 zenon_H11e zenon_H1d2 zenon_H14b zenon_H135 zenon_H25c zenon_H112 zenon_Ha4. % 30.00/30.15 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.00/30.15 exact (zenon_H84 zenon_H88). % 30.00/30.15 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.00/30.15 apply (zenon_L694_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.00/30.15 exact (zenon_H84 zenon_H88). % 30.00/30.15 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.00/30.15 exact (zenon_H74 zenon_H73). % 30.00/30.15 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.00/30.15 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.00/30.15 exact (zenon_H74 zenon_H73). % 30.00/30.15 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.00/30.15 apply (zenon_L48_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.00/30.15 apply (zenon_L552_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.00/30.15 apply (zenon_L252_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.00/30.15 apply (zenon_L4_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.00/30.15 apply (zenon_L584_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.00/30.15 apply (zenon_L698_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.00/30.15 apply (zenon_L42_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.00/30.15 apply (zenon_L641_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.00/30.15 apply (zenon_L683_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.00/30.15 apply (zenon_L696_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.00/30.15 apply (zenon_L705_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.00/30.15 apply (zenon_L490_); trivial. % 30.00/30.15 apply (zenon_L101_); trivial. % 30.00/30.15 apply (zenon_L654_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.00/30.15 apply (zenon_L696_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.00/30.15 apply (zenon_L392_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.00/30.15 apply (zenon_L490_); trivial. % 30.00/30.15 apply (zenon_L101_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.00/30.15 apply (zenon_L554_); trivial. % 30.00/30.15 apply (zenon_L688_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.00/30.15 apply (zenon_L697_); trivial. % 30.00/30.15 apply (zenon_L139_); trivial. % 30.00/30.15 apply (zenon_L140_); trivial. % 30.00/30.15 (* end of lemma zenon_L706_ *) % 30.00/30.15 assert (zenon_L707_ : ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.00/30.15 do 0 intro. intros zenon_H89 zenon_Ha4 zenon_H25c zenon_H135 zenon_H14b zenon_H1d2 zenon_H11e zenon_Hc8 zenon_H83 zenon_H172 zenon_H125 zenon_H246 zenon_Haa zenon_H20 zenon_H124 zenon_H16a zenon_He1 zenon_H1a8 zenon_H18e zenon_H200 zenon_H218 zenon_H108 zenon_H60 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_H1e zenon_H3c zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H2d zenon_H42 zenon_H1a5 zenon_H14e zenon_H18c zenon_H1b1 zenon_H16f zenon_H35 zenon_Hfc zenon_H102 zenon_H173 zenon_H159 zenon_H208 zenon_H19e zenon_H5e zenon_Hd1 zenon_H20e zenon_Hcd zenon_H222 zenon_H101 zenon_Hbd zenon_He7 zenon_H1dc zenon_Hb8 zenon_H3f zenon_H5c zenon_H1d8 zenon_H1fd zenon_H1ca zenon_Hf9 zenon_H156 zenon_H256 zenon_H1c7 zenon_Hee zenon_H23b zenon_Hd9 zenon_H1d5 zenon_H15a zenon_H8d zenon_H10d zenon_H100 zenon_Had zenon_H92 zenon_He4 zenon_H6b zenon_H174 zenon_Hd6 zenon_H225 zenon_Hc0 zenon_H27 zenon_H74 zenon_H84 zenon_H25b zenon_Hb5 zenon_H17d zenon_H112 zenon_H6f. % 30.00/30.15 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.00/30.15 apply (zenon_L199_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.00/30.15 exact (zenon_H18e zenon_H40). % 30.00/30.15 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.00/30.15 apply (zenon_L706_); trivial. % 30.00/30.15 apply (zenon_L152_); trivial. % 30.00/30.15 (* end of lemma zenon_L707_ *) % 30.00/30.15 assert (zenon_L708_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.00/30.15 do 0 intro. intros zenon_H100 zenon_H110 zenon_H112 zenon_Hcc zenon_Hcd zenon_H117 zenon_Had zenon_H6e zenon_Ha4 zenon_H1a5 zenon_He1 zenon_H10d zenon_H1e zenon_H174 zenon_H6b zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H1d5 zenon_H6f zenon_H208 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H60 zenon_H1ca zenon_H3c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H42 zenon_Hd6 zenon_H16f zenon_H15a zenon_H14e zenon_H23b zenon_Hf9 zenon_H3f zenon_H256 zenon_H200 zenon_H5c zenon_H1d8 zenon_Hde zenon_H1bd zenon_Hbd zenon_Hee zenon_H156 zenon_H74 zenon_He4 zenon_H27 zenon_H92 zenon_H84 zenon_H1b1 zenon_Hb8 zenon_He7 zenon_H1dc zenon_H225 zenon_Hc0 zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H108 zenon_H17d zenon_H2d zenon_H1a2 zenon_H18e. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.00/30.15 apply (zenon_L4_); trivial. % 30.00/30.15 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.02/30.16 apply (zenon_L153_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.02/30.16 apply (zenon_L598_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.02/30.16 apply (zenon_L565_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.02/30.16 apply (zenon_L44_); trivial. % 30.02/30.16 apply (zenon_L133_); trivial. % 30.02/30.16 exact (zenon_H18e zenon_H40). % 30.02/30.16 (* end of lemma zenon_L708_ *) % 30.02/30.16 assert (zenon_L709_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.02/30.16 do 0 intro. intros zenon_H8d zenon_Hd9 zenon_H1a2 zenon_H2d zenon_H17d zenon_H108 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_Hc0 zenon_H225 zenon_He7 zenon_H1b1 zenon_H84 zenon_H92 zenon_H27 zenon_He4 zenon_H74 zenon_H156 zenon_Hee zenon_Hbd zenon_H1bd zenon_Hde zenon_H5c zenon_H200 zenon_H256 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H42 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H3c zenon_H1ca zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_H208 zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H6b zenon_H174 zenon_H1e zenon_H1a5 zenon_Ha4 zenon_Had zenon_Hcd zenon_H110 zenon_H100 zenon_H6f zenon_H112 zenon_H117 zenon_H10d zenon_H18e zenon_H1d8 zenon_Hb8 zenon_Hf9 zenon_He1 zenon_He9 zenon_H3f zenon_Hcc zenon_H60 zenon_H1dc zenon_H231. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.16 apply (zenon_L149_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.16 apply (zenon_L708_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.16 apply (zenon_L339_); trivial. % 30.02/30.16 apply (zenon_L568_); trivial. % 30.02/30.16 (* end of lemma zenon_L709_ *) % 30.02/30.16 assert (zenon_L710_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.02/30.16 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_Hd2 zenon_H6f zenon_H1c7 zenon_H1af zenon_H117 zenon_H27 zenon_Hf6 zenon_H112 zenon_H1d8 zenon_H8a zenon_H1e6 zenon_H18e. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.02/30.16 apply (zenon_L4_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.02/30.16 apply (zenon_L125_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.02/30.16 apply (zenon_L188_); trivial. % 30.02/30.16 exact (zenon_H18e zenon_H40). % 30.02/30.16 (* end of lemma zenon_L710_ *) % 30.02/30.16 assert (zenon_L711_ : (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.02/30.16 do 0 intro. intros zenon_H231 zenon_H1dc zenon_H3f zenon_H8a zenon_Hf9 zenon_Hcc zenon_Hd6 zenon_H42 zenon_H2d zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_H1ca zenon_H60 zenon_H17b zenon_H218 zenon_H173 zenon_He1 zenon_H101 zenon_H159 zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hdc zenon_H19a zenon_Hfc zenon_H1e zenon_H35 zenon_H102 zenon_H18e. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.02/30.16 apply (zenon_L568_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.02/30.16 apply (zenon_L154_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.02/30.16 apply (zenon_L555_); trivial. % 30.02/30.16 apply (zenon_L266_); trivial. % 30.02/30.16 (* end of lemma zenon_L711_ *) % 30.02/30.16 assert (zenon_L712_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.02/30.16 do 0 intro. intros zenon_H8d zenon_Hd9 zenon_H18e zenon_H1a2 zenon_H2d zenon_H17d zenon_H108 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_Hc0 zenon_H225 zenon_H1dc zenon_He7 zenon_Hb8 zenon_H1b1 zenon_H84 zenon_H92 zenon_H27 zenon_He4 zenon_H74 zenon_H156 zenon_Hee zenon_Hbd zenon_H1bd zenon_Hde zenon_H1d8 zenon_H5c zenon_H200 zenon_H256 zenon_H3f zenon_Hf9 zenon_H23b zenon_H14e zenon_H15a zenon_H16f zenon_Hd6 zenon_H42 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H3c zenon_H1ca zenon_H60 zenon_H218 zenon_H173 zenon_H101 zenon_H159 zenon_H20e zenon_H208 zenon_H1d5 zenon_H19e zenon_Hd1 zenon_Hfc zenon_H35 zenon_H102 zenon_H6b zenon_H174 zenon_H1e zenon_H10d zenon_H1a5 zenon_Ha4 zenon_Had zenon_H117 zenon_Hcd zenon_Hcc zenon_H112 zenon_H110 zenon_H100 zenon_H6f zenon_H6c zenon_He1 zenon_He2. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.16 apply (zenon_L149_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.16 apply (zenon_L708_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.16 apply (zenon_L157_); trivial. % 30.02/30.16 apply (zenon_L50_); trivial. % 30.02/30.16 (* end of lemma zenon_L712_ *) % 30.02/30.16 assert (zenon_L713_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.02/30.16 do 0 intro. intros zenon_Hb5 zenon_H25b zenon_H1fd zenon_H18c zenon_H1a8 zenon_H16a zenon_H124 zenon_H20 zenon_Haa zenon_H246 zenon_H125 zenon_H172 zenon_H83 zenon_Hc8 zenon_H11e zenon_H1d2 zenon_H14b zenon_H135 zenon_H25c zenon_He2 zenon_H6c zenon_H6f zenon_H100 zenon_H110 zenon_H112 zenon_Hcc zenon_Hcd zenon_Had zenon_Ha4 zenon_H1a5 zenon_H10d zenon_H1e zenon_H174 zenon_H6b zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H1d5 zenon_H208 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H60 zenon_H1ca zenon_H3c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H42 zenon_Hd6 zenon_H16f zenon_H15a zenon_H14e zenon_H23b zenon_Hf9 zenon_H3f zenon_H256 zenon_H200 zenon_H5c zenon_H1d8 zenon_Hde zenon_H1bd zenon_Hbd zenon_Hee zenon_H156 zenon_H74 zenon_He4 zenon_H27 zenon_H92 zenon_H84 zenon_H1b1 zenon_Hb8 zenon_He7 zenon_H1dc zenon_H225 zenon_Hc0 zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H108 zenon_H17d zenon_H2d zenon_H1a2 zenon_H18e zenon_Hd9 zenon_H8d zenon_H17b zenon_He1. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.02/30.16 apply (zenon_L707_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.02/30.16 apply (zenon_L4_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.02/30.16 apply (zenon_L712_); trivial. % 30.02/30.16 apply (zenon_L267_); trivial. % 30.02/30.16 (* end of lemma zenon_L713_ *) % 30.02/30.16 assert (zenon_L714_ : ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.02/30.16 do 0 intro. intros zenon_H1f zenon_H231 zenon_Hb5 zenon_H25b zenon_H1fd zenon_H18c zenon_H1a8 zenon_H16a zenon_H124 zenon_H20 zenon_Haa zenon_H246 zenon_H125 zenon_H172 zenon_H83 zenon_Hc8 zenon_H11e zenon_H1d2 zenon_H14b zenon_H135 zenon_H25c zenon_H6c zenon_H6f zenon_H100 zenon_H110 zenon_H112 zenon_Hcc zenon_Hcd zenon_Had zenon_Ha4 zenon_H1a5 zenon_H10d zenon_H1e zenon_H174 zenon_H6b zenon_H102 zenon_H35 zenon_Hfc zenon_Hd1 zenon_H19e zenon_H1d5 zenon_H208 zenon_H20e zenon_H159 zenon_H101 zenon_H173 zenon_H218 zenon_H60 zenon_H1ca zenon_H3c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H42 zenon_Hd6 zenon_H16f zenon_H15a zenon_H14e zenon_H23b zenon_Hf9 zenon_H3f zenon_H256 zenon_H200 zenon_H5c zenon_H1d8 zenon_Hde zenon_H1bd zenon_Hbd zenon_Hee zenon_H156 zenon_H74 zenon_He4 zenon_H27 zenon_H92 zenon_H84 zenon_H1b1 zenon_Hb8 zenon_He7 zenon_H1dc zenon_H225 zenon_Hc0 zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H108 zenon_H17d zenon_H2d zenon_H1a2 zenon_H18e zenon_Hd9 zenon_H8d zenon_H17b zenon_He1. % 30.02/30.16 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.16 exact (zenon_H74 zenon_H73). % 30.02/30.16 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.02/30.16 apply (zenon_L707_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.02/30.16 apply (zenon_L4_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.16 apply (zenon_L149_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.16 apply (zenon_L708_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.16 apply (zenon_L157_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.16 apply (zenon_L48_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.16 apply (zenon_L710_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.16 apply (zenon_L711_); trivial. % 30.02/30.16 apply (zenon_L137_); trivial. % 30.02/30.16 apply (zenon_L267_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.16 apply (zenon_L552_); trivial. % 30.02/30.16 apply (zenon_L713_); trivial. % 30.02/30.16 (* end of lemma zenon_L714_ *) % 30.02/30.16 assert (zenon_L715_ : ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.02/30.16 do 0 intro. intros zenon_H112 zenon_H17d zenon_Hb5 zenon_H25b zenon_H84 zenon_H74 zenon_H27 zenon_Hc0 zenon_H225 zenon_Hd6 zenon_H174 zenon_H6b zenon_He4 zenon_H92 zenon_Had zenon_H100 zenon_H10d zenon_H8d zenon_H15a zenon_H1d5 zenon_Hd9 zenon_H23b zenon_Hee zenon_H1c7 zenon_H256 zenon_H156 zenon_Hf9 zenon_H1ca zenon_H1fd zenon_H1d8 zenon_H5c zenon_H3f zenon_Hb8 zenon_H1dc zenon_He7 zenon_Hbd zenon_H101 zenon_H222 zenon_Hcd zenon_H20e zenon_Hd1 zenon_H5e zenon_H19e zenon_H208 zenon_H159 zenon_H173 zenon_H102 zenon_Hfc zenon_H35 zenon_H16f zenon_H1b1 zenon_H18c zenon_H14e zenon_H1a5 zenon_H42 zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H60 zenon_H108 zenon_H218 zenon_H200 zenon_H18e zenon_H1a8 zenon_H16a zenon_H124 zenon_H20 zenon_Haa zenon_H246 zenon_H125 zenon_H172 zenon_H83 zenon_Hc8 zenon_H11e zenon_H1d2 zenon_H14b zenon_H135 zenon_H25c zenon_Ha4 zenon_H2d zenon_H1e zenon_H6f zenon_H26 zenon_H17b zenon_He1. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.02/30.16 apply (zenon_L707_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.02/30.16 apply (zenon_L4_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.02/30.16 apply (zenon_L598_); trivial. % 30.02/30.16 apply (zenon_L267_); trivial. % 30.02/30.16 (* end of lemma zenon_L715_ *) % 30.02/30.16 assert (zenon_L716_ : (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 30.02/30.16 do 0 intro. intros zenon_H231 zenon_H6c zenon_H1a2 zenon_H110 zenon_H112 zenon_H17d zenon_Hb5 zenon_H25b zenon_H84 zenon_H74 zenon_H27 zenon_Hc0 zenon_H225 zenon_Hd6 zenon_H174 zenon_H6b zenon_He4 zenon_H92 zenon_Had zenon_H100 zenon_H10d zenon_H8d zenon_H15a zenon_H1d5 zenon_Hd9 zenon_H23b zenon_Hee zenon_H1c7 zenon_H256 zenon_H156 zenon_Hf9 zenon_H1ca zenon_H1fd zenon_H1d8 zenon_H5c zenon_H3f zenon_Hb8 zenon_H1dc zenon_He7 zenon_Hbd zenon_H101 zenon_H222 zenon_Hcd zenon_H20e zenon_Hd1 zenon_H5e zenon_H19e zenon_H208 zenon_H159 zenon_H173 zenon_H102 zenon_Hfc zenon_H35 zenon_H16f zenon_H1b1 zenon_H18c zenon_H14e zenon_H1a5 zenon_H42 zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H3c zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H60 zenon_H108 zenon_H218 zenon_H200 zenon_H18e zenon_H1a8 zenon_H16a zenon_H124 zenon_H20 zenon_Haa zenon_H246 zenon_H125 zenon_H172 zenon_H83 zenon_Hc8 zenon_H11e zenon_H1d2 zenon_H14b zenon_H135 zenon_H25c zenon_Ha4 zenon_H2d zenon_H1e zenon_H6f zenon_H26 zenon_He1. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.02/30.16 exact (zenon_H74 zenon_H73). % 30.02/30.16 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.02/30.16 apply (zenon_L707_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.02/30.16 apply (zenon_L4_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.02/30.16 apply (zenon_L709_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.16 apply (zenon_L707_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.16 apply (zenon_L696_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.16 apply (zenon_L157_); trivial. % 30.02/30.16 apply (zenon_L568_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.02/30.16 apply (zenon_L554_); trivial. % 30.02/30.16 apply (zenon_L715_); trivial. % 30.02/30.16 (* end of lemma zenon_L716_ *) % 30.02/30.16 assert (zenon_L717_ : ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 30.02/30.16 do 0 intro. intros zenon_H69 zenon_He1 zenon_H26 zenon_H6f zenon_H1e zenon_H2d zenon_Ha4 zenon_H25c zenon_H135 zenon_H14b zenon_H1d2 zenon_H11e zenon_Hc8 zenon_H83 zenon_H172 zenon_H125 zenon_H246 zenon_Haa zenon_H20 zenon_H124 zenon_H16a zenon_H1a8 zenon_H18e zenon_H200 zenon_H218 zenon_H108 zenon_H60 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_H3c zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H42 zenon_H1a5 zenon_H14e zenon_H18c zenon_H1b1 zenon_H16f zenon_H35 zenon_Hfc zenon_H102 zenon_H173 zenon_H159 zenon_H208 zenon_H19e zenon_H5e zenon_Hd1 zenon_H20e zenon_Hcd zenon_H222 zenon_H101 zenon_Hbd zenon_He7 zenon_H1dc zenon_Hb8 zenon_H3f zenon_H5c zenon_H1d8 zenon_H1fd zenon_H1ca zenon_Hf9 zenon_H156 zenon_H256 zenon_H1c7 zenon_Hee zenon_H23b zenon_Hd9 zenon_H1d5 zenon_H15a zenon_H8d zenon_H10d zenon_H100 zenon_Had zenon_H92 zenon_He4 zenon_H6b zenon_H174 zenon_Hd6 zenon_H225 zenon_Hc0 zenon_H27 zenon_H74 zenon_H84 zenon_H25b zenon_Hb5 zenon_H110 zenon_H1a2 zenon_H231 zenon_H17d zenon_H112. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.02/30.16 exact (zenon_H84 zenon_H88). % 30.02/30.16 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.02/30.16 apply (zenon_L16_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.02/30.16 apply (zenon_L716_); trivial. % 30.02/30.16 apply (zenon_L139_); trivial. % 30.02/30.16 (* end of lemma zenon_L717_ *) % 30.02/30.16 assert (zenon_L718_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.02/30.16 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H98 zenon_H5e zenon_H222 zenon_Hfe zenon_H1af zenon_H37 zenon_H19e. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.02/30.16 apply (zenon_L157_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.02/30.16 apply (zenon_L514_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.02/30.16 apply (zenon_L170_); trivial. % 30.02/30.16 apply (zenon_L214_); trivial. % 30.02/30.16 (* end of lemma zenon_L718_ *) % 30.02/30.16 assert (zenon_L719_ : (~((op (e3) (e1)) = (op (e3) (op (e3) (e3))))) -> ((op (e3) (e3)) = (e1)) -> False). % 30.02/30.16 do 0 intro. intros zenon_H26c zenon_H112. % 30.02/30.16 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 30.02/30.16 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.02/30.16 congruence. % 30.02/30.16 apply zenon_H2f. apply refl_equal. % 30.02/30.16 apply zenon_H192. apply sym_equal. exact zenon_H112. % 30.02/30.16 (* end of lemma zenon_L719_ *) % 30.02/30.16 assert (zenon_L720_ : ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 30.02/30.16 do 0 intro. intros zenon_Hb3 zenon_H112 zenon_H2c zenon_H3f. % 30.02/30.16 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H3f. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H1b4. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 30.02/30.16 congruence. % 30.02/30.16 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H26d. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_Hb3. % 30.02/30.16 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 30.02/30.16 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26e]. % 30.02/30.16 congruence. % 30.02/30.16 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H26e. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H1b4. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H26c]. % 30.02/30.16 congruence. % 30.02/30.16 apply (zenon_L719_); trivial. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 apply zenon_H191. apply sym_equal. exact zenon_H2c. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 (* end of lemma zenon_L720_ *) % 30.02/30.16 assert (zenon_L721_ : ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.02/30.16 do 0 intro. intros zenon_Hb3 zenon_H112 zenon_H37 zenon_H100. % 30.02/30.16 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e1) (e1)) = (op (e3) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H100. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H1b4. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 30.02/30.16 congruence. % 30.02/30.16 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e1)) = (op (e1) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H1b6. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_Hb3. % 30.02/30.16 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 30.02/30.16 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26e]. % 30.02/30.16 congruence. % 30.02/30.16 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H26e. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H1b4. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H26c]. % 30.02/30.16 congruence. % 30.02/30.16 apply (zenon_L719_); trivial. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 apply zenon_H38. apply sym_equal. exact zenon_H37. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 (* end of lemma zenon_L721_ *) % 30.02/30.16 assert (zenon_L722_ : ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 30.02/30.16 do 0 intro. intros zenon_Hb3 zenon_H112 zenon_H3d zenon_H222. % 30.02/30.16 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H222. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H1b4. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 30.02/30.16 congruence. % 30.02/30.16 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H26f. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_Hb3. % 30.02/30.16 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 30.02/30.16 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26e]. % 30.02/30.16 congruence. % 30.02/30.16 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H26e. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H1b4. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.16 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H26c]. % 30.02/30.16 congruence. % 30.02/30.16 apply (zenon_L719_); trivial. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 apply zenon_H1b5. apply refl_equal. % 30.02/30.16 (* end of lemma zenon_L722_ *) % 30.02/30.16 assert (zenon_L723_ : (((op (e3) (op (e3) (e0))) = (e0))/\(((op (e3) (op (e3) (e1))) = (e1))/\(((op (e3) (op (e3) (e2))) = (e2))/\(((op (e3) (op (e3) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0)))/\(((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1)))/\(((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3)))))))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.02/30.16 do 0 intro. intros zenon_H270 zenon_H42 zenon_H3f zenon_H100 zenon_H222 zenon_H112 zenon_H18e. % 30.02/30.16 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.02/30.16 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.02/30.16 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.02/30.16 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.02/30.16 apply (zenon_L720_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.02/30.16 apply (zenon_L721_); trivial. % 30.02/30.16 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.02/30.16 apply (zenon_L722_); trivial. % 30.02/30.16 exact (zenon_H18e zenon_H40). % 30.02/30.16 (* end of lemma zenon_L723_ *) % 30.02/30.16 assert (zenon_L724_ : (~((op (e0) (e0)) = (op (e0) (op (e0) (e2))))) -> ((op (e0) (e2)) = (e0)) -> False). % 30.02/30.16 do 0 intro. intros zenon_H276 zenon_H10e. % 30.02/30.16 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 30.02/30.16 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.02/30.16 congruence. % 30.02/30.16 apply zenon_H1d. apply refl_equal. % 30.02/30.16 apply zenon_H139. apply sym_equal. exact zenon_H10e. % 30.02/30.16 (* end of lemma zenon_L724_ *) % 30.02/30.16 assert (zenon_L725_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> False). % 30.02/30.16 do 0 intro. intros zenon_H15a zenon_H198 zenon_H10e zenon_Hdc. % 30.02/30.16 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H15a. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H198. % 30.02/30.16 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 30.02/30.16 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 30.02/30.16 congruence. % 30.02/30.16 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H18b | zenon_intro zenon_Hcb ]. % 30.02/30.16 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e0)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H277. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H18b. % 30.02/30.16 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.02/30.16 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 30.02/30.16 congruence. % 30.02/30.16 apply (zenon_L724_); trivial. % 30.02/30.16 apply zenon_Hcb. apply refl_equal. % 30.02/30.16 apply zenon_Hcb. apply refl_equal. % 30.02/30.16 apply zenon_H15b. apply sym_equal. exact zenon_Hdc. % 30.02/30.16 (* end of lemma zenon_L725_ *) % 30.02/30.16 assert (zenon_L726_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> False). % 30.02/30.16 do 0 intro. intros zenon_Hc8 zenon_H198 zenon_H10e zenon_Hc9. % 30.02/30.16 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_Hc8. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H198. % 30.02/30.16 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 30.02/30.16 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 30.02/30.16 congruence. % 30.02/30.16 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H18b | zenon_intro zenon_Hcb ]. % 30.02/30.16 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e0)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H277. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H18b. % 30.02/30.16 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.02/30.16 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 30.02/30.16 congruence. % 30.02/30.16 apply (zenon_L724_); trivial. % 30.02/30.16 apply zenon_Hcb. apply refl_equal. % 30.02/30.16 apply zenon_Hcb. apply refl_equal. % 30.02/30.16 apply zenon_Hca. apply sym_equal. exact zenon_Hc9. % 30.02/30.16 (* end of lemma zenon_L726_ *) % 30.02/30.16 assert (zenon_L727_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> False). % 30.02/30.16 do 0 intro. intros zenon_He7 zenon_H198 zenon_H10e zenon_He2. % 30.02/30.16 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_He7. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H198. % 30.02/30.16 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 30.02/30.16 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 30.02/30.16 congruence. % 30.02/30.16 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H18b | zenon_intro zenon_Hcb ]. % 30.02/30.16 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e0)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H277. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H18b. % 30.02/30.16 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.02/30.16 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 30.02/30.16 congruence. % 30.02/30.16 apply (zenon_L724_); trivial. % 30.02/30.16 apply zenon_Hcb. apply refl_equal. % 30.02/30.16 apply zenon_Hcb. apply refl_equal. % 30.02/30.16 apply zenon_He8. apply sym_equal. exact zenon_He2. % 30.02/30.16 (* end of lemma zenon_L727_ *) % 30.02/30.16 assert (zenon_L728_ : (~((op (e1) (e1)) = (op (e1) (op (e1) (e3))))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.02/30.16 do 0 intro. intros zenon_H278 zenon_H182. % 30.02/30.16 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 30.02/30.16 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.16 congruence. % 30.02/30.16 apply zenon_H22. apply refl_equal. % 30.02/30.16 apply zenon_H1a7. apply sym_equal. exact zenon_H182. % 30.02/30.16 (* end of lemma zenon_L728_ *) % 30.02/30.16 assert (zenon_L729_ : ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 30.02/30.16 do 0 intro. intros zenon_H4e zenon_H182 zenon_H6e zenon_Hd1. % 30.02/30.16 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_Hd1. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_Hc4. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 30.02/30.16 congruence. % 30.02/30.16 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H279. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H4e. % 30.02/30.16 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 30.02/30.16 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 30.02/30.16 congruence. % 30.02/30.16 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H27a. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_Hc4. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 30.02/30.16 congruence. % 30.02/30.16 apply (zenon_L728_); trivial. % 30.02/30.16 apply zenon_Hc5. apply refl_equal. % 30.02/30.16 apply zenon_Hc5. apply refl_equal. % 30.02/30.16 apply zenon_Haf. apply sym_equal. exact zenon_H6e. % 30.02/30.16 apply zenon_Hc5. apply refl_equal. % 30.02/30.16 apply zenon_Hc5. apply refl_equal. % 30.02/30.16 (* end of lemma zenon_L729_ *) % 30.02/30.16 assert (zenon_L730_ : ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.02/30.16 do 0 intro. intros zenon_H4e zenon_H182 zenon_H2c zenon_H35. % 30.02/30.16 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H35. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_Hc4. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 30.02/30.16 congruence. % 30.02/30.16 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_Hc6. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_H4e. % 30.02/30.16 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 30.02/30.16 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 30.02/30.16 congruence. % 30.02/30.16 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e1)))). % 30.02/30.16 intro zenon_D_pnotp. % 30.02/30.16 apply zenon_H27a. % 30.02/30.16 rewrite <- zenon_D_pnotp. % 30.02/30.16 exact zenon_Hc4. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.16 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 30.02/30.16 congruence. % 30.02/30.16 apply (zenon_L728_); trivial. % 30.02/30.16 apply zenon_Hc5. apply refl_equal. % 30.02/30.16 apply zenon_Hc5. apply refl_equal. % 30.02/30.16 apply zenon_H191. apply sym_equal. exact zenon_H2c. % 30.02/30.16 apply zenon_Hc5. apply refl_equal. % 30.02/30.16 apply zenon_Hc5. apply refl_equal. % 30.02/30.16 (* end of lemma zenon_L730_ *) % 30.02/30.16 assert (zenon_L731_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H19e zenon_H4e zenon_H182 zenon_H3d. % 30.02/30.17 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H19e. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H4e. % 30.02/30.17 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 30.02/30.17 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.17 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H27a. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_Hc4. % 30.02/30.17 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.17 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L728_); trivial. % 30.02/30.17 apply zenon_Hc5. apply refl_equal. % 30.02/30.17 apply zenon_Hc5. apply refl_equal. % 30.02/30.17 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 30.02/30.17 (* end of lemma zenon_L731_ *) % 30.02/30.17 assert (zenon_L732_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H100 zenon_H4e zenon_H182 zenon_H40. % 30.02/30.17 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H100. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H4e. % 30.02/30.17 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 30.02/30.17 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.17 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H27a. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_Hc4. % 30.02/30.17 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.17 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L728_); trivial. % 30.02/30.17 apply zenon_Hc5. apply refl_equal. % 30.02/30.17 apply zenon_Hc5. apply refl_equal. % 30.02/30.17 apply zenon_H41. apply sym_equal. exact zenon_H40. % 30.02/30.17 (* end of lemma zenon_L732_ *) % 30.02/30.17 assert (zenon_L733_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H159 zenon_H4e zenon_H182 zenon_H16c. % 30.02/30.17 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H159. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H4e. % 30.02/30.17 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 30.02/30.17 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.17 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H27a. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_Hc4. % 30.02/30.17 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.17 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L728_); trivial. % 30.02/30.17 apply zenon_Hc5. apply refl_equal. % 30.02/30.17 apply zenon_Hc5. apply refl_equal. % 30.02/30.17 apply zenon_H16d. apply sym_equal. exact zenon_H16c. % 30.02/30.17 (* end of lemma zenon_L733_ *) % 30.02/30.17 assert (zenon_L734_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H88 zenon_H89 zenon_H6f. % 30.02/30.17 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 30.02/30.17 cut (((e3) = (e3)) = ((e1) = (e3))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H6f. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H2e. % 30.02/30.17 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.02/30.17 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e0) (e0)) = (e1)) = ((e3) = (e1))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H70. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H88. % 30.02/30.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.17 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 30.02/30.17 congruence. % 30.02/30.17 exact (zenon_H85 zenon_H89). % 30.02/30.17 apply zenon_H22. apply refl_equal. % 30.02/30.17 apply zenon_H2f. apply refl_equal. % 30.02/30.17 apply zenon_H2f. apply refl_equal. % 30.02/30.17 (* end of lemma zenon_L734_ *) % 30.02/30.17 assert (zenon_L735_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H225 zenon_H74 zenon_H35 zenon_Hfd zenon_Hde zenon_H174 zenon_H6f zenon_H88 zenon_H1e zenon_H2d zenon_H10e zenon_He1. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.02/30.17 exact (zenon_H74 zenon_H73). % 30.02/30.17 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.02/30.17 apply (zenon_L95_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.02/30.17 apply (zenon_L192_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.02/30.17 apply (zenon_L734_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.02/30.17 apply (zenon_L4_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.02/30.17 apply (zenon_L87_); trivial. % 30.02/30.17 apply (zenon_L267_); trivial. % 30.02/30.17 (* end of lemma zenon_L735_ *) % 30.02/30.17 assert (zenon_L736_ : (~((op (e1) (e3)) = (op (e1) (op (e1) (e0))))) -> ((op (e1) (e0)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H27b zenon_H6e. % 30.02/30.17 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 30.02/30.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H22. apply refl_equal. % 30.02/30.17 apply zenon_Haf. apply sym_equal. exact zenon_H6e. % 30.02/30.17 (* end of lemma zenon_L736_ *) % 30.02/30.17 assert (zenon_L737_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> ((op (e2) (e3)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H156 zenon_H48 zenon_H6e zenon_H1e1. % 30.02/30.17 cut (((op (e1) (op (e1) (e0))) = (e0)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H156. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H48. % 30.02/30.17 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 30.02/30.17 cut (((op (e1) (op (e1) (e0))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H27c]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.02/30.17 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (op (e1) (e0))) = (op (e1) (e3)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H27c. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H183. % 30.02/30.17 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.17 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L736_); trivial. % 30.02/30.17 apply zenon_H150. apply refl_equal. % 30.02/30.17 apply zenon_H150. apply refl_equal. % 30.02/30.17 apply zenon_H1e2. apply sym_equal. exact zenon_H1e1. % 30.02/30.17 (* end of lemma zenon_L737_ *) % 30.02/30.17 assert (zenon_L738_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_H6e. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.02/30.17 apply (zenon_L49_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.02/30.17 apply (zenon_L207_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.02/30.17 apply (zenon_L208_); trivial. % 30.02/30.17 apply (zenon_L737_); trivial. % 30.02/30.17 (* end of lemma zenon_L738_ *) % 30.02/30.17 assert (zenon_L739_ : (~((op (e1) (e0)) = (op (e1) (op (e1) (e0))))) -> ((op (e1) (e0)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H27d zenon_H69. % 30.02/30.17 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 30.02/30.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H22. apply refl_equal. % 30.02/30.17 apply zenon_H27e. apply sym_equal. exact zenon_H69. % 30.02/30.17 (* end of lemma zenon_L739_ *) % 30.02/30.17 assert (zenon_L740_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H18c zenon_H48 zenon_H69 zenon_Hdf. % 30.02/30.17 cut (((op (e1) (op (e1) (e0))) = (e0)) = ((op (e1) (e0)) = (op (e2) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H18c. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H48. % 30.02/30.17 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f0]. % 30.02/30.17 cut (((op (e1) (op (e1) (e0))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27f]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e0))) = (op (e1) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H27f. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H280. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H27d]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L739_); trivial. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_H1f0. apply sym_equal. exact zenon_Hdf. % 30.02/30.17 (* end of lemma zenon_L740_ *) % 30.02/30.17 assert (zenon_L741_ : (~((op (e1) (e0)) = (op (e1) (op (e1) (e2))))) -> ((op (e1) (e2)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H281 zenon_Hfe. % 30.02/30.17 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 30.02/30.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H22. apply refl_equal. % 30.02/30.17 apply zenon_Hff. apply sym_equal. exact zenon_Hfe. % 30.02/30.17 (* end of lemma zenon_L741_ *) % 30.02/30.17 assert (zenon_L742_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> False). % 30.02/30.17 do 0 intro. intros zenon_Had zenon_H4c zenon_Hfe zenon_He2. % 30.02/30.17 cut (((op (e1) (op (e1) (e2))) = (e2)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_Had. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H4c. % 30.02/30.17 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 30.02/30.17 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H282]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e2))) = (op (e1) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H282. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H280. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H281]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L741_); trivial. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_He8. apply sym_equal. exact zenon_He2. % 30.02/30.17 (* end of lemma zenon_L742_ *) % 30.02/30.17 assert (zenon_L743_ : (~((op (e1) (e0)) = (op (e1) (op (e1) (e3))))) -> ((op (e1) (e3)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H283 zenon_H14f. % 30.02/30.17 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H284]. % 30.02/30.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H22. apply refl_equal. % 30.02/30.17 apply zenon_H284. apply sym_equal. exact zenon_H14f. % 30.02/30.17 (* end of lemma zenon_L743_ *) % 30.02/30.17 assert (zenon_L744_ : ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H4e zenon_H14f zenon_H89 zenon_H15a. % 30.02/30.17 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e0) (e0)) = (op (e1) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H15a. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H280. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H285]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e0)) = (op (e0) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H285. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H4e. % 30.02/30.17 cut (((e3) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 30.02/30.17 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H286. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H280. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H283]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L743_); trivial. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_H1f9. apply sym_equal. exact zenon_H89. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 (* end of lemma zenon_L744_ *) % 30.02/30.17 assert (zenon_L745_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H18c zenon_H35 zenon_H1e zenon_He2 zenon_H4c zenon_Had zenon_H4e zenon_H89 zenon_H15a. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.17 apply (zenon_L740_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.17 apply (zenon_L42_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.17 apply (zenon_L742_); trivial. % 30.02/30.17 apply (zenon_L744_); trivial. % 30.02/30.17 (* end of lemma zenon_L745_ *) % 30.02/30.17 assert (zenon_L746_ : ((op (e3) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H40 zenon_H2c zenon_H3f. % 30.02/30.17 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.17 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H3f. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H1b4. % 30.02/30.17 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.17 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H26d. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H40. % 30.02/30.17 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 30.02/30.17 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H1b5. apply refl_equal. % 30.02/30.17 apply zenon_H191. apply sym_equal. exact zenon_H2c. % 30.02/30.17 apply zenon_H1b5. apply refl_equal. % 30.02/30.17 apply zenon_H1b5. apply refl_equal. % 30.02/30.17 (* end of lemma zenon_L746_ *) % 30.02/30.17 assert (zenon_L747_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.02/30.17 do 0 intro. intros zenon_He4 zenon_H74 zenon_Hfd zenon_Hd1 zenon_Hde zenon_H174 zenon_H15a zenon_H4e zenon_Had zenon_H4c zenon_H1e zenon_H35 zenon_H18c zenon_H48 zenon_Hdf zenon_H172 zenon_H3f zenon_H40 zenon_H2d zenon_H10e zenon_H17b zenon_He1. % 30.02/30.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.17 exact (zenon_H74 zenon_H73). % 30.02/30.17 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.17 apply (zenon_L154_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.17 apply (zenon_L49_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.02/30.17 apply (zenon_L745_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.02/30.17 apply (zenon_L746_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.02/30.17 apply (zenon_L87_); trivial. % 30.02/30.17 apply (zenon_L267_); trivial. % 30.02/30.17 (* end of lemma zenon_L747_ *) % 30.02/30.17 assert (zenon_L748_ : ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H4a zenon_Hfd zenon_H26 zenon_H1a5. % 30.02/30.17 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 30.02/30.17 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H1a5. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H19b. % 30.02/30.17 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 30.02/30.17 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e1) (op (e1) (e1))) = (e1)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H1a6. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H4a. % 30.02/30.17 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 30.02/30.17 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 30.02/30.17 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (op (e1) (e1))) = (op (e1) (e2)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H287. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H19b. % 30.02/30.17 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 30.02/30.17 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 30.02/30.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H22. apply refl_equal. % 30.02/30.17 apply zenon_H149. apply sym_equal. exact zenon_Hfd. % 30.02/30.17 apply zenon_H19c. apply refl_equal. % 30.02/30.17 apply zenon_H19c. apply refl_equal. % 30.02/30.17 apply zenon_H2b. apply sym_equal. exact zenon_H26. % 30.02/30.17 apply zenon_H19c. apply refl_equal. % 30.02/30.17 apply zenon_H19c. apply refl_equal. % 30.02/30.17 (* end of lemma zenon_L748_ *) % 30.02/30.17 assert (zenon_L749_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_Had zenon_H48 zenon_H69 zenon_H8b. % 30.02/30.17 cut (((op (e1) (op (e1) (e0))) = (e0)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_Had. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H48. % 30.02/30.17 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 30.02/30.17 cut (((op (e1) (op (e1) (e0))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27f]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e0))) = (op (e1) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H27f. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H280. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H27d]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L739_); trivial. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_H1ed. apply sym_equal. exact zenon_H8b. % 30.02/30.17 (* end of lemma zenon_L749_ *) % 30.02/30.17 assert (zenon_L750_ : ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (op (op (e2) (e2)) (e2)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H1a0 zenon_H1b9 zenon_H262. % 30.02/30.17 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 30.02/30.17 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e1) = (op (op (e2) (e2)) (e2)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H262. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H160. % 30.02/30.17 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 30.02/30.17 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H263]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e3) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H263. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H1a0. % 30.02/30.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.17 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 30.02/30.17 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H1f3. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H160. % 30.02/30.17 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 30.02/30.17 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L196_); trivial. % 30.02/30.17 apply zenon_H161. apply refl_equal. % 30.02/30.17 apply zenon_H161. apply refl_equal. % 30.02/30.17 apply zenon_H22. apply refl_equal. % 30.02/30.17 apply zenon_H161. apply refl_equal. % 30.02/30.17 apply zenon_H161. apply refl_equal. % 30.02/30.17 (* end of lemma zenon_L750_ *) % 30.02/30.17 assert (zenon_L751_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_Hb1 zenon_H1a0 zenon_H1b9. % 30.02/30.17 apply (zenon_notand_s _ _ ax18); [ zenon_intro zenon_H165 | zenon_intro zenon_H289 ]. % 30.02/30.17 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 30.02/30.17 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (e2) (e2))))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H165. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H166. % 30.02/30.17 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 30.02/30.17 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e3) (e3)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H168. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_Hb1. % 30.02/30.17 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.02/30.17 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 30.02/30.17 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))))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H1f7. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H166. % 30.02/30.17 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 30.02/30.17 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L195_); trivial. % 30.02/30.17 apply zenon_H167. apply refl_equal. % 30.02/30.17 apply zenon_H167. apply refl_equal. % 30.02/30.17 apply zenon_H1d. apply refl_equal. % 30.02/30.17 apply zenon_H167. apply refl_equal. % 30.02/30.17 apply zenon_H167. apply refl_equal. % 30.02/30.17 apply (zenon_notand_s _ _ zenon_H289); [ zenon_intro zenon_H262 | zenon_intro zenon_H1de ]. % 30.02/30.17 apply (zenon_L750_); trivial. % 30.02/30.17 apply zenon_H1de. apply sym_equal. exact zenon_H1b9. % 30.02/30.17 (* end of lemma zenon_L751_ *) % 30.02/30.17 assert (zenon_L752_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H14e zenon_H4c zenon_H15e zenon_Hf4. % 30.02/30.17 cut (((op (e1) (op (e1) (e2))) = (e2)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H14e. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H4c. % 30.02/30.17 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 30.02/30.17 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H28a]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.02/30.17 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (op (e1) (e2))) = (op (e1) (e3)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H28a. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H183. % 30.02/30.17 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.17 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 30.02/30.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H22. apply refl_equal. % 30.02/30.17 apply zenon_H1fb. apply sym_equal. exact zenon_H15e. % 30.02/30.17 apply zenon_H150. apply refl_equal. % 30.02/30.17 apply zenon_H150. apply refl_equal. % 30.02/30.17 apply zenon_H116. apply sym_equal. exact zenon_Hf4. % 30.02/30.17 (* end of lemma zenon_L752_ *) % 30.02/30.17 assert (zenon_L753_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H113 zenon_H40 zenon_Hbc. % 30.02/30.17 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e3)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H113. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H40. % 30.02/30.17 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 30.02/30.17 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H1b5. apply refl_equal. % 30.02/30.17 apply zenon_H17e. apply sym_equal. exact zenon_Hbc. % 30.02/30.17 (* end of lemma zenon_L753_ *) % 30.02/30.17 assert (zenon_L754_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H11b zenon_H1a0 zenon_H1b9 zenon_H9c zenon_H15e zenon_H4c zenon_H14e zenon_H113 zenon_H40. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.02/30.17 apply (zenon_L751_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.02/30.17 apply (zenon_L198_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.02/30.17 apply (zenon_L752_); trivial. % 30.02/30.17 apply (zenon_L753_); trivial. % 30.02/30.17 (* end of lemma zenon_L754_ *) % 30.02/30.17 assert (zenon_L755_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H1d2 zenon_H1dc zenon_H56 zenon_Hc9 zenon_H6b zenon_H11b zenon_H1a0 zenon_H9c zenon_H15e zenon_H4c zenon_H14e zenon_H113 zenon_H40. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.02/30.17 apply (zenon_L177_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.02/30.17 exact (zenon_H56 zenon_H25). % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.02/30.17 apply (zenon_L552_); trivial. % 30.02/30.17 apply (zenon_L754_); trivial. % 30.02/30.17 (* end of lemma zenon_L755_ *) % 30.02/30.17 assert (zenon_L756_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_Hbd zenon_H69 zenon_H48 zenon_Had zenon_H1e zenon_H3f zenon_H40 zenon_H113 zenon_H14e zenon_H4c zenon_H15e zenon_H1a0 zenon_H11b zenon_H6b zenon_Hc9 zenon_H56 zenon_H1dc zenon_H1d2 zenon_Hf6 zenon_H1e1. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.17 apply (zenon_L749_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.17 apply (zenon_L29_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.17 apply (zenon_L755_); trivial. % 30.02/30.17 apply (zenon_L690_); trivial. % 30.02/30.17 (* end of lemma zenon_L756_ *) % 30.02/30.17 assert (zenon_L757_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H200 zenon_He1 zenon_H17b zenon_H2d zenon_H172 zenon_H18c zenon_H35 zenon_H4e zenon_H15a zenon_H174 zenon_Hde zenon_Hd1 zenon_H74 zenon_He4 zenon_H3c zenon_H27 zenon_H10e zenon_H1a2 zenon_H1a5 zenon_Hfd zenon_H4a zenon_H28c zenon_Hbd zenon_H69 zenon_H48 zenon_Had zenon_H1e zenon_H3f zenon_H40 zenon_H113 zenon_H14e zenon_H4c zenon_H15e zenon_H11b zenon_H6b zenon_Hc9 zenon_H56 zenon_H1dc zenon_H1d2 zenon_Hf6. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.02/30.17 apply (zenon_L747_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.02/30.17 apply (zenon_L207_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.02/30.17 apply (zenon_L208_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.02/30.17 apply (zenon_L748_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.02/30.17 exact (zenon_H28c zenon_H19a). % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.02/30.17 exact (zenon_H56 zenon_H25). % 30.02/30.17 apply (zenon_L756_); trivial. % 30.02/30.17 (* end of lemma zenon_L757_ *) % 30.02/30.17 assert (zenon_L758_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H182 zenon_H16c zenon_H6f. % 30.02/30.17 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 30.02/30.17 cut (((e3) = (e3)) = ((e1) = (e3))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H6f. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H2e. % 30.02/30.17 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.02/30.17 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e1) (e3)) = (e1)) = ((e3) = (e1))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H70. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H182. % 30.02/30.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.17 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 30.02/30.17 congruence. % 30.02/30.17 exact (zenon_H28d zenon_H16c). % 30.02/30.17 apply zenon_H22. apply refl_equal. % 30.02/30.17 apply zenon_H2f. apply refl_equal. % 30.02/30.17 apply zenon_H2f. apply refl_equal. % 30.02/30.17 (* end of lemma zenon_L758_ *) % 30.02/30.17 assert (zenon_L759_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H16f zenon_H156 zenon_Hf6 zenon_H1d2 zenon_H1dc zenon_H56 zenon_Hc9 zenon_H6b zenon_H11b zenon_H4c zenon_H14e zenon_H113 zenon_H3f zenon_H1e zenon_Had zenon_H48 zenon_H69 zenon_Hbd zenon_H28c zenon_H4a zenon_Hfd zenon_H1a5 zenon_H1a2 zenon_H10e zenon_H27 zenon_H3c zenon_He4 zenon_H74 zenon_Hd1 zenon_Hde zenon_H174 zenon_H15a zenon_H4e zenon_H35 zenon_H18c zenon_H172 zenon_H2d zenon_H17b zenon_He1 zenon_H200 zenon_H19e zenon_Hfc zenon_H42 zenon_H182 zenon_H6f. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.17 apply (zenon_L738_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.17 apply (zenon_L158_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.02/30.17 apply (zenon_L730_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.02/30.17 apply (zenon_L203_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.02/30.17 apply (zenon_L731_); trivial. % 30.02/30.17 apply (zenon_L757_); trivial. % 30.02/30.17 apply (zenon_L758_); trivial. % 30.02/30.17 (* end of lemma zenon_L759_ *) % 30.02/30.17 assert (zenon_L760_ : (~((op (e1) (e0)) = (op (e1) (op (e1) (e1))))) -> ((op (e1) (e1)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H28e zenon_Hc3. % 30.02/30.17 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 30.02/30.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H22. apply refl_equal. % 30.02/30.17 apply zenon_H245. apply sym_equal. exact zenon_Hc3. % 30.02/30.17 (* end of lemma zenon_L760_ *) % 30.02/30.17 assert (zenon_L761_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H28f zenon_H4a zenon_Hc3 zenon_H182. % 30.02/30.17 cut (((op (e1) (op (e1) (e1))) = (e1)) = ((op (e1) (e0)) = (op (e1) (e3)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H28f. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H4a. % 30.02/30.17 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 30.02/30.17 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H290]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e1))) = (op (e1) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H290. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H280. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H28e]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L760_); trivial. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_H1a7. apply sym_equal. exact zenon_H182. % 30.02/30.17 (* end of lemma zenon_L761_ *) % 30.02/30.17 assert (zenon_L762_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H18c zenon_H182 zenon_H4a zenon_H28f zenon_He2 zenon_H4c zenon_Had zenon_H4e zenon_H89 zenon_H15a. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.17 apply (zenon_L740_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.17 apply (zenon_L761_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.17 apply (zenon_L742_); trivial. % 30.02/30.17 apply (zenon_L744_); trivial. % 30.02/30.17 (* end of lemma zenon_L762_ *) % 30.02/30.17 assert (zenon_L763_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H18c zenon_H4a zenon_Hc3 zenon_H6c. % 30.02/30.17 cut (((op (e1) (op (e1) (e1))) = (e1)) = ((op (e1) (e0)) = (op (e2) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H18c. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H4a. % 30.02/30.17 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18d]. % 30.02/30.17 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H290]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e1))) = (op (e1) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H290. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H280. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H28e]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L760_); trivial. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_H18d. apply sym_equal. exact zenon_H6c. % 30.02/30.17 (* end of lemma zenon_L763_ *) % 30.02/30.17 assert (zenon_L764_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H1a5 zenon_H10e zenon_Hfe. % 30.02/30.17 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H1a5. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H10e. % 30.02/30.17 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 30.02/30.17 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H10f. apply refl_equal. % 30.02/30.17 apply zenon_Hff. apply sym_equal. exact zenon_Hfe. % 30.02/30.17 (* end of lemma zenon_L764_ *) % 30.02/30.17 assert (zenon_L765_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H172 zenon_H8b zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_H18c zenon_H10e zenon_H1a5 zenon_H4e zenon_H89 zenon_H15a. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.17 apply (zenon_L749_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.17 apply (zenon_L763_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.17 apply (zenon_L764_); trivial. % 30.02/30.17 apply (zenon_L744_); trivial. % 30.02/30.17 (* end of lemma zenon_L765_ *) % 30.02/30.17 assert (zenon_L766_ : (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H2d zenon_H40 zenon_H95. % 30.02/30.17 cut (((op (e3) (e1)) = (e3)) = ((e0) = (e3))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H2d. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H40. % 30.02/30.17 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.02/30.17 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 30.02/30.17 congruence. % 30.02/30.17 exact (zenon_H291 zenon_H95). % 30.02/30.17 apply zenon_H2f. apply refl_equal. % 30.02/30.17 (* end of lemma zenon_L766_ *) % 30.02/30.17 assert (zenon_L767_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H200 zenon_H4c zenon_He2 zenon_H28f zenon_H182 zenon_H1e zenon_H3c zenon_H27 zenon_Hbd zenon_H15a zenon_H89 zenon_H4e zenon_H1a5 zenon_H18c zenon_H4a zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_H40 zenon_H2d zenon_H10e zenon_H10d zenon_Hf6. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.02/30.17 apply (zenon_L762_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.02/30.17 apply (zenon_L207_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.02/30.17 apply (zenon_L208_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.17 apply (zenon_L765_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.17 apply (zenon_L766_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.17 apply (zenon_L63_); trivial. % 30.02/30.17 apply (zenon_L690_); trivial. % 30.02/30.17 (* end of lemma zenon_L767_ *) % 30.02/30.17 assert (zenon_L768_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H92 zenon_H20 zenon_H10d zenon_H28f zenon_H159 zenon_H225 zenon_H6f zenon_H42 zenon_Hfc zenon_H19e zenon_H200 zenon_He1 zenon_H2d zenon_H172 zenon_H18c zenon_H35 zenon_H4e zenon_H15a zenon_H174 zenon_Hde zenon_Hd1 zenon_H74 zenon_He4 zenon_H3c zenon_H27 zenon_H10e zenon_H1a2 zenon_H1a5 zenon_Hfd zenon_H4a zenon_H28c zenon_Hbd zenon_H69 zenon_H48 zenon_Had zenon_H1e zenon_H3f zenon_H113 zenon_H14e zenon_H4c zenon_H11b zenon_H6b zenon_H56 zenon_H1dc zenon_H1d2 zenon_Hf6 zenon_H156 zenon_H16f zenon_H18f zenon_H1a8 zenon_Hcd. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.02/30.17 apply (zenon_L735_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.02/30.17 apply (zenon_L16_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.02/30.17 exact (zenon_H74 zenon_H73). % 30.02/30.17 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.02/30.17 apply (zenon_L95_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.02/30.17 apply (zenon_L192_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.17 exact (zenon_H74 zenon_H73). % 30.02/30.17 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.17 apply (zenon_L154_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.17 apply (zenon_L120_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.17 exact (zenon_H18f zenon_Hd2). % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.17 exact (zenon_H28c zenon_H19a). % 30.02/30.17 apply (zenon_L759_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.17 apply (zenon_L16_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.17 exact (zenon_H18f zenon_Hd2). % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.17 exact (zenon_H28c zenon_H19a). % 30.02/30.17 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.17 apply (zenon_L729_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.17 apply (zenon_L158_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.02/30.17 apply (zenon_L730_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.02/30.17 apply (zenon_L203_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.02/30.17 apply (zenon_L731_); trivial. % 30.02/30.17 apply (zenon_L767_); trivial. % 30.02/30.17 apply (zenon_L733_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.02/30.17 apply (zenon_L4_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.02/30.17 apply (zenon_L87_); trivial. % 30.02/30.17 apply (zenon_L267_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.02/30.17 exact (zenon_H74 zenon_H73). % 30.02/30.17 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.02/30.17 apply (zenon_L95_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.02/30.17 apply (zenon_L192_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.17 exact (zenon_H74 zenon_H73). % 30.02/30.17 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.17 apply (zenon_L154_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.17 apply (zenon_L639_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.17 exact (zenon_H18f zenon_Hd2). % 30.02/30.17 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.17 exact (zenon_H28c zenon_H19a). % 30.02/30.17 apply (zenon_L759_); trivial. % 30.02/30.17 apply (zenon_L386_); trivial. % 30.02/30.17 (* end of lemma zenon_L768_ *) % 30.02/30.17 assert (zenon_L769_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> False). % 30.02/30.17 do 0 intro. intros zenon_Had zenon_H4a zenon_Hc3 zenon_H90. % 30.02/30.17 cut (((op (e1) (op (e1) (e1))) = (e1)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_Had. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H4a. % 30.02/30.17 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H26a]. % 30.02/30.17 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H290]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e1))) = (op (e1) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H290. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H280. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.17 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H28e]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L760_); trivial. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_Hd4. apply refl_equal. % 30.02/30.17 apply zenon_H26a. apply sym_equal. exact zenon_H90. % 30.02/30.17 (* end of lemma zenon_L769_ *) % 30.02/30.17 assert (zenon_L770_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H14e zenon_H48 zenon_H6e zenon_Hb1. % 30.02/30.17 cut (((op (e1) (op (e1) (e0))) = (e0)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H14e. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H48. % 30.02/30.17 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 30.02/30.17 cut (((op (e1) (op (e1) (e0))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H27c]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.02/30.17 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (op (e1) (e0))) = (op (e1) (e3)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H27c. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H183. % 30.02/30.17 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.17 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L736_); trivial. % 30.02/30.17 apply zenon_H150. apply refl_equal. % 30.02/30.17 apply zenon_H150. apply refl_equal. % 30.02/30.17 apply zenon_Hb2. apply sym_equal. exact zenon_Hb1. % 30.02/30.17 (* end of lemma zenon_L770_ *) % 30.02/30.17 assert (zenon_L771_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H90 zenon_H40 zenon_H2d zenon_H10e zenon_H10d zenon_H14e zenon_H48 zenon_H6e. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.17 apply (zenon_L27_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.17 apply (zenon_L766_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.17 apply (zenon_L63_); trivial. % 30.02/30.17 apply (zenon_L770_); trivial. % 30.02/30.17 (* end of lemma zenon_L771_ *) % 30.02/30.17 assert (zenon_L772_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_Hb1 zenon_H8b zenon_H17d. % 30.02/30.17 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.02/30.17 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H17d. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_Ha5. % 30.02/30.17 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.02/30.17 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H292]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H292. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_Hb1. % 30.02/30.17 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 30.02/30.17 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_Ha6. apply refl_equal. % 30.02/30.17 apply zenon_H1ed. apply sym_equal. exact zenon_H8b. % 30.02/30.17 apply zenon_Ha6. apply refl_equal. % 30.02/30.17 apply zenon_Ha6. apply refl_equal. % 30.02/30.17 (* end of lemma zenon_L772_ *) % 30.02/30.17 assert (zenon_L773_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H11b zenon_H17d zenon_H8b zenon_H182 zenon_H15e zenon_H4c zenon_H14e zenon_H113 zenon_H40. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.02/30.17 apply (zenon_L772_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.02/30.17 apply (zenon_L137_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.02/30.17 apply (zenon_L752_); trivial. % 30.02/30.17 apply (zenon_L753_); trivial. % 30.02/30.17 (* end of lemma zenon_L773_ *) % 30.02/30.17 assert (zenon_L774_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.02/30.17 do 0 intro. intros zenon_Hbd zenon_H182 zenon_H17d zenon_H2d zenon_H40 zenon_H113 zenon_H14e zenon_H4c zenon_H15e zenon_H11b zenon_H1a0 zenon_H1b9. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.17 apply (zenon_L773_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.17 apply (zenon_L766_); trivial. % 30.02/30.17 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.17 apply (zenon_L754_); trivial. % 30.02/30.17 apply (zenon_L751_); trivial. % 30.02/30.17 (* end of lemma zenon_L774_ *) % 30.02/30.17 assert (zenon_L775_ : ((op (e3) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H40 zenon_H3d zenon_H222. % 30.02/30.17 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.17 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H222. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H1b4. % 30.02/30.17 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.17 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H26f. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H40. % 30.02/30.17 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 30.02/30.17 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.17 congruence. % 30.02/30.17 apply zenon_H1b5. apply refl_equal. % 30.02/30.17 apply zenon_H3e. apply sym_equal. exact zenon_H3d. % 30.02/30.17 apply zenon_H1b5. apply refl_equal. % 30.02/30.17 apply zenon_H1b5. apply refl_equal. % 30.02/30.17 (* end of lemma zenon_L775_ *) % 30.02/30.17 assert (zenon_L776_ : ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (op (op (e1) (e1)) (e1)))) -> False). % 30.02/30.17 do 0 intro. intros zenon_H1ba zenon_Hfd zenon_H24d. % 30.02/30.17 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 30.02/30.17 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e0) = (op (op (e1) (e1)) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H24d. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H13e. % 30.02/30.17 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 30.02/30.17 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H24e]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e2) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H24e. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H1ba. % 30.02/30.17 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.02/30.17 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 30.02/30.17 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H141. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H13e. % 30.02/30.17 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 30.02/30.17 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L77_); trivial. % 30.02/30.17 apply zenon_H13f. apply refl_equal. % 30.02/30.17 apply zenon_H13f. apply refl_equal. % 30.02/30.17 apply zenon_H1d. apply refl_equal. % 30.02/30.17 apply zenon_H13f. apply refl_equal. % 30.02/30.17 apply zenon_H13f. apply refl_equal. % 30.02/30.17 (* end of lemma zenon_L776_ *) % 30.02/30.17 assert (zenon_L777_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 30.02/30.17 do 0 intro. intros zenon_H1b9 zenon_H1ba zenon_Hfd. % 30.02/30.17 apply (zenon_notand_s _ _ ax16); [ zenon_intro zenon_H242 | zenon_intro zenon_H293 ]. % 30.02/30.17 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 30.02/30.17 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e3) = (op (op (e1) (e1)) (op (e1) (e1))))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H242. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H145. % 30.02/30.17 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 30.02/30.17 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 30.02/30.17 congruence. % 30.02/30.17 cut (((op (e2) (e2)) = (e3)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e3))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H243. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H1b9. % 30.02/30.17 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.02/30.17 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 30.02/30.17 congruence. % 30.02/30.17 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 30.02/30.17 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))))). % 30.02/30.17 intro zenon_D_pnotp. % 30.02/30.17 apply zenon_H148. % 30.02/30.17 rewrite <- zenon_D_pnotp. % 30.02/30.17 exact zenon_H145. % 30.02/30.17 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 30.02/30.17 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 30.02/30.17 congruence. % 30.02/30.17 apply (zenon_L76_); trivial. % 30.02/30.17 apply zenon_H146. apply refl_equal. % 30.02/30.17 apply zenon_H146. apply refl_equal. % 30.02/30.17 apply zenon_H2f. apply refl_equal. % 30.02/30.17 apply zenon_H146. apply refl_equal. % 30.02/30.17 apply zenon_H146. apply refl_equal. % 30.02/30.17 apply (zenon_notand_s _ _ zenon_H293); [ zenon_intro zenon_H24d | zenon_intro zenon_H149 ]. % 30.02/30.18 apply (zenon_L776_); trivial. % 30.02/30.18 apply zenon_H149. apply sym_equal. exact zenon_Hfd. % 30.02/30.18 (* end of lemma zenon_L777_ *) % 30.02/30.18 assert (zenon_L778_ : (~((op (e1) (e3)) = (op (e1) (op (e1) (e3))))) -> ((op (e1) (e3)) = (e3)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H294 zenon_H16c. % 30.02/30.18 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 30.02/30.18 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.18 congruence. % 30.02/30.18 apply zenon_H22. apply refl_equal. % 30.02/30.18 apply zenon_H16d. apply sym_equal. exact zenon_H16c. % 30.02/30.18 (* end of lemma zenon_L778_ *) % 30.02/30.18 assert (zenon_L779_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H156 zenon_H4e zenon_H16c zenon_H1c5. % 30.02/30.18 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H156. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H4e. % 30.02/30.18 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 30.02/30.18 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H295]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.02/30.18 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e3)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H295. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H183. % 30.02/30.18 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.18 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L778_); trivial. % 30.02/30.18 apply zenon_H150. apply refl_equal. % 30.02/30.18 apply zenon_H150. apply refl_equal. % 30.02/30.18 apply zenon_H1c6. apply sym_equal. exact zenon_H1c5. % 30.02/30.18 (* end of lemma zenon_L779_ *) % 30.02/30.18 assert (zenon_L780_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H40 zenon_Hfd zenon_H1ba zenon_H156 zenon_H4e zenon_H16c. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.02/30.18 apply (zenon_L332_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.02/30.18 apply (zenon_L775_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.02/30.18 apply (zenon_L777_); trivial. % 30.02/30.18 apply (zenon_L779_); trivial. % 30.02/30.18 (* end of lemma zenon_L780_ *) % 30.02/30.18 assert (zenon_L781_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H296 zenon_Hcd zenon_Hf6 zenon_H1dc zenon_H3f zenon_H69 zenon_H27 zenon_H3c zenon_He4 zenon_H74 zenon_Hd1 zenon_Hde zenon_H174 zenon_H15a zenon_H35 zenon_H18c zenon_H172 zenon_He1 zenon_H200 zenon_H19e zenon_Hfc zenon_H42 zenon_H6f zenon_H225 zenon_H159 zenon_H28f zenon_H92 zenon_H4e zenon_H156 zenon_Hfd zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H1a2 zenon_H1a5 zenon_H4a zenon_H28c zenon_H1d2 zenon_Hd6 zenon_H56 zenon_Hc9 zenon_H6b zenon_Hbd zenon_H17d zenon_H113 zenon_H14e zenon_H4c zenon_H11b zenon_H100 zenon_H20 zenon_H90 zenon_H10e zenon_H10d zenon_H48 zenon_H16f zenon_H18f zenon_Had zenon_H1a8 zenon_H2d zenon_H40. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.02/30.18 apply (zenon_L768_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.02/30.18 apply (zenon_L769_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.18 apply (zenon_L639_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.18 exact (zenon_H18f zenon_Hd2). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.18 exact (zenon_H28c zenon_H19a). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.18 apply (zenon_L771_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.18 apply (zenon_L150_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.02/30.18 apply (zenon_L748_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.02/30.18 exact (zenon_H28c zenon_H19a). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.02/30.18 exact (zenon_H56 zenon_H25). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.02/30.18 apply (zenon_L161_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.02/30.18 exact (zenon_H56 zenon_H25). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.02/30.18 apply (zenon_L552_); trivial. % 30.02/30.18 apply (zenon_L774_); trivial. % 30.02/30.18 apply (zenon_L780_); trivial. % 30.02/30.18 apply (zenon_L766_); trivial. % 30.02/30.18 (* end of lemma zenon_L781_ *) % 30.02/30.18 assert (zenon_L782_ : ((op (e1) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 30.02/30.18 do 0 intro. intros zenon_Hc3 zenon_Hfd zenon_Hde. % 30.02/30.18 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 30.02/30.18 cut (((e2) = (e2)) = ((e0) = (e2))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_Hde. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Hce. % 30.02/30.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 30.02/30.18 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e1) (e1)) = (e0)) = ((e2) = (e0))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H154. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Hc3. % 30.02/30.18 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.02/30.18 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 30.02/30.18 congruence. % 30.02/30.18 exact (zenon_H13b zenon_Hfd). % 30.02/30.18 apply zenon_H1d. apply refl_equal. % 30.02/30.18 apply zenon_H57. apply refl_equal. % 30.02/30.18 apply zenon_H57. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L782_ *) % 30.02/30.18 assert (zenon_L783_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H83 zenon_Hd9 zenon_H10e zenon_H84 zenon_H74 zenon_H4e zenon_H14f zenon_H15a. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 30.02/30.18 apply (zenon_L242_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 30.02/30.18 exact (zenon_H84 zenon_H88). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_L744_); trivial. % 30.02/30.18 (* end of lemma zenon_L783_ *) % 30.02/30.18 assert (zenon_L784_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H18c zenon_H4c zenon_Hfe zenon_Hc9. % 30.02/30.18 cut (((op (e1) (op (e1) (e2))) = (e2)) = ((op (e1) (e0)) = (op (e2) (e0)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H18c. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H4c. % 30.02/30.18 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 30.02/30.18 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H282]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.18 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e2))) = (op (e1) (e0)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H282. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H280. % 30.02/30.18 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.18 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H281]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L741_); trivial. % 30.02/30.18 apply zenon_Hd4. apply refl_equal. % 30.02/30.18 apply zenon_Hd4. apply refl_equal. % 30.02/30.18 apply zenon_Hca. apply sym_equal. exact zenon_Hc9. % 30.02/30.18 (* end of lemma zenon_L784_ *) % 30.02/30.18 assert (zenon_L785_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H172 zenon_H8b zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_Hc9 zenon_H4c zenon_H18c zenon_H83 zenon_Hd9 zenon_H10e zenon_H84 zenon_H74 zenon_H4e zenon_H15a. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.18 apply (zenon_L749_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.18 apply (zenon_L763_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.18 apply (zenon_L784_); trivial. % 30.02/30.18 apply (zenon_L783_); trivial. % 30.02/30.18 (* end of lemma zenon_L785_ *) % 30.02/30.18 assert (zenon_L786_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H92 zenon_Hcd zenon_Hde zenon_H172 zenon_H48 zenon_Had zenon_H4a zenon_H4c zenon_H18c zenon_H83 zenon_Hd9 zenon_H10e zenon_H84 zenon_H74 zenon_H4e zenon_H15a zenon_Hd1 zenon_Hfd zenon_He4 zenon_H8b zenon_H20. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.02/30.18 exact (zenon_H84 zenon_H88). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.18 apply (zenon_L48_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.18 apply (zenon_L749_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.18 apply (zenon_L782_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.18 apply (zenon_L784_); trivial. % 30.02/30.18 apply (zenon_L783_); trivial. % 30.02/30.18 apply (zenon_L288_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.18 apply (zenon_L154_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.18 apply (zenon_L785_); trivial. % 30.02/30.18 apply (zenon_L288_); trivial. % 30.02/30.18 apply (zenon_L27_); trivial. % 30.02/30.18 (* end of lemma zenon_L786_ *) % 30.02/30.18 assert (zenon_L787_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H19e zenon_Hfd zenon_H55. % 30.02/30.18 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H19e. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Hfd. % 30.02/30.18 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 30.02/30.18 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.18 congruence. % 30.02/30.18 apply zenon_Hc5. apply refl_equal. % 30.02/30.18 apply zenon_H1c2. apply sym_equal. exact zenon_H55. % 30.02/30.18 (* end of lemma zenon_L787_ *) % 30.02/30.18 assert (zenon_L788_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H172 zenon_H8b zenon_H48 zenon_Had zenon_H35 zenon_H1e zenon_Hc9 zenon_H4c zenon_H18c zenon_H4e zenon_H89 zenon_H15a. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.18 apply (zenon_L749_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.18 apply (zenon_L42_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.18 apply (zenon_L784_); trivial. % 30.02/30.18 apply (zenon_L744_); trivial. % 30.02/30.18 (* end of lemma zenon_L788_ *) % 30.02/30.18 assert (zenon_L789_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H8d zenon_H15a zenon_H4e zenon_H18c zenon_H4c zenon_H35 zenon_Had zenon_H172 zenon_H48 zenon_H156 zenon_H10e zenon_H27 zenon_H3c zenon_H1e zenon_Hde zenon_H200 zenon_He1 zenon_Hc9 zenon_H2d zenon_H8b. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.18 apply (zenon_L788_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.18 apply (zenon_L738_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.18 apply (zenon_L273_); trivial. % 30.02/30.18 apply (zenon_L25_); trivial. % 30.02/30.18 (* end of lemma zenon_L789_ *) % 30.02/30.18 assert (zenon_L790_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.02/30.18 do 0 intro. intros zenon_He4 zenon_H74 zenon_Hfd zenon_Hd1 zenon_H2d zenon_He1 zenon_H200 zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_H172 zenon_Had zenon_H35 zenon_H4c zenon_H18c zenon_H4e zenon_H15a zenon_H8d zenon_H8b zenon_Hde. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.18 apply (zenon_L154_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.18 apply (zenon_L789_); trivial. % 30.02/30.18 apply (zenon_L288_); trivial. % 30.02/30.18 (* end of lemma zenon_L790_ *) % 30.02/30.18 assert (zenon_L791_ : (((op (e2) (op (e2) (e0))) = (e0))/\(((op (e2) (op (e2) (e1))) = (e1))/\(((op (e2) (op (e2) (e2))) = (e2))/\(((op (e2) (op (e2) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0)))/\(((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3)))))))))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e1) (e1)) = (e2)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H5a zenon_H28c zenon_Hfd. % 30.02/30.18 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.02/30.18 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.02/30.18 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.02/30.18 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.02/30.18 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.02/30.18 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H13b | zenon_intro zenon_H19a ]. % 30.02/30.18 exact (zenon_H13b zenon_Hfd). % 30.02/30.18 exact (zenon_H28c zenon_H19a). % 30.02/30.18 (* end of lemma zenon_L791_ *) % 30.02/30.18 assert (zenon_L792_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e1)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H29e zenon_H88. % 30.02/30.18 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 30.02/30.18 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 30.02/30.18 congruence. % 30.02/30.18 exact (zenon_H84 zenon_H88). % 30.02/30.18 exact (zenon_H84 zenon_H88). % 30.02/30.18 (* end of lemma zenon_L792_ *) % 30.02/30.18 assert (zenon_L793_ : (~((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H29f zenon_H88. % 30.02/30.18 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.02/30.18 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 30.02/30.18 congruence. % 30.02/30.18 exact (zenon_H84 zenon_H88). % 30.02/30.18 apply zenon_H1d. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L793_ *) % 30.02/30.18 assert (zenon_L794_ : ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((e3) = (op (op (e0) (e0)) (e0)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H6e zenon_H88 zenon_H77. % 30.02/30.18 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 30.02/30.18 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e3) = (op (op (e0) (e0)) (e0)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H77. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H78. % 30.02/30.18 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 30.02/30.18 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e1) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H7a. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H6e. % 30.02/30.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.02/30.18 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 30.02/30.18 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H2a0. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H78. % 30.02/30.18 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 30.02/30.18 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H29f]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L793_); trivial. % 30.02/30.18 apply zenon_H79. apply refl_equal. % 30.02/30.18 apply zenon_H79. apply refl_equal. % 30.02/30.18 apply zenon_H2f. apply refl_equal. % 30.02/30.18 apply zenon_H79. apply refl_equal. % 30.02/30.18 apply zenon_H79. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L794_ *) % 30.02/30.18 assert (zenon_L795_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> False). % 30.02/30.18 do 0 intro. intros zenon_Hfd zenon_H6e zenon_H88. % 30.02/30.18 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_H253 | zenon_intro zenon_H2a1 ]. % 30.02/30.18 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 30.02/30.18 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e2) = (op (op (e0) (e0)) (op (e0) (e0))))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H253. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H7e. % 30.02/30.18 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 30.02/30.18 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H254]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e1) (e1)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H254. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Hfd. % 30.02/30.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 30.02/30.18 cut (((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2a2]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 30.02/30.18 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H2a2. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H7e. % 30.02/30.18 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 30.02/30.18 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H29e]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L792_); trivial. % 30.02/30.18 apply zenon_H7f. apply refl_equal. % 30.02/30.18 apply zenon_H7f. apply refl_equal. % 30.02/30.18 apply zenon_H57. apply refl_equal. % 30.02/30.18 apply zenon_H7f. apply refl_equal. % 30.02/30.18 apply zenon_H7f. apply refl_equal. % 30.02/30.18 apply (zenon_notand_s _ _ zenon_H2a1); [ zenon_intro zenon_H77 | zenon_intro zenon_H2a3 ]. % 30.02/30.18 apply (zenon_L794_); trivial. % 30.02/30.18 apply zenon_H2a3. apply sym_equal. exact zenon_H88. % 30.02/30.18 (* end of lemma zenon_L795_ *) % 30.02/30.18 assert (zenon_L796_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H83 zenon_Hd9 zenon_H10e zenon_H6e zenon_Hfd zenon_H74 zenon_H85. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 30.02/30.18 apply (zenon_L242_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 30.02/30.18 apply (zenon_L795_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 exact (zenon_H85 zenon_H89). % 30.02/30.18 (* end of lemma zenon_L796_ *) % 30.02/30.18 assert (zenon_L797_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H26 zenon_H88 zenon_Hd9. % 30.02/30.18 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H10f ]. % 30.02/30.18 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_Hd9. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H211. % 30.02/30.18 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.02/30.18 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H212. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H26. % 30.02/30.18 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2a3]. % 30.02/30.18 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.02/30.18 congruence. % 30.02/30.18 apply zenon_H10f. apply refl_equal. % 30.02/30.18 apply zenon_H2a3. apply sym_equal. exact zenon_H88. % 30.02/30.18 apply zenon_H10f. apply refl_equal. % 30.02/30.18 apply zenon_H10f. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L797_ *) % 30.02/30.18 assert (zenon_L798_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_Hb1 zenon_H95 zenon_H113. % 30.02/30.18 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H113. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Ha5. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H114. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Hb1. % 30.02/30.18 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.02/30.18 congruence. % 30.02/30.18 apply zenon_Ha6. apply refl_equal. % 30.02/30.18 apply zenon_H96. apply sym_equal. exact zenon_H95. % 30.02/30.18 apply zenon_Ha6. apply refl_equal. % 30.02/30.18 apply zenon_Ha6. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L798_ *) % 30.02/30.18 assert (zenon_L799_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_Hf4 zenon_Heb zenon_H110. % 30.02/30.18 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H110. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Ha5. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H111. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Hf4. % 30.02/30.18 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.02/30.18 congruence. % 30.02/30.18 apply zenon_Ha6. apply refl_equal. % 30.02/30.18 apply zenon_Hec. apply sym_equal. exact zenon_Heb. % 30.02/30.18 apply zenon_Ha6. apply refl_equal. % 30.02/30.18 apply zenon_Ha6. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L799_ *) % 30.02/30.18 assert (zenon_L800_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H11b zenon_H113 zenon_H95 zenon_H3f zenon_H2c zenon_Hb3 zenon_H110 zenon_Heb zenon_Hb9. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.02/30.18 apply (zenon_L798_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.02/30.18 apply (zenon_L720_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.02/30.18 apply (zenon_L799_); trivial. % 30.02/30.18 exact (zenon_Hb9 zenon_Hbc). % 30.02/30.18 (* end of lemma zenon_L800_ *) % 30.02/30.18 assert (zenon_L801_ : ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (op (op (e3) (e3)) (e3)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H17b zenon_Hb1 zenon_H22a. % 30.02/30.18 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 30.02/30.18 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e2) = (op (op (e3) (e3)) (e3)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H22a. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H131. % 30.02/30.18 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 30.02/30.18 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22b]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e0) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H22b. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H17b. % 30.02/30.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 30.02/30.18 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 30.02/30.18 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H134. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H131. % 30.02/30.18 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 30.02/30.18 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L72_); trivial. % 30.02/30.18 apply zenon_H132. apply refl_equal. % 30.02/30.18 apply zenon_H132. apply refl_equal. % 30.02/30.18 apply zenon_H57. apply refl_equal. % 30.02/30.18 apply zenon_H132. apply refl_equal. % 30.02/30.18 apply zenon_H132. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L801_ *) % 30.02/30.18 assert (zenon_L802_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (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) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H125 zenon_Hde zenon_Hfd zenon_Hfc zenon_Hcd zenon_H25 zenon_Hbd zenon_H8a zenon_H2d zenon_Hb9 zenon_H110 zenon_Hb3 zenon_H2c zenon_H3f zenon_H113 zenon_H11b zenon_H10e zenon_H10d zenon_H88 zenon_H17b. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.02/30.18 apply (zenon_L192_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.02/30.18 apply (zenon_L58_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.02/30.18 apply (zenon_L44_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.18 apply (zenon_L25_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.18 apply (zenon_L800_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.18 apply (zenon_L63_); trivial. % 30.02/30.18 apply (zenon_notand_s _ _ ax27); [ zenon_intro zenon_H2a5 | zenon_intro zenon_H2a4 ]. % 30.02/30.18 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 30.02/30.18 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (e3) (e3))))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H2a5. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H12c. % 30.02/30.18 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 30.02/30.18 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2a6]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e0) (e0)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H2a6. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H88. % 30.02/30.18 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.18 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 30.02/30.18 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H12f. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H12c. % 30.02/30.18 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 30.02/30.18 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L71_); trivial. % 30.02/30.18 apply zenon_H12d. apply refl_equal. % 30.02/30.18 apply zenon_H12d. apply refl_equal. % 30.02/30.18 apply zenon_H22. apply refl_equal. % 30.02/30.18 apply zenon_H12d. apply refl_equal. % 30.02/30.18 apply zenon_H12d. apply refl_equal. % 30.02/30.18 apply (zenon_notand_s _ _ zenon_H2a4); [ zenon_intro zenon_H22a | zenon_intro zenon_Hb2 ]. % 30.02/30.18 apply (zenon_L801_); trivial. % 30.02/30.18 apply zenon_Hb2. apply sym_equal. exact zenon_Hb1. % 30.02/30.18 (* end of lemma zenon_L802_ *) % 30.02/30.18 assert (zenon_L803_ : (~((op (e3) (e1)) = (op (e3) (op (e3) (e2))))) -> ((op (e3) (e2)) = (e1)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H2a7 zenon_H1a0. % 30.02/30.18 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 30.02/30.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.02/30.18 congruence. % 30.02/30.18 apply zenon_H2f. apply refl_equal. % 30.02/30.18 apply zenon_H1a1. apply sym_equal. exact zenon_H1a0. % 30.02/30.18 (* end of lemma zenon_L803_ *) % 30.02/30.18 assert (zenon_L804_ : ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e2)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H9b zenon_H1a0 zenon_Hfd zenon_H100. % 30.02/30.18 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.18 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e1) (e1)) = (op (e3) (e1)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H100. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H1b4. % 30.02/30.18 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.18 cut (((op (e3) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e3) (op (e3) (e2))) = (e2)) = ((op (e3) (e1)) = (op (e1) (e1)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H1b6. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H9b. % 30.02/30.18 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 30.02/30.18 cut (((op (e3) (op (e3) (e2))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a8]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.18 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (op (e3) (e2))) = (op (e3) (e1)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H2a8. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H1b4. % 30.02/30.18 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.18 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2a7]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L803_); trivial. % 30.02/30.18 apply zenon_H1b5. apply refl_equal. % 30.02/30.18 apply zenon_H1b5. apply refl_equal. % 30.02/30.18 apply zenon_H149. apply sym_equal. exact zenon_Hfd. % 30.02/30.18 apply zenon_H1b5. apply refl_equal. % 30.02/30.18 apply zenon_H1b5. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L804_ *) % 30.02/30.18 assert (zenon_L805_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H135 zenon_He1 zenon_H76 zenon_Hfd zenon_H19e zenon_Hcd zenon_H25 zenon_H17b zenon_H218. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.02/30.18 apply (zenon_L273_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.02/30.18 apply (zenon_L787_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.02/30.18 apply (zenon_L44_); trivial. % 30.02/30.18 apply (zenon_L405_); trivial. % 30.02/30.18 (* end of lemma zenon_L805_ *) % 30.02/30.18 assert (zenon_L806_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H1a2 zenon_Hd9 zenon_H88 zenon_H28c zenon_H218 zenon_H17b zenon_Hcd zenon_H19e zenon_H76 zenon_He1 zenon_H135 zenon_H9b zenon_Hfd zenon_H100. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.02/30.18 apply (zenon_L797_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.02/30.18 exact (zenon_H28c zenon_H19a). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.02/30.18 apply (zenon_L805_); trivial. % 30.02/30.18 apply (zenon_L804_); trivial. % 30.02/30.18 (* end of lemma zenon_L806_ *) % 30.02/30.18 assert (zenon_L807_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e1))) -> ((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))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H8d zenon_H85 zenon_H100 zenon_Hfd zenon_H9b zenon_H135 zenon_H19e zenon_Hcd zenon_H17b zenon_H218 zenon_H28c zenon_H88 zenon_Hd9 zenon_H1a2 zenon_He1 zenon_He2. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.18 exact (zenon_H85 zenon_H89). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.18 apply (zenon_L795_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.18 apply (zenon_L806_); trivial. % 30.02/30.18 apply (zenon_L50_); trivial. % 30.02/30.18 (* end of lemma zenon_L807_ *) % 30.02/30.18 assert (zenon_L808_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e1))) -> ((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))))) -> (~((e2) = (e3))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H225 zenon_H35 zenon_He4 zenon_Hd1 zenon_H10e zenon_H2d zenon_H74 zenon_H83 zenon_H10d zenon_H11b zenon_H113 zenon_H3f zenon_Hb3 zenon_H110 zenon_Hb9 zenon_Hbd zenon_Hfc zenon_Hde zenon_H125 zenon_H174 zenon_H8d zenon_H85 zenon_H100 zenon_Hfd zenon_H9b zenon_H135 zenon_H19e zenon_Hcd zenon_H218 zenon_H28c zenon_H88 zenon_Hd9 zenon_H1a2 zenon_He1. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.02/30.18 apply (zenon_L95_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.02/30.18 apply (zenon_L192_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.18 apply (zenon_L154_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.02/30.18 exact (zenon_H85 zenon_H89). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.18 exact (zenon_H85 zenon_H89). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.18 apply (zenon_L796_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.18 apply (zenon_L273_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.02/30.18 apply (zenon_L797_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.02/30.18 exact (zenon_H28c zenon_H19a). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.02/30.18 apply (zenon_L802_); trivial. % 30.02/30.18 apply (zenon_L804_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.02/30.18 apply (zenon_L87_); trivial. % 30.02/30.18 apply (zenon_L267_); trivial. % 30.02/30.18 apply (zenon_L807_); trivial. % 30.02/30.18 (* end of lemma zenon_L808_ *) % 30.02/30.18 assert (zenon_L809_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 30.02/30.18 do 0 intro. intros zenon_Hc8 zenon_H88 zenon_H6c. % 30.02/30.18 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_Hc8. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H88. % 30.02/30.18 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18d]. % 30.02/30.18 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.02/30.18 congruence. % 30.02/30.18 apply zenon_Hcb. apply refl_equal. % 30.02/30.18 apply zenon_H18d. apply sym_equal. exact zenon_H6c. % 30.02/30.18 (* end of lemma zenon_L809_ *) % 30.02/30.18 assert (zenon_L810_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H83 zenon_Hd9 zenon_H10e zenon_H6c zenon_Hc8 zenon_H74 zenon_H85. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 30.02/30.18 apply (zenon_L242_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 30.02/30.18 apply (zenon_L809_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 exact (zenon_H85 zenon_H89). % 30.02/30.18 (* end of lemma zenon_L810_ *) % 30.02/30.18 assert (zenon_L811_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.02/30.18 do 0 intro. intros zenon_He4 zenon_Hd1 zenon_H6f zenon_He1 zenon_H83 zenon_Hd9 zenon_H10e zenon_Hfd zenon_H74 zenon_H85 zenon_H8d zenon_H90 zenon_Hcd. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.18 apply (zenon_L154_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.18 exact (zenon_H85 zenon_H89). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.18 apply (zenon_L796_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.18 apply (zenon_L273_); trivial. % 30.02/30.18 apply (zenon_L39_); trivial. % 30.02/30.18 apply (zenon_L386_); trivial. % 30.02/30.18 (* end of lemma zenon_L811_ *) % 30.02/30.18 assert (zenon_L812_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e1))) -> ((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))))) -> (~((e2) = (e3))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H225 zenon_H35 zenon_H10e zenon_He4 zenon_H74 zenon_Hd1 zenon_Hdf zenon_Hde zenon_H8d zenon_H85 zenon_H100 zenon_Hfd zenon_H9b zenon_H135 zenon_H19e zenon_Hcd zenon_H218 zenon_H28c zenon_H88 zenon_Hd9 zenon_H1a2 zenon_He1. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.02/30.18 apply (zenon_L95_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.02/30.18 apply (zenon_L192_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.18 apply (zenon_L154_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.18 apply (zenon_L49_); trivial. % 30.02/30.18 apply (zenon_L807_); trivial. % 30.02/30.18 (* end of lemma zenon_L812_ *) % 30.02/30.18 assert (zenon_L813_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H92 zenon_H100 zenon_H9b zenon_H135 zenon_H19e zenon_H218 zenon_H28c zenon_H1a2 zenon_Hde zenon_Hdf zenon_H35 zenon_H225 zenon_Hc8 zenon_He4 zenon_Hd1 zenon_H6f zenon_He1 zenon_H83 zenon_Hd9 zenon_H10e zenon_Hfd zenon_H74 zenon_H85 zenon_H8d zenon_Hcd. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.02/30.18 apply (zenon_L812_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.02/30.18 apply (zenon_L95_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.02/30.18 apply (zenon_L192_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.18 apply (zenon_L48_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.18 apply (zenon_L49_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 30.02/30.18 apply (zenon_L242_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 30.02/30.18 apply (zenon_L807_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 exact (zenon_H85 zenon_H89). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.02/30.18 apply (zenon_L810_); trivial. % 30.02/30.18 apply (zenon_L811_); trivial. % 30.02/30.18 (* end of lemma zenon_L813_ *) % 30.02/30.18 assert (zenon_L814_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.02/30.18 do 0 intro. intros zenon_He4 zenon_Hd1 zenon_H2d zenon_He1 zenon_H83 zenon_Hd9 zenon_H10e zenon_Hfd zenon_H74 zenon_H85 zenon_H8d zenon_H8b zenon_Hde. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.18 apply (zenon_L154_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.18 exact (zenon_H85 zenon_H89). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.18 apply (zenon_L796_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.18 apply (zenon_L273_); trivial. % 30.02/30.18 apply (zenon_L25_); trivial. % 30.02/30.18 apply (zenon_L288_); trivial. % 30.02/30.18 (* end of lemma zenon_L814_ *) % 30.02/30.18 assert (zenon_L815_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e1))) -> ((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))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H225 zenon_H74 zenon_H35 zenon_Hde zenon_H10e zenon_H8d zenon_H85 zenon_H100 zenon_Hfd zenon_H9b zenon_H135 zenon_He1 zenon_H19e zenon_Hcd zenon_H218 zenon_H28c zenon_H88 zenon_Hd9 zenon_H1a2 zenon_H17d zenon_Hbc. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.02/30.18 apply (zenon_L95_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.02/30.18 apply (zenon_L192_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.18 exact (zenon_H85 zenon_H89). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.18 apply (zenon_L795_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.18 apply (zenon_L806_); trivial. % 30.02/30.18 apply (zenon_L110_); trivial. % 30.02/30.18 (* end of lemma zenon_L815_ *) % 30.02/30.18 assert (zenon_L816_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H8d zenon_H85 zenon_H74 zenon_Hfd zenon_H10e zenon_Hd9 zenon_H83 zenon_H6f zenon_H6c zenon_H17d zenon_Hbc. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.18 exact (zenon_H85 zenon_H89). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.18 apply (zenon_L796_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.18 apply (zenon_L157_); trivial. % 30.02/30.18 apply (zenon_L110_); trivial. % 30.02/30.18 (* end of lemma zenon_L816_ *) % 30.02/30.18 assert (zenon_L817_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H185 zenon_H17b zenon_Hde. % 30.02/30.18 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 30.02/30.18 cut (((e2) = (e2)) = ((e0) = (e2))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_Hde. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Hce. % 30.02/30.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 30.02/30.18 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H154. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H185. % 30.02/30.18 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.02/30.18 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 30.02/30.18 congruence. % 30.02/30.18 exact (zenon_H17c zenon_H17b). % 30.02/30.18 apply zenon_H1d. apply refl_equal. % 30.02/30.18 apply zenon_H57. apply refl_equal. % 30.02/30.18 apply zenon_H57. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L817_ *) % 30.02/30.18 assert (zenon_L818_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H65 zenon_H198 zenon_H10e zenon_He9. % 30.02/30.18 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e0)) = (op (e0) (e1)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H65. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H198. % 30.02/30.18 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 30.02/30.18 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H18b | zenon_intro zenon_Hcb ]. % 30.02/30.18 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e0)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H277. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H18b. % 30.02/30.18 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.02/30.18 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L724_); trivial. % 30.02/30.18 apply zenon_Hcb. apply refl_equal. % 30.02/30.18 apply zenon_Hcb. apply refl_equal. % 30.02/30.18 apply zenon_H153. apply sym_equal. exact zenon_He9. % 30.02/30.18 (* end of lemma zenon_L818_ *) % 30.02/30.18 assert (zenon_L819_ : ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_Hf4 zenon_H17b zenon_Ha4. % 30.02/30.18 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_Ha4. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Ha5. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_Ha7. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Hf4. % 30.02/30.18 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 30.02/30.18 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.02/30.18 congruence. % 30.02/30.18 apply zenon_Ha6. apply refl_equal. % 30.02/30.18 apply zenon_H223. apply sym_equal. exact zenon_H17b. % 30.02/30.18 apply zenon_Ha6. apply refl_equal. % 30.02/30.18 apply zenon_Ha6. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L819_ *) % 30.02/30.18 assert (zenon_L820_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H225 zenon_H74 zenon_H3c zenon_H55 zenon_Hde zenon_H10e zenon_Hf4 zenon_Ha4. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.02/30.18 apply (zenon_L88_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.02/30.18 apply (zenon_L192_); trivial. % 30.02/30.18 apply (zenon_L819_); trivial. % 30.02/30.18 (* end of lemma zenon_L820_ *) % 30.02/30.18 assert (zenon_L821_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_Hcc zenon_He1 zenon_H2a9. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.02/30.18 apply (zenon_L87_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.02/30.18 apply (zenon_L752_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.02/30.18 apply (zenon_L544_); trivial. % 30.02/30.18 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.18 (* end of lemma zenon_L821_ *) % 30.02/30.18 assert (zenon_L822_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_Ha4 zenon_Hde zenon_H3c zenon_H74 zenon_H225 zenon_H2a9 zenon_He1 zenon_H14e zenon_H4c zenon_H10e zenon_H2d zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.02/30.18 apply (zenon_L142_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.02/30.18 apply (zenon_L820_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.02/30.18 apply (zenon_L821_); trivial. % 30.02/30.18 apply (zenon_L56_); trivial. % 30.02/30.18 (* end of lemma zenon_L822_ *) % 30.02/30.18 assert (zenon_L823_ : (~((op (e1) (e1)) = (op (e1) (op (e1) (e2))))) -> ((op (e1) (e2)) = (e1)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H2aa zenon_H19a. % 30.02/30.18 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 30.02/30.18 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.18 congruence. % 30.02/30.18 apply zenon_H22. apply refl_equal. % 30.02/30.18 apply zenon_H1b2. apply sym_equal. exact zenon_H19a. % 30.02/30.18 (* end of lemma zenon_L823_ *) % 30.02/30.18 assert (zenon_L824_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H19e zenon_H4c zenon_H19a zenon_H55. % 30.02/30.18 cut (((op (e1) (op (e1) (e2))) = (e2)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H19e. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H4c. % 30.02/30.18 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 30.02/30.18 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ab]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.18 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e2))) = (op (e1) (e1)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H2ab. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_Hc4. % 30.02/30.18 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.18 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2aa]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L823_); trivial. % 30.02/30.18 apply zenon_Hc5. apply refl_equal. % 30.02/30.18 apply zenon_Hc5. apply refl_equal. % 30.02/30.18 apply zenon_H1c2. apply sym_equal. exact zenon_H55. % 30.02/30.18 (* end of lemma zenon_L824_ *) % 30.02/30.18 assert (zenon_L825_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_Hcc zenon_He1 zenon_H2a9. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.02/30.18 apply (zenon_L87_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.02/30.18 apply (zenon_L235_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.02/30.18 apply (zenon_L544_); trivial. % 30.02/30.18 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.18 (* end of lemma zenon_L825_ *) % 30.02/30.18 assert (zenon_L826_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_H4c zenon_H19e zenon_H2a9 zenon_He1 zenon_H19a zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.02/30.18 apply (zenon_L142_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.02/30.18 apply (zenon_L824_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.02/30.18 apply (zenon_L825_); trivial. % 30.02/30.18 apply (zenon_L56_); trivial. % 30.02/30.18 (* end of lemma zenon_L826_ *) % 30.02/30.18 assert (zenon_L827_ : (~((op (e1) (e2)) = (op (e1) (op (e1) (e3))))) -> ((op (e1) (e3)) = (e2)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H2ac zenon_H155. % 30.02/30.18 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 30.02/30.18 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.18 congruence. % 30.02/30.18 apply zenon_H22. apply refl_equal. % 30.02/30.18 apply zenon_H158. apply sym_equal. exact zenon_H155. % 30.02/30.18 (* end of lemma zenon_L827_ *) % 30.02/30.18 assert (zenon_L828_ : ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H4e zenon_H155 zenon_H117 zenon_H1a5. % 30.02/30.18 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 30.02/30.18 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H1a5. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H19b. % 30.02/30.18 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 30.02/30.18 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 30.02/30.18 congruence. % 30.02/30.18 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H1a6. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H4e. % 30.02/30.18 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 30.02/30.18 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 30.02/30.18 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e2)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H2ad. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H19b. % 30.02/30.18 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 30.02/30.18 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2ac]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L827_); trivial. % 30.02/30.18 apply zenon_H19c. apply refl_equal. % 30.02/30.18 apply zenon_H19c. apply refl_equal. % 30.02/30.18 apply zenon_H119. apply sym_equal. exact zenon_H117. % 30.02/30.18 apply zenon_H19c. apply refl_equal. % 30.02/30.18 apply zenon_H19c. apply refl_equal. % 30.02/30.18 (* end of lemma zenon_L828_ *) % 30.02/30.18 assert (zenon_L829_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H20e zenon_H4e zenon_H155 zenon_H1b9. % 30.02/30.18 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H20e. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H4e. % 30.02/30.18 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 30.02/30.18 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 30.02/30.18 congruence. % 30.02/30.18 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 30.02/30.18 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e2)))). % 30.02/30.18 intro zenon_D_pnotp. % 30.02/30.18 apply zenon_H2ad. % 30.02/30.18 rewrite <- zenon_D_pnotp. % 30.02/30.18 exact zenon_H19b. % 30.02/30.18 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 30.02/30.18 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2ac]. % 30.02/30.18 congruence. % 30.02/30.18 apply (zenon_L827_); trivial. % 30.02/30.18 apply zenon_H19c. apply refl_equal. % 30.02/30.18 apply zenon_H19c. apply refl_equal. % 30.02/30.18 apply zenon_H1de. apply sym_equal. exact zenon_H1b9. % 30.02/30.18 (* end of lemma zenon_L829_ *) % 30.02/30.18 assert (zenon_L830_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H1fd zenon_H1a5 zenon_Hf4 zenon_H4c zenon_H14e zenon_H155 zenon_H4e zenon_H20e zenon_H2a9. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.02/30.18 apply (zenon_L828_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.02/30.18 apply (zenon_L752_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.02/30.18 apply (zenon_L829_); trivial. % 30.02/30.18 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.18 (* end of lemma zenon_L830_ *) % 30.02/30.18 assert (zenon_L831_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H173 zenon_Hf6 zenon_H2d zenon_H10e zenon_H6f zenon_He1 zenon_H19e zenon_H18c zenon_H135 zenon_H35 zenon_He9 zenon_Hcd zenon_H19a zenon_H1fd zenon_H1a5 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H20e zenon_H2a9. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.02/30.18 apply (zenon_L826_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.02/30.18 apply (zenon_L95_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.02/30.18 apply (zenon_L159_); trivial. % 30.02/30.18 apply (zenon_L830_); trivial. % 30.02/30.18 (* end of lemma zenon_L831_ *) % 30.02/30.18 assert (zenon_L832_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H172 zenon_H8b zenon_H48 zenon_Had zenon_He9 zenon_Hc9 zenon_H4c zenon_H18c zenon_H4e zenon_H89 zenon_H15a. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.18 apply (zenon_L749_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.18 apply (zenon_L382_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.18 apply (zenon_L784_); trivial. % 30.02/30.18 apply (zenon_L744_); trivial. % 30.02/30.18 (* end of lemma zenon_L832_ *) % 30.02/30.18 assert (zenon_L833_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H225 zenon_H8b zenon_H8d zenon_H15a zenon_H4e zenon_H18c zenon_H4c zenon_Had zenon_H48 zenon_H172 zenon_H6f zenon_H68 zenon_He1 zenon_H83 zenon_Hd9 zenon_H84 zenon_H74 zenon_He7 zenon_Hcd zenon_He4 zenon_Hde zenon_H10e zenon_Hf4 zenon_Ha4. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.18 exact (zenon_H74 zenon_H73). % 30.02/30.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.18 apply (zenon_L48_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.18 apply (zenon_L832_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.18 apply (zenon_L18_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.18 apply (zenon_L273_); trivial. % 30.02/30.18 apply (zenon_L354_); trivial. % 30.02/30.18 apply (zenon_L288_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.02/30.18 apply (zenon_L192_); trivial. % 30.02/30.18 apply (zenon_L819_); trivial. % 30.02/30.18 (* end of lemma zenon_L833_ *) % 30.02/30.18 assert (zenon_L834_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H1a8 zenon_H6f zenon_H18f zenon_H1a5 zenon_H26 zenon_H4e zenon_H6e zenon_Hd1. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.18 apply (zenon_L18_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.18 exact (zenon_H18f zenon_Hd2). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.18 apply (zenon_L136_); trivial. % 30.02/30.18 apply (zenon_L729_); trivial. % 30.02/30.18 (* end of lemma zenon_L834_ *) % 30.02/30.18 assert (zenon_L835_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.02/30.18 do 0 intro. intros zenon_H8d zenon_H15a zenon_H10e zenon_H18c zenon_H4a zenon_Had zenon_H48 zenon_H172 zenon_Hd1 zenon_H4e zenon_H26 zenon_H1a5 zenon_H18f zenon_H1a8 zenon_H6f zenon_H6c zenon_H2d zenon_H8b. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.18 apply (zenon_L765_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.18 apply (zenon_L834_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.18 apply (zenon_L157_); trivial. % 30.02/30.18 apply (zenon_L25_); trivial. % 30.02/30.18 (* end of lemma zenon_L835_ *) % 30.02/30.18 assert (zenon_L836_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.02/30.18 do 0 intro. intros zenon_H92 zenon_Ha4 zenon_Hf4 zenon_Hde zenon_He4 zenon_Hcd zenon_He7 zenon_H74 zenon_H84 zenon_Hd9 zenon_H83 zenon_He1 zenon_H4c zenon_H225 zenon_H2d zenon_H6f zenon_H1a8 zenon_H18f zenon_H1a5 zenon_H26 zenon_H4e zenon_Hd1 zenon_H172 zenon_H48 zenon_Had zenon_H4a zenon_H18c zenon_H10e zenon_H15a zenon_H8d zenon_H8b zenon_H20. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.02/30.18 exact (zenon_H84 zenon_H88). % 30.02/30.18 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.02/30.18 apply (zenon_L833_); trivial. % 30.02/30.18 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.02/30.18 apply (zenon_L835_); trivial. % 30.02/30.18 apply (zenon_L27_); trivial. % 30.02/30.18 (* end of lemma zenon_L836_ *) % 30.02/30.18 assert (zenon_L837_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H8d zenon_H15a zenon_H18c zenon_H4a zenon_Had zenon_H48 zenon_H172 zenon_Hd1 zenon_H4e zenon_H26 zenon_H1a5 zenon_H18f zenon_H1a8 zenon_H6f zenon_H225 zenon_H4c zenon_He1 zenon_Hcd zenon_He4 zenon_Hde zenon_Ha4 zenon_H92 zenon_Hf4 zenon_H10d zenon_Hb8 zenon_He7 zenon_H74 zenon_H84 zenon_H10e zenon_Hd9 zenon_H83 zenon_H100 zenon_H37 zenon_H2a9 zenon_H2d. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.19 apply (zenon_L836_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.19 apply (zenon_L513_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.19 apply (zenon_L63_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.02/30.19 apply (zenon_L354_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.02/30.19 apply (zenon_L150_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.02/30.19 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.19 apply (zenon_L107_); trivial. % 30.02/30.19 (* end of lemma zenon_L837_ *) % 30.02/30.19 assert (zenon_L838_ : (~((op (e1) (e3)) = (op (e1) (op (e1) (e1))))) -> ((op (e1) (e1)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H2ae zenon_H37. % 30.02/30.19 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 30.02/30.19 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.19 congruence. % 30.02/30.19 apply zenon_H22. apply refl_equal. % 30.02/30.19 apply zenon_H38. apply sym_equal. exact zenon_H37. % 30.02/30.19 (* end of lemma zenon_L838_ *) % 30.02/30.19 assert (zenon_L839_ : ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H4a zenon_H37 zenon_H33 zenon_H16a. % 30.02/30.19 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H16a. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H183. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 30.02/30.19 congruence. % 30.02/30.19 cut (((op (e1) (op (e1) (e1))) = (e1)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H184. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H4a. % 30.02/30.19 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 30.02/30.19 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2af]. % 30.02/30.19 congruence. % 30.02/30.19 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (op (e1) (e1))) = (op (e1) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H2af. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H183. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2ae]. % 30.02/30.19 congruence. % 30.02/30.19 apply (zenon_L838_); trivial. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 apply zenon_H34. apply sym_equal. exact zenon_H33. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 (* end of lemma zenon_L839_ *) % 30.02/30.19 assert (zenon_L840_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H2b0 zenon_H19a zenon_H182. % 30.02/30.19 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H2b0. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H19a. % 30.02/30.19 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 30.02/30.19 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 30.02/30.19 congruence. % 30.02/30.19 apply zenon_H19c. apply refl_equal. % 30.02/30.19 apply zenon_H1a7. apply sym_equal. exact zenon_H182. % 30.02/30.19 (* end of lemma zenon_L840_ *) % 30.02/30.19 assert (zenon_L841_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H156 zenon_H4a zenon_H37 zenon_H1e5. % 30.02/30.19 cut (((op (e1) (op (e1) (e1))) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H156. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H4a. % 30.02/30.19 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 30.02/30.19 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2af]. % 30.02/30.19 congruence. % 30.02/30.19 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (op (e1) (e1))) = (op (e1) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H2af. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H183. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2ae]. % 30.02/30.19 congruence. % 30.02/30.19 apply (zenon_L838_); trivial. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 apply zenon_H205. apply sym_equal. exact zenon_H1e5. % 30.02/30.19 (* end of lemma zenon_L841_ *) % 30.02/30.19 assert (zenon_L842_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H2b1 zenon_H16a zenon_H19a zenon_H2b0 zenon_H37 zenon_H4a zenon_H156 zenon_H1ab. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.02/30.19 apply (zenon_L839_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.02/30.19 apply (zenon_L840_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.02/30.19 apply (zenon_L841_); trivial. % 30.02/30.19 exact (zenon_H1ab zenon_H112). % 30.02/30.19 (* end of lemma zenon_L842_ *) % 30.02/30.19 assert (zenon_L843_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H172 zenon_H8b zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_Hc9 zenon_H4c zenon_H18c zenon_H4e zenon_H89 zenon_H15a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.19 apply (zenon_L749_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.19 apply (zenon_L763_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.19 apply (zenon_L784_); trivial. % 30.02/30.19 apply (zenon_L744_); trivial. % 30.02/30.19 (* end of lemma zenon_L843_ *) % 30.02/30.19 assert (zenon_L844_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H8d zenon_H15a zenon_H18c zenon_H4c zenon_H4a zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_Hd1 zenon_H182 zenon_H4e zenon_He1 zenon_Hc9 zenon_H2d zenon_H8b. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.19 apply (zenon_L843_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.19 apply (zenon_L729_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.19 apply (zenon_L273_); trivial. % 30.02/30.19 apply (zenon_L25_); trivial. % 30.02/30.19 (* end of lemma zenon_L844_ *) % 30.02/30.19 assert (zenon_L845_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H1c5 zenon_H108 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.02/30.19 apply (zenon_L87_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.02/30.19 apply (zenon_L171_); trivial. % 30.02/30.19 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.19 (* end of lemma zenon_L845_ *) % 30.02/30.19 assert (zenon_L846_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H1a2 zenon_H100 zenon_H83 zenon_Hd9 zenon_H84 zenon_H74 zenon_He7 zenon_Hb8 zenon_H92 zenon_Ha4 zenon_Hde zenon_He4 zenon_Hcd zenon_H225 zenon_H6f zenon_H1a8 zenon_H18f zenon_H1a5 zenon_H20 zenon_H1ab zenon_H156 zenon_H2b0 zenon_H16a zenon_H2b1 zenon_H56 zenon_H1d5 zenon_H19e zenon_H10d zenon_H37 zenon_H8d zenon_H15a zenon_H18c zenon_H4a zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_Hd1 zenon_H182 zenon_H4e zenon_He1 zenon_Hc9 zenon_Hbd zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.02/30.19 apply (zenon_L837_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.02/30.19 apply (zenon_L842_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.02/30.19 exact (zenon_H56 zenon_H25). % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.02/30.19 apply (zenon_L273_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.02/30.19 apply (zenon_L131_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.19 apply (zenon_L844_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.19 apply (zenon_L513_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.19 apply (zenon_L63_); trivial. % 30.02/30.19 apply (zenon_L751_); trivial. % 30.02/30.19 apply (zenon_L845_); trivial. % 30.02/30.19 (* end of lemma zenon_L846_ *) % 30.02/30.19 assert (zenon_L847_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_Hf4 zenon_He2 zenon_H17d. % 30.02/30.19 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.02/30.19 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H17d. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_Ha5. % 30.02/30.19 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.02/30.19 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H292]. % 30.02/30.19 congruence. % 30.02/30.19 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H292. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_Hf4. % 30.02/30.19 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 30.02/30.19 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.02/30.19 congruence. % 30.02/30.19 apply zenon_Ha6. apply refl_equal. % 30.02/30.19 apply zenon_He8. apply sym_equal. exact zenon_He2. % 30.02/30.19 apply zenon_Ha6. apply refl_equal. % 30.02/30.19 apply zenon_Ha6. apply refl_equal. % 30.02/30.19 (* end of lemma zenon_L847_ *) % 30.02/30.19 assert (zenon_L848_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H185 zenon_H16b zenon_H2d. % 30.02/30.19 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 30.02/30.19 cut (((e3) = (e3)) = ((e0) = (e3))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H2d. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H2e. % 30.02/30.19 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.02/30.19 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 30.02/30.19 congruence. % 30.02/30.19 cut (((op (e0) (e3)) = (e0)) = ((e3) = (e0))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H30. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H185. % 30.02/30.19 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.02/30.19 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H224]. % 30.02/30.19 congruence. % 30.02/30.19 exact (zenon_H224 zenon_H16b). % 30.02/30.19 apply zenon_H1d. apply refl_equal. % 30.02/30.19 apply zenon_H2f. apply refl_equal. % 30.02/30.19 apply zenon_H2f. apply refl_equal. % 30.02/30.19 (* end of lemma zenon_L848_ *) % 30.02/30.19 assert (zenon_L849_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H2b4 zenon_H2d zenon_H16b zenon_H15a zenon_H4e zenon_H74 zenon_H84 zenon_H10e zenon_Hd9 zenon_H83 zenon_H6e zenon_H48 zenon_H156 zenon_H95 zenon_H113. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.02/30.19 apply (zenon_L848_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.02/30.19 apply (zenon_L783_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.02/30.19 apply (zenon_L737_); trivial. % 30.02/30.19 apply (zenon_L798_); trivial. % 30.02/30.19 (* end of lemma zenon_L849_ *) % 30.02/30.19 assert (zenon_L850_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_Hbd zenon_H69 zenon_Had zenon_H113 zenon_H156 zenon_H83 zenon_Hd9 zenon_H84 zenon_H74 zenon_H4e zenon_H15a zenon_H16b zenon_H2d zenon_H2b4 zenon_H10e zenon_H10d zenon_H14e zenon_H48 zenon_H6e. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.19 apply (zenon_L749_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.19 apply (zenon_L849_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.19 apply (zenon_L63_); trivial. % 30.02/30.19 apply (zenon_L770_); trivial. % 30.02/30.19 (* end of lemma zenon_L850_ *) % 30.02/30.19 assert (zenon_L851_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H8d zenon_Hf4 zenon_H48 zenon_H14e zenon_H10d zenon_H10e zenon_H2b4 zenon_H2d zenon_H16b zenon_H15a zenon_H4e zenon_H74 zenon_H84 zenon_Hd9 zenon_H83 zenon_H156 zenon_H113 zenon_Had zenon_H69 zenon_Hbd zenon_He1 zenon_Hc9 zenon_H6f zenon_H90. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.19 apply (zenon_L538_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.19 apply (zenon_L850_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.19 apply (zenon_L273_); trivial. % 30.02/30.19 apply (zenon_L39_); trivial. % 30.02/30.19 (* end of lemma zenon_L851_ *) % 30.02/30.19 assert (zenon_L852_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_He4 zenon_Hf6 zenon_H1fd zenon_H2d zenon_H10e zenon_H4c zenon_H14e zenon_He1 zenon_H2a9 zenon_H225 zenon_H74 zenon_H3c zenon_Ha4 zenon_H18c zenon_H135 zenon_Hdf zenon_Hde zenon_Hf4 zenon_H17d. % 30.02/30.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.19 exact (zenon_H74 zenon_H73). % 30.02/30.19 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.19 apply (zenon_L822_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.19 apply (zenon_L49_); trivial. % 30.02/30.19 apply (zenon_L847_); trivial. % 30.02/30.19 (* end of lemma zenon_L852_ *) % 30.02/30.19 assert (zenon_L853_ : (((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 (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H2b7 zenon_H8b zenon_Hb5 zenon_H19a zenon_Hee zenon_H110 zenon_Hf4 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.02/30.19 apply (zenon_L297_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.02/30.19 apply (zenon_L337_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.02/30.19 apply (zenon_L799_); trivial. % 30.02/30.19 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.19 (* end of lemma zenon_L853_ *) % 30.02/30.19 assert (zenon_L854_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H1a8 zenon_Hcd zenon_Hdc zenon_H18f zenon_H2a9 zenon_Hf4 zenon_H110 zenon_Hee zenon_Hb5 zenon_H8b zenon_H2b7 zenon_H20 zenon_H14f. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.19 apply (zenon_L48_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.19 exact (zenon_H18f zenon_Hd2). % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.19 apply (zenon_L853_); trivial. % 30.02/30.19 apply (zenon_L658_); trivial. % 30.02/30.19 (* end of lemma zenon_L854_ *) % 30.02/30.19 assert (zenon_L855_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H172 zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_H18c zenon_H10e zenon_H1a5 zenon_H1a8 zenon_Hcd zenon_Hdc zenon_H18f zenon_H2a9 zenon_Hf4 zenon_H110 zenon_Hee zenon_Hb5 zenon_H8b zenon_H2b7 zenon_H20. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.19 apply (zenon_L749_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.19 apply (zenon_L763_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.19 apply (zenon_L764_); trivial. % 30.02/30.19 apply (zenon_L854_); trivial. % 30.02/30.19 (* end of lemma zenon_L855_ *) % 30.02/30.19 assert (zenon_L856_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H1fd zenon_H1a5 zenon_H155 zenon_H4e zenon_Hf4 zenon_H4c zenon_H14e zenon_H1c5 zenon_H108 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.02/30.19 apply (zenon_L828_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.02/30.19 apply (zenon_L171_); trivial. % 30.02/30.19 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.19 (* end of lemma zenon_L856_ *) % 30.02/30.19 assert (zenon_L857_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H40 zenon_H20e zenon_H1fd zenon_H1a5 zenon_H155 zenon_H4e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.02/30.19 apply (zenon_L332_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.02/30.19 apply (zenon_L775_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.02/30.19 apply (zenon_L829_); trivial. % 30.02/30.19 apply (zenon_L856_); trivial. % 30.02/30.19 (* end of lemma zenon_L857_ *) % 30.02/30.19 assert (zenon_L858_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e1)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H16f zenon_Hd1 zenon_H100 zenon_H40 zenon_Hf4 zenon_H4c zenon_H14e zenon_H159 zenon_H4e zenon_H182. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.19 apply (zenon_L729_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.19 apply (zenon_L150_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_L733_); trivial. % 30.02/30.19 (* end of lemma zenon_L858_ *) % 30.02/30.19 assert (zenon_L859_ : ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H4e zenon_H16c zenon_H16b zenon_H16a. % 30.02/30.19 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H16a. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H183. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 30.02/30.19 congruence. % 30.02/30.19 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H184. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H4e. % 30.02/30.19 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 30.02/30.19 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H295]. % 30.02/30.19 congruence. % 30.02/30.19 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H295. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H183. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 30.02/30.19 congruence. % 30.02/30.19 apply (zenon_L778_); trivial. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 apply zenon_H21a. apply sym_equal. exact zenon_H16b. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 (* end of lemma zenon_L859_ *) % 30.02/30.19 assert (zenon_L860_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H16f zenon_H89 zenon_H15a zenon_H100 zenon_H40 zenon_H6f zenon_H19a zenon_H4e zenon_H16b zenon_H16a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.19 apply (zenon_L241_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.19 apply (zenon_L150_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.19 apply (zenon_L235_); trivial. % 30.02/30.19 apply (zenon_L859_); trivial. % 30.02/30.19 (* end of lemma zenon_L860_ *) % 30.02/30.19 assert (zenon_L861_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H172 zenon_H6e zenon_H48 zenon_H14e zenon_H10d zenon_H2b4 zenon_H2d zenon_H16b zenon_H156 zenon_H113 zenon_Had zenon_Hbd zenon_H6c zenon_H4a zenon_H18c zenon_H1a5 zenon_H83 zenon_Hd9 zenon_H10e zenon_H84 zenon_H74 zenon_H4e zenon_H15a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.19 apply (zenon_L850_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.19 apply (zenon_L763_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.19 apply (zenon_L764_); trivial. % 30.02/30.19 apply (zenon_L783_); trivial. % 30.02/30.19 (* end of lemma zenon_L861_ *) % 30.02/30.19 assert (zenon_L862_ : ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H40 zenon_H8a zenon_H97. % 30.02/30.19 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.02/30.19 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (e0)) = (op (e3) (e1)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H97. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H1b4. % 30.02/30.19 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.19 cut (((op (e3) (e1)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2ba]. % 30.02/30.19 congruence. % 30.02/30.19 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e0)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H2ba. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H40. % 30.02/30.19 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 30.02/30.19 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.02/30.19 congruence. % 30.02/30.19 apply zenon_H1b5. apply refl_equal. % 30.02/30.19 apply zenon_H1e3. apply sym_equal. exact zenon_H8a. % 30.02/30.19 apply zenon_H1b5. apply refl_equal. % 30.02/30.19 apply zenon_H1b5. apply refl_equal. % 30.02/30.19 (* end of lemma zenon_L862_ *) % 30.02/30.19 assert (zenon_L863_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H8d zenon_H159 zenon_H4c zenon_Hf4 zenon_H100 zenon_Hd1 zenon_H16f zenon_H16a zenon_H18f zenon_H1a8 zenon_H15a zenon_H4e zenon_H74 zenon_H84 zenon_H10e zenon_Hd9 zenon_H83 zenon_H1a5 zenon_H18c zenon_H4a zenon_Hbd zenon_Had zenon_H113 zenon_H156 zenon_H16b zenon_H2d zenon_H2b4 zenon_H10d zenon_H14e zenon_H48 zenon_H172 zenon_H6f zenon_H6c zenon_H40 zenon_H97. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.19 apply (zenon_L120_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.19 exact (zenon_H18f zenon_Hd2). % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.19 apply (zenon_L860_); trivial. % 30.02/30.19 apply (zenon_L858_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.19 apply (zenon_L861_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.19 apply (zenon_L157_); trivial. % 30.02/30.19 apply (zenon_L862_); trivial. % 30.02/30.19 (* end of lemma zenon_L863_ *) % 30.02/30.19 assert (zenon_L864_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H18c zenon_H4e zenon_H14f zenon_H76. % 30.02/30.19 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e0)) = (op (e2) (e0)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H18c. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H4e. % 30.02/30.19 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 30.02/30.19 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 30.02/30.19 congruence. % 30.02/30.19 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.19 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e0)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H286. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H280. % 30.02/30.19 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.19 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H283]. % 30.02/30.19 congruence. % 30.02/30.19 apply (zenon_L743_); trivial. % 30.02/30.19 apply zenon_Hd4. apply refl_equal. % 30.02/30.19 apply zenon_Hd4. apply refl_equal. % 30.02/30.19 apply zenon_H1da. apply sym_equal. exact zenon_H76. % 30.02/30.19 (* end of lemma zenon_L864_ *) % 30.02/30.19 assert (zenon_L865_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H2b4 zenon_H2d zenon_H16b zenon_H76 zenon_H4e zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H6e. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.02/30.19 apply (zenon_L848_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.02/30.19 apply (zenon_L864_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.02/30.19 apply (zenon_L737_); trivial. % 30.02/30.19 apply (zenon_L770_); trivial. % 30.02/30.19 (* end of lemma zenon_L865_ *) % 30.02/30.19 assert (zenon_L866_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H16f zenon_H48 zenon_H156 zenon_H18c zenon_H76 zenon_H2d zenon_H2b4 zenon_H100 zenon_H40 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.19 apply (zenon_L865_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.19 apply (zenon_L150_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_L859_); trivial. % 30.02/30.19 (* end of lemma zenon_L866_ *) % 30.02/30.19 assert (zenon_L867_ : (~((op (e1) (e1)) = (op (e1) (op (e1) (e1))))) -> ((op (e1) (e1)) = (e1)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H2bb zenon_Hd2. % 30.02/30.19 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 30.02/30.19 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.19 congruence. % 30.02/30.19 apply zenon_H22. apply refl_equal. % 30.02/30.19 apply zenon_Hd3. apply sym_equal. exact zenon_Hd2. % 30.02/30.19 (* end of lemma zenon_L867_ *) % 30.02/30.19 assert (zenon_L868_ : ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H4a zenon_Hd2 zenon_H1f zenon_H35. % 30.02/30.19 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H35. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_Hc4. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 30.02/30.19 congruence. % 30.02/30.19 cut (((op (e1) (op (e1) (e1))) = (e1)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_Hc6. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H4a. % 30.02/30.19 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 30.02/30.19 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2bc]. % 30.02/30.19 congruence. % 30.02/30.19 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e1))) = (op (e1) (e1)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H2bc. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_Hc4. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 30.02/30.19 congruence. % 30.02/30.19 apply (zenon_L867_); trivial. % 30.02/30.19 apply zenon_Hc5. apply refl_equal. % 30.02/30.19 apply zenon_Hc5. apply refl_equal. % 30.02/30.19 apply zenon_H20b. apply sym_equal. exact zenon_H1f. % 30.02/30.19 apply zenon_Hc5. apply refl_equal. % 30.02/30.19 apply zenon_Hc5. apply refl_equal. % 30.02/30.19 (* end of lemma zenon_L868_ *) % 30.02/30.19 assert (zenon_L869_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 30.02/30.19 do 0 intro. intros zenon_Ha4 zenon_H185 zenon_Hb1. % 30.02/30.19 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_Ha4. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H185. % 30.02/30.19 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 30.02/30.19 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.02/30.19 congruence. % 30.02/30.19 apply zenon_H16e. apply refl_equal. % 30.02/30.19 apply zenon_Hb2. apply sym_equal. exact zenon_Hb1. % 30.02/30.19 (* end of lemma zenon_L869_ *) % 30.02/30.19 assert (zenon_L870_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H218 zenon_H33 zenon_H1e5. % 30.02/30.19 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H218. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H33. % 30.02/30.19 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 30.02/30.19 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.02/30.19 congruence. % 30.02/30.19 apply zenon_H16e. apply refl_equal. % 30.02/30.19 apply zenon_H205. apply sym_equal. exact zenon_H1e5. % 30.02/30.19 (* end of lemma zenon_L870_ *) % 30.02/30.19 assert (zenon_L871_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_H33 zenon_H218 zenon_Hf6 zenon_Hf4 zenon_H156 zenon_H4e zenon_H16c. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.02/30.19 apply (zenon_L690_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.02/30.19 apply (zenon_L870_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.02/30.19 apply (zenon_L56_); trivial. % 30.02/30.19 apply (zenon_L779_); trivial. % 30.02/30.19 (* end of lemma zenon_L871_ *) % 30.02/30.19 assert (zenon_L872_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H159 zenon_H4a zenon_Hd2 zenon_H182. % 30.02/30.19 cut (((op (e1) (op (e1) (e1))) = (e1)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H159. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H4a. % 30.02/30.19 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 30.02/30.19 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2bc]. % 30.02/30.19 congruence. % 30.02/30.19 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e1))) = (op (e1) (e1)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H2bc. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_Hc4. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 30.02/30.19 congruence. % 30.02/30.19 apply (zenon_L867_); trivial. % 30.02/30.19 apply zenon_Hc5. apply refl_equal. % 30.02/30.19 apply zenon_Hc5. apply refl_equal. % 30.02/30.19 apply zenon_H1a7. apply sym_equal. exact zenon_H182. % 30.02/30.19 (* end of lemma zenon_L872_ *) % 30.02/30.19 assert (zenon_L873_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H256 zenon_H15a zenon_H89 zenon_Hd2 zenon_H4a zenon_H159 zenon_H1b9 zenon_H20e zenon_H4e zenon_H16b zenon_H16a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 30.02/30.19 apply (zenon_L744_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 30.02/30.19 apply (zenon_L872_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 30.02/30.19 apply (zenon_L829_); trivial. % 30.02/30.19 apply (zenon_L859_); trivial. % 30.02/30.19 (* end of lemma zenon_L873_ *) % 30.02/30.19 assert (zenon_L874_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (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 (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_Hbd zenon_H1a5 zenon_H18c zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_H40 zenon_H2d zenon_H10e zenon_H10d zenon_H2bd zenon_H16c zenon_H156 zenon_Hf6 zenon_H218 zenon_H1e6 zenon_Ha4 zenon_Hf4 zenon_H256 zenon_H15a zenon_H89 zenon_Hd2 zenon_H4a zenon_H159 zenon_H1b9 zenon_H20e zenon_H4e zenon_H16a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.19 apply (zenon_L765_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.19 apply (zenon_L766_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.19 apply (zenon_L63_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H185 | zenon_intro zenon_H2be ]. % 30.02/30.19 apply (zenon_L869_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H33 | zenon_intro zenon_H2bf ]. % 30.02/30.19 apply (zenon_L871_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H17b | zenon_intro zenon_H16b ]. % 30.02/30.19 apply (zenon_L819_); trivial. % 30.02/30.19 apply (zenon_L873_); trivial. % 30.02/30.19 (* end of lemma zenon_L874_ *) % 30.02/30.19 assert (zenon_L875_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H14e zenon_H4e zenon_H16c zenon_Hbc. % 30.02/30.19 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H14e. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H4e. % 30.02/30.19 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 30.02/30.19 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H295]. % 30.02/30.19 congruence. % 30.02/30.19 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H295. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H183. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.19 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 30.02/30.19 congruence. % 30.02/30.19 apply (zenon_L778_); trivial. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 apply zenon_H150. apply refl_equal. % 30.02/30.19 apply zenon_H17e. apply sym_equal. exact zenon_Hbc. % 30.02/30.19 (* end of lemma zenon_L875_ *) % 30.02/30.19 assert (zenon_L876_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_Hb8 zenon_He7 zenon_H74 zenon_H84 zenon_Hd9 zenon_H83 zenon_H16a zenon_H20e zenon_H1b9 zenon_H159 zenon_H4a zenon_Hd2 zenon_H89 zenon_H15a zenon_H256 zenon_Hf4 zenon_Ha4 zenon_H1e6 zenon_H218 zenon_Hf6 zenon_H156 zenon_H2bd zenon_H10d zenon_H10e zenon_H2d zenon_H172 zenon_H48 zenon_Had zenon_H6c zenon_H18c zenon_H1a5 zenon_Hbd zenon_H2a9 zenon_H14e zenon_H4e zenon_H16c. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.02/30.19 apply (zenon_L354_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.02/30.19 apply (zenon_L874_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.02/30.19 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.19 apply (zenon_L875_); trivial. % 30.02/30.19 (* end of lemma zenon_L876_ *) % 30.02/30.19 assert (zenon_L877_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_Hb8 zenon_He7 zenon_H89 zenon_H222 zenon_H3d zenon_H1a0 zenon_H6f zenon_H14e zenon_H4e zenon_H16c. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.02/30.19 apply (zenon_L199_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.02/30.19 apply (zenon_L775_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.02/30.19 apply (zenon_L540_); trivial. % 30.02/30.19 apply (zenon_L875_); trivial. % 30.02/30.19 (* end of lemma zenon_L877_ *) % 30.02/30.19 assert (zenon_L878_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H1a2 zenon_Hfc zenon_H56 zenon_H1d5 zenon_Hc8 zenon_H6f zenon_H222 zenon_H16c zenon_H4e zenon_Hbd zenon_H1a5 zenon_H18c zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_H10d zenon_H2bd zenon_H156 zenon_Hf6 zenon_H218 zenon_H1e6 zenon_Ha4 zenon_H256 zenon_H15a zenon_H89 zenon_Hd2 zenon_H4a zenon_H159 zenon_H20e zenon_H16a zenon_H83 zenon_Hd9 zenon_H84 zenon_H74 zenon_He7 zenon_Hb8 zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.02/30.19 apply (zenon_L598_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.02/30.19 apply (zenon_L876_); trivial. % 30.02/30.19 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.02/30.19 apply (zenon_L130_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.02/30.19 exact (zenon_H56 zenon_H25). % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.02/30.19 apply (zenon_L332_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.02/30.19 apply (zenon_L877_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.02/30.19 apply (zenon_L876_); trivial. % 30.02/30.19 apply (zenon_L845_); trivial. % 30.02/30.19 (* end of lemma zenon_L878_ *) % 30.02/30.19 assert (zenon_L879_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H16f zenon_H1a2 zenon_Hfc zenon_H56 zenon_H1d5 zenon_Hc8 zenon_H6f zenon_H222 zenon_H4e zenon_Hbd zenon_H1a5 zenon_H18c zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_H10d zenon_H2bd zenon_H156 zenon_Hf6 zenon_H218 zenon_H1e6 zenon_Ha4 zenon_H256 zenon_H15a zenon_H89 zenon_Hd2 zenon_H4a zenon_H159 zenon_H20e zenon_H16a zenon_H83 zenon_Hd9 zenon_H84 zenon_H74 zenon_He7 zenon_Hb8 zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.19 apply (zenon_L241_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.19 apply (zenon_L125_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_L878_); trivial. % 30.02/30.19 (* end of lemma zenon_L879_ *) % 30.02/30.19 assert (zenon_L880_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H100 zenon_H4a zenon_Hd2 zenon_H98. % 30.02/30.19 cut (((op (e1) (op (e1) (e1))) = (e1)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H100. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H4a. % 30.02/30.19 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 30.02/30.19 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2bc]. % 30.02/30.19 congruence. % 30.02/30.19 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e1))) = (op (e1) (e1)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H2bc. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_Hc4. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.02/30.19 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 30.02/30.19 congruence. % 30.02/30.19 apply (zenon_L867_); trivial. % 30.02/30.19 apply zenon_Hc5. apply refl_equal. % 30.02/30.19 apply zenon_Hc5. apply refl_equal. % 30.02/30.19 apply zenon_H99. apply sym_equal. exact zenon_H98. % 30.02/30.19 (* end of lemma zenon_L880_ *) % 30.02/30.19 assert (zenon_L881_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H23b zenon_H20 zenon_H8b zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.02/30.19 apply (zenon_L27_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.02/30.19 apply (zenon_L880_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.02/30.19 apply (zenon_L699_); trivial. % 30.02/30.19 exact (zenon_H1ab zenon_H112). % 30.02/30.19 (* end of lemma zenon_L881_ *) % 30.02/30.19 assert (zenon_L882_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H1e6 zenon_H6e zenon_H48 zenon_H156 zenon_H33 zenon_H218 zenon_Hc9 zenon_H20d zenon_H108 zenon_H1b9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.02/30.19 apply (zenon_L737_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.02/30.19 apply (zenon_L870_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.02/30.19 apply (zenon_L627_); trivial. % 30.02/30.19 apply (zenon_L171_); trivial. % 30.02/30.19 (* end of lemma zenon_L882_ *) % 30.02/30.19 assert (zenon_L883_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H20d zenon_Hc9 zenon_H218 zenon_H33 zenon_H156 zenon_H48 zenon_H6e zenon_H1e6 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.02/30.19 apply (zenon_L87_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.02/30.19 apply (zenon_L882_); trivial. % 30.02/30.19 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.19 (* end of lemma zenon_L883_ *) % 30.02/30.19 assert (zenon_L884_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.02/30.19 do 0 intro. intros zenon_He4 zenon_Hf6 zenon_H225 zenon_H74 zenon_H3c zenon_Ha4 zenon_H135 zenon_H2d zenon_He1 zenon_H1fd zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H20d zenon_H218 zenon_H33 zenon_H156 zenon_H48 zenon_H1e6 zenon_H2a9 zenon_H172 zenon_Had zenon_H6c zenon_H4a zenon_H18c zenon_H1a5 zenon_H4e zenon_H15a zenon_H8d zenon_H8b zenon_Hde. % 30.02/30.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.19 exact (zenon_H74 zenon_H73). % 30.02/30.19 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.19 apply (zenon_L822_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.19 apply (zenon_L765_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.19 apply (zenon_L883_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.19 apply (zenon_L273_); trivial. % 30.02/30.19 apply (zenon_L25_); trivial. % 30.02/30.19 apply (zenon_L288_); trivial. % 30.02/30.19 (* end of lemma zenon_L884_ *) % 30.02/30.19 assert (zenon_L885_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.02/30.19 do 0 intro. intros zenon_Hc0 zenon_H35 zenon_H1ab zenon_H10d zenon_H100 zenon_H23b zenon_H92 zenon_H84 zenon_Hd2 zenon_Hd1 zenon_Hde zenon_H8d zenon_H15a zenon_H4e zenon_H1a5 zenon_H18c zenon_H4a zenon_Had zenon_H172 zenon_H2a9 zenon_H1e6 zenon_H48 zenon_H156 zenon_H218 zenon_H20d zenon_H108 zenon_H14e zenon_H4c zenon_Hf4 zenon_H10e zenon_H1fd zenon_He1 zenon_H2d zenon_H135 zenon_Ha4 zenon_H3c zenon_H74 zenon_H225 zenon_Hf6 zenon_He4 zenon_H8b zenon_H20. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.02/30.19 exact (zenon_H84 zenon_H88). % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.02/30.19 apply (zenon_L868_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.02/30.19 apply (zenon_L881_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.02/30.19 exact (zenon_H84 zenon_H88). % 30.02/30.19 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.02/30.19 apply (zenon_L45_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.02/30.19 apply (zenon_L884_); trivial. % 30.02/30.19 apply (zenon_L27_); trivial. % 30.02/30.19 (* end of lemma zenon_L885_ *) % 30.02/30.19 assert (zenon_L886_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H16a zenon_H185 zenon_H14f. % 30.02/30.19 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 30.02/30.19 intro zenon_D_pnotp. % 30.02/30.19 apply zenon_H16a. % 30.02/30.19 rewrite <- zenon_D_pnotp. % 30.02/30.19 exact zenon_H185. % 30.02/30.19 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H284]. % 30.02/30.19 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.02/30.19 congruence. % 30.02/30.19 apply zenon_H16e. apply refl_equal. % 30.02/30.19 apply zenon_H284. apply sym_equal. exact zenon_H14f. % 30.02/30.19 (* end of lemma zenon_L886_ *) % 30.02/30.19 assert (zenon_L887_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_Hf4 zenon_H14e zenon_H4e zenon_Hbc. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 30.02/30.19 apply (zenon_L886_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 30.02/30.19 apply (zenon_L730_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 30.02/30.19 apply (zenon_L525_); trivial. % 30.02/30.19 apply (zenon_L875_); trivial. % 30.02/30.19 (* end of lemma zenon_L887_ *) % 30.02/30.19 assert (zenon_L888_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_Hb8 zenon_Had zenon_H6e zenon_H95 zenon_H2d zenon_H1dc zenon_H1b9 zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_Hf4 zenon_H14e zenon_H4e. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.02/30.19 apply (zenon_L34_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.02/30.19 apply (zenon_L766_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.02/30.19 apply (zenon_L200_); trivial. % 30.02/30.19 apply (zenon_L887_); trivial. % 30.02/30.19 (* end of lemma zenon_L888_ *) % 30.02/30.19 assert (zenon_L889_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H2b4 zenon_H14e zenon_Hf4 zenon_H2c zenon_H35 zenon_H16a zenon_H256 zenon_H1b9 zenon_H1dc zenon_H2d zenon_Had zenon_Hb8 zenon_H15a zenon_H4e zenon_H74 zenon_H84 zenon_H10e zenon_Hd9 zenon_H83 zenon_H6e zenon_H48 zenon_H156 zenon_H95 zenon_H113. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.02/30.19 apply (zenon_L888_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.02/30.19 apply (zenon_L783_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.02/30.19 apply (zenon_L737_); trivial. % 30.02/30.19 apply (zenon_L798_); trivial. % 30.02/30.19 (* end of lemma zenon_L889_ *) % 30.02/30.19 assert (zenon_L890_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (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) (e2)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (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) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_Hbd zenon_H20 zenon_He4 zenon_Hf6 zenon_H225 zenon_H3c zenon_Ha4 zenon_H135 zenon_He1 zenon_H1fd zenon_H4c zenon_H108 zenon_H20d zenon_H218 zenon_H1e6 zenon_H2a9 zenon_H172 zenon_H4a zenon_H18c zenon_H1a5 zenon_H8d zenon_Hde zenon_Hd1 zenon_Hd2 zenon_H92 zenon_H23b zenon_H100 zenon_H1ab zenon_Hc0 zenon_H113 zenon_H156 zenon_H83 zenon_Hd9 zenon_H84 zenon_H74 zenon_H4e zenon_H15a zenon_Hb8 zenon_Had zenon_H2d zenon_H1dc zenon_H1b9 zenon_H256 zenon_H16a zenon_H35 zenon_H2c zenon_Hf4 zenon_H2b4 zenon_H10e zenon_H10d zenon_H14e zenon_H48 zenon_H6e. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.19 apply (zenon_L885_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.19 apply (zenon_L889_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.19 apply (zenon_L63_); trivial. % 30.02/30.19 apply (zenon_L770_); trivial. % 30.02/30.19 (* end of lemma zenon_L890_ *) % 30.02/30.19 assert (zenon_L891_ : (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H6f zenon_H26 zenon_H6e zenon_H48 zenon_H14e zenon_H10d zenon_H10e zenon_H2b4 zenon_Hf4 zenon_H2c zenon_H35 zenon_H16a zenon_H256 zenon_H1dc zenon_H2d zenon_Had zenon_Hb8 zenon_H15a zenon_H4e zenon_H74 zenon_H84 zenon_Hd9 zenon_H83 zenon_H156 zenon_H113 zenon_Hc0 zenon_H1ab zenon_H100 zenon_H23b zenon_H92 zenon_Hd2 zenon_Hd1 zenon_Hde zenon_H8d zenon_H1a5 zenon_H18c zenon_H4a zenon_H172 zenon_H1e6 zenon_H218 zenon_H20d zenon_H108 zenon_H4c zenon_H1fd zenon_He1 zenon_H135 zenon_Ha4 zenon_H3c zenon_H225 zenon_Hf6 zenon_He4 zenon_H20 zenon_Hbd zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.02/30.19 apply (zenon_L598_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.02/30.19 apply (zenon_L890_); trivial. % 30.02/30.19 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.19 (* end of lemma zenon_L891_ *) % 30.02/30.19 assert (zenon_L892_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H23b zenon_H8a zenon_H6f zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.02/30.19 apply (zenon_L39_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.02/30.19 apply (zenon_L880_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.02/30.19 apply (zenon_L699_); trivial. % 30.02/30.19 exact (zenon_H1ab zenon_H112). % 30.02/30.19 (* end of lemma zenon_L892_ *) % 30.02/30.19 assert (zenon_L893_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H16f zenon_H89 zenon_H15a zenon_Hd2 zenon_H6f zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.19 apply (zenon_L241_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.19 apply (zenon_L125_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_L859_); trivial. % 30.02/30.19 (* end of lemma zenon_L893_ *) % 30.02/30.19 assert (zenon_L894_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H16f zenon_H48 zenon_H156 zenon_H18c zenon_H76 zenon_H2d zenon_H2b4 zenon_Hd2 zenon_H6f zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.19 apply (zenon_L865_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.19 apply (zenon_L125_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_L859_); trivial. % 30.02/30.19 (* end of lemma zenon_L894_ *) % 30.02/30.19 assert (zenon_L895_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H16f zenon_Had zenon_H8a zenon_Hd2 zenon_H6f zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.19 apply (zenon_L34_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.19 apply (zenon_L125_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_L859_); trivial. % 30.02/30.19 (* end of lemma zenon_L895_ *) % 30.02/30.19 assert (zenon_L896_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.02/30.19 do 0 intro. intros zenon_He4 zenon_Hf6 zenon_H225 zenon_H74 zenon_H3c zenon_Hde zenon_Ha4 zenon_H18c zenon_H135 zenon_H6f zenon_He1 zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H20d zenon_H218 zenon_H33 zenon_H156 zenon_H48 zenon_H1e6 zenon_H2a9 zenon_H8d zenon_H90 zenon_Hcd. % 30.02/30.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.19 exact (zenon_H74 zenon_H73). % 30.02/30.19 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.19 apply (zenon_L822_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.19 apply (zenon_L538_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.19 apply (zenon_L883_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.19 apply (zenon_L273_); trivial. % 30.02/30.19 apply (zenon_L39_); trivial. % 30.02/30.19 apply (zenon_L386_); trivial. % 30.02/30.19 (* end of lemma zenon_L896_ *) % 30.02/30.19 assert (zenon_L897_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.02/30.19 do 0 intro. intros zenon_Hbd zenon_H69 zenon_Had zenon_H40 zenon_H2d zenon_H10e zenon_H10d zenon_H14e zenon_H48 zenon_H6e. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.19 apply (zenon_L749_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.19 apply (zenon_L766_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.19 apply (zenon_L63_); trivial. % 30.02/30.19 apply (zenon_L770_); trivial. % 30.02/30.19 (* end of lemma zenon_L897_ *) % 30.02/30.19 assert (zenon_L898_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H174 zenon_H3f zenon_H26 zenon_H8d zenon_H15a zenon_H10d zenon_H10e zenon_H90 zenon_H20 zenon_Hbd zenon_H40 zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H48 zenon_H16f zenon_Had zenon_Hd2 zenon_H6f zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.02/30.19 apply (zenon_L538_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.02/30.19 apply (zenon_L746_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.02/30.19 apply (zenon_L598_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.19 apply (zenon_L893_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.19 apply (zenon_L771_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.19 apply (zenon_L866_); trivial. % 30.02/30.19 apply (zenon_L895_); trivial. % 30.02/30.19 (* end of lemma zenon_L898_ *) % 30.02/30.19 assert (zenon_L899_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H92 zenon_H84 zenon_H97 zenon_H69 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_H20e zenon_H159 zenon_H4a zenon_H256 zenon_Ha4 zenon_H1e6 zenon_H218 zenon_Hf6 zenon_H2bd zenon_H172 zenon_H1a5 zenon_H174 zenon_H3f zenon_H26 zenon_H8d zenon_H15a zenon_H10d zenon_H10e zenon_H20 zenon_Hbd zenon_H40 zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H48 zenon_H16f zenon_Had zenon_Hd2 zenon_H6f zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.02/30.19 exact (zenon_H84 zenon_H88). % 30.02/30.19 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.02/30.19 apply (zenon_L16_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.19 apply (zenon_L897_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.19 apply (zenon_L125_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.19 apply (zenon_L752_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.02/30.19 apply (zenon_L332_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.02/30.19 apply (zenon_L775_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.02/30.19 apply (zenon_L874_); trivial. % 30.02/30.19 apply (zenon_L779_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.02/30.19 apply (zenon_L746_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.02/30.19 apply (zenon_L87_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.19 apply (zenon_L893_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.19 apply (zenon_L897_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.19 apply (zenon_L157_); trivial. % 30.02/30.19 apply (zenon_L862_); trivial. % 30.02/30.19 apply (zenon_L898_); trivial. % 30.02/30.19 (* end of lemma zenon_L899_ *) % 30.02/30.19 assert (zenon_L900_ : (((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 (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H2b7 zenon_H8b zenon_Hb5 zenon_H112 zenon_H110 zenon_Hf4 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.02/30.19 apply (zenon_L297_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.02/30.19 apply (zenon_L133_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.02/30.19 apply (zenon_L799_); trivial. % 30.02/30.19 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.19 (* end of lemma zenon_L900_ *) % 30.02/30.19 assert (zenon_L901_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((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 (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H23b zenon_H20 zenon_H40 zenon_H6f zenon_H26 zenon_H10d zenon_H2b7 zenon_H8b zenon_Hb5 zenon_H110 zenon_Hf4 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.02/30.19 apply (zenon_L27_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.02/30.19 apply (zenon_L80_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.02/30.19 apply (zenon_L699_); trivial. % 30.02/30.19 apply (zenon_L900_); trivial. % 30.02/30.19 (* end of lemma zenon_L901_ *) % 30.02/30.19 assert (zenon_L902_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_H222 zenon_H40 zenon_H20d zenon_Hc9 zenon_H218 zenon_H33 zenon_H156 zenon_H48 zenon_H6e zenon_H1e6 zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.02/30.19 apply (zenon_L273_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.02/30.19 apply (zenon_L775_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.02/30.19 apply (zenon_L882_); trivial. % 30.02/30.19 apply (zenon_L845_); trivial. % 30.02/30.19 (* end of lemma zenon_L902_ *) % 30.02/30.19 assert (zenon_L903_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (~((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)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.19 do 0 intro. intros zenon_H8d zenon_H15a zenon_H2a9 zenon_H108 zenon_H10e zenon_H2d zenon_H1fd zenon_H1e6 zenon_H48 zenon_H156 zenon_H33 zenon_H218 zenon_H20d zenon_H40 zenon_H222 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H16f zenon_Had zenon_Hd2 zenon_H6f zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.19 apply (zenon_L893_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.19 apply (zenon_L902_); trivial. % 30.02/30.19 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.19 apply (zenon_L273_); trivial. % 30.02/30.19 apply (zenon_L895_); trivial. % 30.02/30.19 (* end of lemma zenon_L903_ *) % 30.02/30.19 assert (zenon_L904_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_He4 zenon_H225 zenon_H74 zenon_H3c zenon_Hde zenon_Ha4 zenon_H18c zenon_H135 zenon_H4e zenon_H156 zenon_Hf6 zenon_H218 zenon_H33 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2d zenon_H40 zenon_Had zenon_H48 zenon_H69 zenon_Hbd zenon_H14e zenon_H4c zenon_H100 zenon_H1d5 zenon_He1 zenon_H222 zenon_H20d zenon_H1fd zenon_H108 zenon_H2a9 zenon_H16f zenon_Hf4 zenon_H17d. % 30.02/30.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.20 exact (zenon_H74 zenon_H73). % 30.02/30.20 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.20 apply (zenon_L822_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.20 apply (zenon_L902_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.20 apply (zenon_L150_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.20 apply (zenon_L752_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.20 apply (zenon_L749_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.20 apply (zenon_L766_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.20 apply (zenon_L63_); trivial. % 30.02/30.20 apply (zenon_L871_); trivial. % 30.02/30.20 apply (zenon_L847_); trivial. % 30.02/30.20 (* end of lemma zenon_L904_ *) % 30.02/30.20 assert (zenon_L905_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_Hc0 zenon_H35 zenon_H16a zenon_H6f zenon_Hd2 zenon_H2b4 zenon_H20 zenon_H15a zenon_H8d zenon_H3f zenon_H174 zenon_H1a5 zenon_H172 zenon_H2bd zenon_H256 zenon_H4a zenon_H159 zenon_H20e zenon_Hc8 zenon_H97 zenon_H84 zenon_H92 zenon_He4 zenon_H225 zenon_H74 zenon_H3c zenon_Hde zenon_Ha4 zenon_H18c zenon_H135 zenon_H4e zenon_H156 zenon_Hf6 zenon_H218 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2d zenon_H40 zenon_Had zenon_H48 zenon_H69 zenon_Hbd zenon_H14e zenon_H4c zenon_H100 zenon_H1d5 zenon_He1 zenon_H222 zenon_H20d zenon_H1fd zenon_H108 zenon_H2a9 zenon_H16f zenon_Hf4 zenon_H17d. % 30.02/30.20 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.02/30.20 exact (zenon_H84 zenon_H88). % 30.02/30.20 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.02/30.20 apply (zenon_L868_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.02/30.20 apply (zenon_L899_); trivial. % 30.02/30.20 apply (zenon_L904_); trivial. % 30.02/30.20 (* end of lemma zenon_L905_ *) % 30.02/30.20 assert (zenon_L906_ : ((op (e1) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 30.02/30.20 do 0 intro. intros zenon_Hc3 zenon_Hd2 zenon_H20. % 30.02/30.20 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 30.02/30.20 cut (((e1) = (e1)) = ((e0) = (e1))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H20. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H21. % 30.02/30.20 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.20 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 30.02/30.20 congruence. % 30.02/30.20 cut (((op (e1) (e1)) = (e0)) = ((e1) = (e0))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H23. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_Hc3. % 30.02/30.20 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.02/30.20 cut (((op (e1) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 30.02/30.20 congruence. % 30.02/30.20 exact (zenon_H18f zenon_Hd2). % 30.02/30.20 apply zenon_H1d. apply refl_equal. % 30.02/30.20 apply zenon_H22. apply refl_equal. % 30.02/30.20 apply zenon_H22. apply refl_equal. % 30.02/30.20 (* end of lemma zenon_L906_ *) % 30.02/30.20 assert (zenon_L907_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H1d5 zenon_H14f zenon_H4e zenon_H18c zenon_H222 zenon_H40 zenon_Hcc zenon_He1 zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.02/30.20 apply (zenon_L864_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.02/30.20 apply (zenon_L775_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.02/30.20 apply (zenon_L544_); trivial. % 30.02/30.20 apply (zenon_L845_); trivial. % 30.02/30.20 (* end of lemma zenon_L907_ *) % 30.02/30.20 assert (zenon_L908_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H135 zenon_Hdc zenon_Ha4 zenon_Hde zenon_H3c zenon_H74 zenon_H225 zenon_H2a9 zenon_H108 zenon_H14e zenon_H4c zenon_H10e zenon_H2d zenon_H1fd zenon_He1 zenon_H40 zenon_H222 zenon_H18c zenon_H4e zenon_H14f zenon_H1d5 zenon_Hf4 zenon_Hf6. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.02/30.20 apply (zenon_L142_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.02/30.20 apply (zenon_L820_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.02/30.20 apply (zenon_L907_); trivial. % 30.02/30.20 apply (zenon_L56_); trivial. % 30.02/30.20 (* end of lemma zenon_L908_ *) % 30.02/30.20 assert (zenon_L909_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H20 zenon_Hd2 zenon_H1a5 zenon_H135 zenon_Hdc zenon_Ha4 zenon_Hde zenon_H3c zenon_H74 zenon_H225 zenon_H2a9 zenon_H108 zenon_H14e zenon_H4c zenon_H10e zenon_H2d zenon_H1fd zenon_He1 zenon_H40 zenon_H222 zenon_H18c zenon_H4e zenon_H1d5 zenon_Hf4 zenon_Hf6. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.20 apply (zenon_L740_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.20 apply (zenon_L906_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.20 apply (zenon_L764_); trivial. % 30.02/30.20 apply (zenon_L908_); trivial. % 30.02/30.20 (* end of lemma zenon_L909_ *) % 30.02/30.20 assert (zenon_L910_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((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 (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_He4 zenon_Hf6 zenon_H1d5 zenon_H4e zenon_H18c zenon_H222 zenon_H40 zenon_He1 zenon_H1fd zenon_H2d zenon_H10e zenon_H4c zenon_H14e zenon_H108 zenon_H2a9 zenon_H225 zenon_H74 zenon_H3c zenon_Ha4 zenon_H135 zenon_H1a5 zenon_Hd2 zenon_H20 zenon_H48 zenon_H172 zenon_Hdf zenon_Hde zenon_Hf4 zenon_H17d. % 30.02/30.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.20 exact (zenon_H74 zenon_H73). % 30.02/30.20 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.20 apply (zenon_L909_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.20 apply (zenon_L49_); trivial. % 30.02/30.20 apply (zenon_L847_); trivial. % 30.02/30.20 (* end of lemma zenon_L910_ *) % 30.02/30.20 assert (zenon_L911_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H172 zenon_H8b zenon_Had zenon_H6c zenon_H4a zenon_H1d5 zenon_H4e zenon_H18c zenon_H222 zenon_H40 zenon_H20d zenon_Hc9 zenon_H218 zenon_H33 zenon_H156 zenon_H48 zenon_H6e zenon_H1e6 zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.20 apply (zenon_L749_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.20 apply (zenon_L763_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.20 apply (zenon_L784_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.02/30.20 apply (zenon_L864_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.02/30.20 apply (zenon_L775_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.02/30.20 apply (zenon_L882_); trivial. % 30.02/30.20 apply (zenon_L845_); trivial. % 30.02/30.20 (* end of lemma zenon_L911_ *) % 30.02/30.20 assert (zenon_L912_ : (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H20 zenon_H88 zenon_H64. % 30.02/30.20 cut (((op (e0) (e0)) = (e1)) = ((e0) = (e1))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H20. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H88. % 30.02/30.20 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.20 cut (((op (e0) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1b3]. % 30.02/30.20 congruence. % 30.02/30.20 exact (zenon_H1b3 zenon_H64). % 30.02/30.20 apply zenon_H22. apply refl_equal. % 30.02/30.20 (* end of lemma zenon_L912_ *) % 30.02/30.20 assert (zenon_L913_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.02/30.20 do 0 intro. intros zenon_Had zenon_H4e zenon_H14f zenon_H8a. % 30.02/30.20 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_Had. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H4e. % 30.02/30.20 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 30.02/30.20 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 30.02/30.20 congruence. % 30.02/30.20 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.02/30.20 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e0)))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H286. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H280. % 30.02/30.20 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.02/30.20 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H283]. % 30.02/30.20 congruence. % 30.02/30.20 apply (zenon_L743_); trivial. % 30.02/30.20 apply zenon_Hd4. apply refl_equal. % 30.02/30.20 apply zenon_Hd4. apply refl_equal. % 30.02/30.20 apply zenon_H1e3. apply sym_equal. exact zenon_H8a. % 30.02/30.20 (* end of lemma zenon_L913_ *) % 30.02/30.20 assert (zenon_L914_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H172 zenon_H68 zenon_H20 zenon_H35 zenon_H1e zenon_Hc9 zenon_H4c zenon_H18c zenon_Had zenon_H4e zenon_H8a. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.20 apply (zenon_L16_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.20 apply (zenon_L42_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.20 apply (zenon_L784_); trivial. % 30.02/30.20 apply (zenon_L913_); trivial. % 30.02/30.20 (* end of lemma zenon_L914_ *) % 30.02/30.20 assert (zenon_L915_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H1a8 zenon_H69 zenon_H20 zenon_H18f zenon_Hf6 zenon_Hf4 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_He1 zenon_H2a9 zenon_H19e zenon_H4c zenon_Hdc zenon_H18c zenon_H135 zenon_H4e zenon_H6e zenon_Hd1. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.20 apply (zenon_L16_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.20 exact (zenon_H18f zenon_Hd2). % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.20 apply (zenon_L826_); trivial. % 30.02/30.20 apply (zenon_L729_); trivial. % 30.02/30.20 (* end of lemma zenon_L915_ *) % 30.02/30.20 assert (zenon_L916_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H1a8 zenon_H6e zenon_H18f zenon_Hf6 zenon_Hf4 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_He1 zenon_H2a9 zenon_H19e zenon_H4c zenon_Hdc zenon_H18c zenon_H135 zenon_H20 zenon_H14f. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.20 apply (zenon_L18_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.20 exact (zenon_H18f zenon_Hd2). % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.20 apply (zenon_L826_); trivial. % 30.02/30.20 apply (zenon_L658_); trivial. % 30.02/30.20 (* end of lemma zenon_L916_ *) % 30.02/30.20 assert (zenon_L917_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H16f zenon_Had zenon_H8a zenon_H1ab zenon_H156 zenon_H4a zenon_H2b0 zenon_H19a zenon_H2b1 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.20 apply (zenon_L34_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.20 apply (zenon_L842_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.20 apply (zenon_L752_); trivial. % 30.02/30.20 apply (zenon_L859_); trivial. % 30.02/30.20 (* end of lemma zenon_L917_ *) % 30.02/30.20 assert (zenon_L918_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H6c zenon_H4a zenon_H18c zenon_H10e zenon_H1a5 zenon_Had zenon_H4e zenon_H8a. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.20 apply (zenon_L740_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.20 apply (zenon_L763_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.20 apply (zenon_L764_); trivial. % 30.02/30.20 apply (zenon_L913_); trivial. % 30.02/30.20 (* end of lemma zenon_L918_ *) % 30.02/30.20 assert (zenon_L919_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.02/30.20 do 0 intro. intros zenon_Hbd zenon_H2d zenon_Hc9 zenon_He1 zenon_H4e zenon_H182 zenon_Hd1 zenon_H172 zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_H4c zenon_H18c zenon_H15a zenon_H8d zenon_H37 zenon_Hf4 zenon_H10e zenon_H10d zenon_Hf6 zenon_H1e1. % 30.02/30.20 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.02/30.20 apply (zenon_L844_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.02/30.20 apply (zenon_L513_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.02/30.20 apply (zenon_L63_); trivial. % 30.02/30.20 apply (zenon_L690_); trivial. % 30.02/30.20 (* end of lemma zenon_L919_ *) % 30.02/30.20 assert (zenon_L920_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H200 zenon_H8a zenon_H1a5 zenon_H1e zenon_H27 zenon_H135 zenon_Hf6 zenon_H10d zenon_H37 zenon_H8d zenon_H15a zenon_H18c zenon_H4a zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_Hd1 zenon_H182 zenon_H4e zenon_Hbd zenon_Ha4 zenon_H3c zenon_H74 zenon_H225 zenon_H2a9 zenon_He1 zenon_H14e zenon_H4c zenon_Hf4 zenon_H10e zenon_H2d zenon_H1fd zenon_Hde. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.02/30.20 apply (zenon_L918_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.02/30.20 apply (zenon_L207_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.02/30.20 apply (zenon_L208_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.02/30.20 apply (zenon_L919_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.02/30.20 apply (zenon_L820_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.02/30.20 apply (zenon_L821_); trivial. % 30.02/30.20 apply (zenon_L294_); trivial. % 30.02/30.20 (* end of lemma zenon_L920_ *) % 30.02/30.20 assert (zenon_L921_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H1a8 zenon_H18f zenon_H16a zenon_H16b zenon_H2b1 zenon_H2b0 zenon_H156 zenon_H1ab zenon_H16f zenon_Hde zenon_H1fd zenon_H2d zenon_H10e zenon_He1 zenon_H2a9 zenon_H225 zenon_H74 zenon_H3c zenon_Ha4 zenon_Hbd zenon_Hd1 zenon_H172 zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_H18c zenon_H15a zenon_H8d zenon_H10d zenon_Hf6 zenon_H135 zenon_H27 zenon_H1e zenon_H1a5 zenon_H8a zenon_H200 zenon_Hf4 zenon_H4c zenon_H14e zenon_H159 zenon_H4e. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.20 apply (zenon_L120_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.20 exact (zenon_H18f zenon_Hd2). % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.20 apply (zenon_L917_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.20 apply (zenon_L34_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.20 apply (zenon_L920_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.20 apply (zenon_L752_); trivial. % 30.02/30.20 apply (zenon_L733_); trivial. % 30.02/30.20 (* end of lemma zenon_L921_ *) % 30.02/30.20 assert (zenon_L922_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H35 zenon_He9 zenon_H19e zenon_H3d. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.02/30.20 apply (zenon_L763_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.02/30.20 exact (zenon_H18f zenon_Hd2). % 30.02/30.20 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.02/30.20 apply (zenon_L95_); trivial. % 30.02/30.20 apply (zenon_L131_); trivial. % 30.02/30.20 (* end of lemma zenon_L922_ *) % 30.02/30.20 assert (zenon_L923_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H1ab zenon_H156 zenon_H2b0 zenon_H19a zenon_H16a zenon_H2b1 zenon_H19e zenon_He9 zenon_H35 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H20e zenon_H1fd zenon_H1a5 zenon_H155 zenon_H4e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.02/30.20 apply (zenon_L4_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.02/30.20 apply (zenon_L842_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.02/30.20 apply (zenon_L922_); trivial. % 30.02/30.20 apply (zenon_L857_); trivial. % 30.02/30.20 (* end of lemma zenon_L923_ *) % 30.02/30.20 assert (zenon_L924_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H173 zenon_Hc9 zenon_Hcd zenon_H42 zenon_H2d zenon_H1e zenon_H1ab zenon_H156 zenon_H2b0 zenon_H19a zenon_H16a zenon_H2b1 zenon_H19e zenon_He9 zenon_H35 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H20e zenon_H1fd zenon_H1a5 zenon_H4e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.02/30.20 apply (zenon_L142_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.02/30.20 apply (zenon_L95_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.02/30.20 apply (zenon_L159_); trivial. % 30.02/30.20 apply (zenon_L923_); trivial. % 30.02/30.20 (* end of lemma zenon_L924_ *) % 30.02/30.20 assert (zenon_L925_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H6c zenon_H4a zenon_H18c zenon_H10e zenon_H1a5 zenon_H4e zenon_H89 zenon_H15a. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.20 apply (zenon_L740_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.20 apply (zenon_L763_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.20 apply (zenon_L764_); trivial. % 30.02/30.20 apply (zenon_L744_); trivial. % 30.02/30.20 (* end of lemma zenon_L925_ *) % 30.02/30.20 assert (zenon_L926_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H200 zenon_H89 zenon_H1a5 zenon_H1e zenon_H3c zenon_H27 zenon_Hbd zenon_H2d zenon_Hc9 zenon_He1 zenon_H4e zenon_H182 zenon_Hd1 zenon_H172 zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_H4c zenon_H18c zenon_H15a zenon_H8d zenon_H37 zenon_Hf4 zenon_H10e zenon_H10d zenon_Hf6. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.02/30.20 apply (zenon_L925_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.02/30.20 apply (zenon_L207_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.02/30.20 apply (zenon_L208_); trivial. % 30.02/30.20 apply (zenon_L919_); trivial. % 30.02/30.20 (* end of lemma zenon_L926_ *) % 30.02/30.20 assert (zenon_L927_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H16f zenon_Hf6 zenon_H10d zenon_H10e zenon_H8d zenon_H15a zenon_H18c zenon_H4a zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_Hd1 zenon_H182 zenon_H4e zenon_He1 zenon_Hc9 zenon_H2d zenon_Hbd zenon_H27 zenon_H3c zenon_H1e zenon_H1a5 zenon_H89 zenon_H200 zenon_Hf4 zenon_H4c zenon_H14e zenon_H16a zenon_H16b. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.20 apply (zenon_L729_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.20 apply (zenon_L926_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.20 apply (zenon_L752_); trivial. % 30.02/30.20 apply (zenon_L101_); trivial. % 30.02/30.20 (* end of lemma zenon_L927_ *) % 30.02/30.20 assert (zenon_L928_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H1a8 zenon_H2a9 zenon_H108 zenon_H1fd zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H102 zenon_H18f zenon_H35 zenon_He9 zenon_H19e zenon_H2b1 zenon_H2b0 zenon_H156 zenon_H1ab zenon_H42 zenon_Hcd zenon_H173 zenon_H16f zenon_Hf6 zenon_H10d zenon_H10e zenon_H8d zenon_H15a zenon_H18c zenon_H4a zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_Hd1 zenon_H4e zenon_He1 zenon_Hc9 zenon_H2d zenon_Hbd zenon_H27 zenon_H3c zenon_H1e zenon_H1a5 zenon_H89 zenon_H200 zenon_Hf4 zenon_H4c zenon_H14e zenon_H16a zenon_H16b. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.20 apply (zenon_L120_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.20 exact (zenon_H18f zenon_Hd2). % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.20 apply (zenon_L924_); trivial. % 30.02/30.20 apply (zenon_L927_); trivial. % 30.02/30.20 (* end of lemma zenon_L928_ *) % 30.02/30.20 assert (zenon_L929_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H16f zenon_H48 zenon_H18c zenon_H76 zenon_H2d zenon_H2b4 zenon_H1ab zenon_H156 zenon_H4a zenon_H2b0 zenon_H19a zenon_H2b1 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.02/30.20 apply (zenon_L865_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.02/30.20 apply (zenon_L842_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.02/30.20 apply (zenon_L752_); trivial. % 30.02/30.20 apply (zenon_L859_); trivial. % 30.02/30.20 (* end of lemma zenon_L929_ *) % 30.02/30.20 assert (zenon_L930_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H90 zenon_H4a zenon_Had zenon_H10e zenon_H1a5 zenon_H18c zenon_H4e zenon_H76. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.20 apply (zenon_L740_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.20 apply (zenon_L769_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.20 apply (zenon_L764_); trivial. % 30.02/30.20 apply (zenon_L864_); trivial. % 30.02/30.20 (* end of lemma zenon_L930_ *) % 30.02/30.20 assert (zenon_L931_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H8d zenon_Hf4 zenon_H48 zenon_H156 zenon_H10e zenon_H27 zenon_H3c zenon_H1e zenon_Hde zenon_H200 zenon_He1 zenon_Hc9 zenon_H6f zenon_H90. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.20 apply (zenon_L538_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.20 apply (zenon_L738_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.20 apply (zenon_L273_); trivial. % 30.02/30.20 apply (zenon_L39_); trivial. % 30.02/30.20 (* end of lemma zenon_L931_ *) % 30.02/30.20 assert (zenon_L932_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.02/30.20 do 0 intro. intros zenon_He4 zenon_H74 zenon_H172 zenon_Hdf zenon_H4a zenon_Had zenon_H1a5 zenon_H18c zenon_H4e zenon_H1a8 zenon_H18f zenon_Hf6 zenon_H1fd zenon_H2d zenon_H2a9 zenon_H19e zenon_H4c zenon_H135 zenon_H20 zenon_H6f zenon_He1 zenon_H200 zenon_Hde zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_Hf4 zenon_H8d zenon_H90 zenon_Hcd. % 30.02/30.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.02/30.20 exact (zenon_H74 zenon_H73). % 30.02/30.20 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.02/30.20 apply (zenon_L538_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.20 apply (zenon_L740_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.20 apply (zenon_L769_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.20 apply (zenon_L764_); trivial. % 30.02/30.20 apply (zenon_L916_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.02/30.20 apply (zenon_L930_); trivial. % 30.02/30.20 apply (zenon_L39_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.02/30.20 apply (zenon_L931_); trivial. % 30.02/30.20 apply (zenon_L386_); trivial. % 30.02/30.20 (* end of lemma zenon_L932_ *) % 30.02/30.20 assert (zenon_L933_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H135 zenon_H76 zenon_Hd5 zenon_Hcd zenon_H2a9 zenon_He1 zenon_H14e zenon_H4c zenon_Hf4 zenon_H10e zenon_H2d zenon_H1fd zenon_Hde zenon_H1e1. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.02/30.20 apply (zenon_L273_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.02/30.20 apply (zenon_L212_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.02/30.20 apply (zenon_L821_); trivial. % 30.02/30.20 apply (zenon_L294_); trivial. % 30.02/30.20 (* end of lemma zenon_L933_ *) % 30.02/30.20 assert (zenon_L934_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H156 zenon_H182 zenon_H1e5. % 30.02/30.20 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H156. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H182. % 30.02/30.20 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 30.02/30.20 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.02/30.20 congruence. % 30.02/30.20 apply zenon_H150. apply refl_equal. % 30.02/30.20 apply zenon_H205. apply sym_equal. exact zenon_H1e5. % 30.02/30.20 (* end of lemma zenon_L934_ *) % 30.02/30.20 assert (zenon_L935_ : ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_Hdc zenon_H16a zenon_H16b zenon_H2b1 zenon_H2b0 zenon_H1ab zenon_H2b4 zenon_H16f zenon_H90 zenon_H8d zenon_H48 zenon_H200 zenon_H20 zenon_H19e zenon_Hf6 zenon_H18f zenon_H1a8 zenon_H4e zenon_H18c zenon_H1a5 zenon_Had zenon_H4a zenon_H172 zenon_H74 zenon_He4 zenon_H1e zenon_H3c zenon_H27 zenon_H208 zenon_H6f zenon_Hde zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_He1 zenon_H2a9 zenon_Hcd zenon_H76 zenon_H135 zenon_H56 zenon_H156. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.02/30.20 apply (zenon_L48_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.02/30.20 exact (zenon_H18f zenon_Hd2). % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.02/30.20 apply (zenon_L929_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.02/30.20 apply (zenon_L932_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.02/30.20 apply (zenon_L207_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.02/30.20 apply (zenon_L208_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.02/30.20 apply (zenon_L157_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.02/30.20 apply (zenon_L933_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.02/30.20 exact (zenon_H56 zenon_H25). % 30.02/30.20 apply (zenon_L934_); trivial. % 30.02/30.20 (* end of lemma zenon_L935_ *) % 30.02/30.20 assert (zenon_L936_ : ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (op (op (e0) (e0)) (e0)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_Hdc zenon_H88 zenon_H21d. % 30.02/30.20 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 30.02/30.20 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e2) = (op (op (e0) (e0)) (e0)))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H21d. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H78. % 30.02/30.20 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 30.02/30.20 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 30.02/30.20 congruence. % 30.02/30.20 cut (((op (e1) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H21e. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_Hdc. % 30.02/30.20 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 30.02/30.20 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 30.02/30.20 congruence. % 30.02/30.20 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 30.02/30.20 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H2a0. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H78. % 30.02/30.20 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 30.02/30.20 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H29f]. % 30.02/30.20 congruence. % 30.02/30.20 apply (zenon_L793_); trivial. % 30.02/30.20 apply zenon_H79. apply refl_equal. % 30.02/30.20 apply zenon_H79. apply refl_equal. % 30.02/30.20 apply zenon_H57. apply refl_equal. % 30.02/30.20 apply zenon_H79. apply refl_equal. % 30.02/30.20 apply zenon_H79. apply refl_equal. % 30.02/30.20 (* end of lemma zenon_L936_ *) % 30.02/30.20 assert (zenon_L937_ : ((op (e1) (e1)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H37 zenon_Hdc zenon_H88. % 30.02/30.20 apply (zenon_notand_s _ _ ax11); [ zenon_intro zenon_H216 | zenon_intro zenon_H2c0 ]. % 30.02/30.20 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 30.02/30.20 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e3) = (op (op (e0) (e0)) (op (e0) (e0))))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H216. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H7e. % 30.02/30.20 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 30.02/30.20 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H217]. % 30.02/30.20 congruence. % 30.02/30.20 cut (((op (e1) (e1)) = (e3)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e3))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H217. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H37. % 30.02/30.20 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.02/30.20 cut (((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2a2]. % 30.02/30.20 congruence. % 30.02/30.20 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 30.02/30.20 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H2a2. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H7e. % 30.02/30.20 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 30.02/30.20 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H29e]. % 30.02/30.20 congruence. % 30.02/30.20 apply (zenon_L792_); trivial. % 30.02/30.20 apply zenon_H7f. apply refl_equal. % 30.02/30.20 apply zenon_H7f. apply refl_equal. % 30.02/30.20 apply zenon_H2f. apply refl_equal. % 30.02/30.20 apply zenon_H7f. apply refl_equal. % 30.02/30.20 apply zenon_H7f. apply refl_equal. % 30.02/30.20 apply (zenon_notand_s _ _ zenon_H2c0); [ zenon_intro zenon_H21d | zenon_intro zenon_H2a3 ]. % 30.02/30.20 apply (zenon_L936_); trivial. % 30.02/30.20 apply zenon_H2a3. apply sym_equal. exact zenon_H88. % 30.02/30.20 (* end of lemma zenon_L937_ *) % 30.02/30.20 assert (zenon_L938_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H18c zenon_H35 zenon_H1e zenon_H10e zenon_H1a5 zenon_Had zenon_H4e zenon_H8a. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.02/30.20 apply (zenon_L740_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.02/30.20 apply (zenon_L42_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.02/30.20 apply (zenon_L764_); trivial. % 30.02/30.20 apply (zenon_L913_); trivial. % 30.02/30.20 (* end of lemma zenon_L938_ *) % 30.02/30.20 assert (zenon_L939_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H1fd zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H2d zenon_H142 zenon_H2a9. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.02/30.20 apply (zenon_L87_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.02/30.20 apply (zenon_L752_); trivial. % 30.02/30.20 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.02/30.20 apply (zenon_L175_); trivial. % 30.02/30.20 exact (zenon_H2a9 zenon_Hb6). % 30.02/30.20 (* end of lemma zenon_L939_ *) % 30.02/30.20 assert (zenon_L940_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H2c1 zenon_H88 zenon_H33. % 30.02/30.20 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e0) (e3)))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H2c1. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H88. % 30.02/30.20 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 30.02/30.20 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.02/30.20 congruence. % 30.02/30.20 apply zenon_Hcb. apply refl_equal. % 30.02/30.20 apply zenon_H34. apply sym_equal. exact zenon_H33. % 30.02/30.20 (* end of lemma zenon_L940_ *) % 30.02/30.20 assert (zenon_L941_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e2)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H2c2 zenon_Hf4. % 30.02/30.20 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 30.02/30.20 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 30.02/30.20 congruence. % 30.02/30.20 exact (zenon_H231 zenon_Hf4). % 30.02/30.20 exact (zenon_H231 zenon_Hf4). % 30.02/30.20 (* end of lemma zenon_L941_ *) % 30.02/30.20 assert (zenon_L942_ : (~((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H2c3 zenon_Hf4. % 30.02/30.20 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.02/30.20 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 30.02/30.20 congruence. % 30.02/30.20 exact (zenon_H231 zenon_Hf4). % 30.02/30.20 apply zenon_H2f. apply refl_equal. % 30.02/30.20 (* end of lemma zenon_L942_ *) % 30.02/30.20 assert (zenon_L943_ : ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (op (op (e3) (e3)) (e3)))) -> False). % 30.02/30.20 do 0 intro. intros zenon_H1e5 zenon_Hf4 zenon_H130. % 30.02/30.20 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 30.02/30.20 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e1) = (op (op (e3) (e3)) (e3)))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H130. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H131. % 30.02/30.20 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 30.02/30.20 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 30.02/30.20 congruence. % 30.02/30.20 cut (((op (e2) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H133. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H1e5. % 30.02/30.20 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.02/30.20 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c4]. % 30.02/30.20 congruence. % 30.02/30.20 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 30.02/30.20 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H2c4. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H131. % 30.02/30.20 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 30.02/30.20 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 30.02/30.20 congruence. % 30.02/30.20 apply (zenon_L942_); trivial. % 30.02/30.20 apply zenon_H132. apply refl_equal. % 30.02/30.20 apply zenon_H132. apply refl_equal. % 30.02/30.20 apply zenon_H22. apply refl_equal. % 30.02/30.20 apply zenon_H132. apply refl_equal. % 30.02/30.20 apply zenon_H132. apply refl_equal. % 30.02/30.20 (* end of lemma zenon_L943_ *) % 30.02/30.20 assert (zenon_L944_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> False). % 30.02/30.20 do 0 intro. intros zenon_H142 zenon_H1e5 zenon_Hf4. % 30.02/30.20 apply (zenon_notand_s _ _ ax24); [ zenon_intro zenon_H22e | zenon_intro zenon_H2c5 ]. % 30.02/30.20 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 30.02/30.20 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H22e. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H12c. % 30.02/30.20 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 30.02/30.20 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 30.02/30.20 congruence. % 30.02/30.20 cut (((op (e2) (e2)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H22f. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H142. % 30.02/30.20 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.02/30.20 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2c6]. % 30.02/30.20 congruence. % 30.02/30.20 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 30.02/30.20 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))))). % 30.02/30.20 intro zenon_D_pnotp. % 30.02/30.20 apply zenon_H2c6. % 30.02/30.20 rewrite <- zenon_D_pnotp. % 30.02/30.20 exact zenon_H12c. % 30.02/30.20 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 30.02/30.20 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 30.02/30.20 congruence. % 30.02/30.20 apply (zenon_L941_); trivial. % 30.02/30.20 apply zenon_H12d. apply refl_equal. % 30.02/30.20 apply zenon_H12d. apply refl_equal. % 30.02/30.20 apply zenon_H1d. apply refl_equal. % 30.02/30.20 apply zenon_H12d. apply refl_equal. % 30.02/30.20 apply zenon_H12d. apply refl_equal. % 30.02/30.20 apply (zenon_notand_s _ _ zenon_H2c5); [ zenon_intro zenon_H130 | zenon_intro zenon_H116 ]. % 30.02/30.20 apply (zenon_L943_); trivial. % 30.08/30.21 apply zenon_H116. apply sym_equal. exact zenon_Hf4. % 30.08/30.21 (* end of lemma zenon_L944_ *) % 30.08/30.21 assert (zenon_L945_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.08/30.21 do 0 intro. intros zenon_H8d zenon_H15a zenon_H4e zenon_H48 zenon_H156 zenon_H2b1 zenon_H88 zenon_H2c1 zenon_H20 zenon_Hf4 zenon_H1ab zenon_H3c zenon_H1e zenon_Hde zenon_H200 zenon_H18c zenon_H4c zenon_H35 zenon_Had zenon_H172 zenon_He1 zenon_Hc9 zenon_H2d zenon_H8b. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.21 apply (zenon_L788_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.08/30.21 apply (zenon_L749_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.08/30.21 apply (zenon_L42_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.08/30.21 apply (zenon_L784_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.21 apply (zenon_L49_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.21 apply (zenon_L207_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.08/30.21 apply (zenon_L940_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.08/30.21 apply (zenon_L658_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.08/30.21 apply (zenon_L944_); trivial. % 30.08/30.21 exact (zenon_H1ab zenon_H112). % 30.08/30.21 apply (zenon_L737_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.21 apply (zenon_L273_); trivial. % 30.08/30.21 apply (zenon_L25_); trivial. % 30.08/30.21 (* end of lemma zenon_L945_ *) % 30.08/30.21 assert (zenon_L946_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.08/30.21 do 0 intro. intros zenon_He4 zenon_H74 zenon_H2b7 zenon_Hb5 zenon_Hee zenon_H110 zenon_H2a9 zenon_H18f zenon_Hcd zenon_H1a8 zenon_H1a5 zenon_H10e zenon_H2d zenon_He1 zenon_H172 zenon_Had zenon_H35 zenon_H4c zenon_H18c zenon_H200 zenon_H1e zenon_H3c zenon_H1ab zenon_Hf4 zenon_H20 zenon_H2c1 zenon_H88 zenon_H2b1 zenon_H156 zenon_H48 zenon_H4e zenon_H15a zenon_H8d zenon_H8b zenon_Hde. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.21 exact (zenon_H74 zenon_H73). % 30.08/30.21 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.08/30.21 apply (zenon_L749_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.08/30.21 apply (zenon_L42_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.08/30.21 apply (zenon_L764_); trivial. % 30.08/30.21 apply (zenon_L854_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.21 apply (zenon_L945_); trivial. % 30.08/30.21 apply (zenon_L288_); trivial. % 30.08/30.21 (* end of lemma zenon_L946_ *) % 30.08/30.21 assert (zenon_L947_ : ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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 (e3) (e2)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H69 zenon_H16f zenon_H4a zenon_H156 zenon_H56 zenon_H1a2 zenon_Hd9 zenon_H2b0 zenon_H1d5 zenon_H135 zenon_H19e zenon_H10d zenon_He4 zenon_H74 zenon_H2b7 zenon_Hb5 zenon_Hee zenon_H110 zenon_H18f zenon_Hcd zenon_H1a8 zenon_H1a5 zenon_He1 zenon_H172 zenon_Had zenon_H35 zenon_H18c zenon_H200 zenon_H1e zenon_H3c zenon_H1ab zenon_H20 zenon_H2c1 zenon_H88 zenon_H2b1 zenon_H48 zenon_H15a zenon_H8d zenon_Hde zenon_Hbd zenon_H1fd zenon_H2d zenon_H10e zenon_H108 zenon_H2a9 zenon_H8a zenon_H27 zenon_Hf6 zenon_Hd1 zenon_Ha4 zenon_H225 zenon_H208 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.08/30.21 apply (zenon_L16_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.08/30.21 exact (zenon_H18f zenon_Hd2). % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.08/30.21 apply (zenon_L917_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.08/30.21 apply (zenon_L729_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.21 apply (zenon_L938_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.21 apply (zenon_L207_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.21 apply (zenon_L939_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.08/30.21 apply (zenon_L920_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.08/30.21 apply (zenon_L797_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.08/30.21 apply (zenon_L842_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.08/30.21 exact (zenon_H56 zenon_H25). % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.08/30.21 apply (zenon_L933_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.08/30.21 apply (zenon_L731_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.08/30.21 apply (zenon_L946_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.08/30.21 apply (zenon_L513_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.08/30.21 apply (zenon_L63_); trivial. % 30.08/30.21 apply (zenon_L751_); trivial. % 30.08/30.21 apply (zenon_L845_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.08/30.21 exact (zenon_H56 zenon_H25). % 30.08/30.21 apply (zenon_L841_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.08/30.21 apply (zenon_L752_); trivial. % 30.08/30.21 apply (zenon_L859_); trivial. % 30.08/30.21 (* end of lemma zenon_L947_ *) % 30.08/30.21 assert (zenon_L948_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H1fd zenon_H89 zenon_Hd9 zenon_H37 zenon_Hfc zenon_H1c5 zenon_H108 zenon_H2a9. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.08/30.21 apply (zenon_L149_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.08/30.21 apply (zenon_L203_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.08/30.21 apply (zenon_L171_); trivial. % 30.08/30.21 exact (zenon_H2a9 zenon_Hb6). % 30.08/30.21 (* end of lemma zenon_L948_ *) % 30.08/30.21 assert (zenon_L949_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H135 zenon_Hdc zenon_H3c zenon_H2a9 zenon_H108 zenon_Hfc zenon_H37 zenon_Hd9 zenon_H89 zenon_H1fd zenon_He1 zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H35 zenon_He9 zenon_H19e zenon_Hc8 zenon_H1d5 zenon_Hf4 zenon_Hf6. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.21 apply (zenon_L142_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.21 apply (zenon_L88_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.08/30.21 apply (zenon_L332_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.08/30.21 apply (zenon_L922_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.08/30.21 apply (zenon_L544_); trivial. % 30.08/30.21 apply (zenon_L948_); trivial. % 30.08/30.21 apply (zenon_L56_); trivial. % 30.08/30.21 (* end of lemma zenon_L949_ *) % 30.08/30.21 assert (zenon_L950_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.08/30.21 do 0 intro. intros zenon_H1a8 zenon_Hcd zenon_H2d zenon_H10e zenon_H6f zenon_H16f zenon_Hd1 zenon_Hf6 zenon_H1d5 zenon_Hc8 zenon_H19e zenon_He9 zenon_H35 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_He1 zenon_H1fd zenon_H89 zenon_Hd9 zenon_Hfc zenon_H108 zenon_H2a9 zenon_H3c zenon_Hdc zenon_H135 zenon_Hf4 zenon_H4c zenon_H14e zenon_H159 zenon_H4e. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.08/30.21 apply (zenon_L48_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.08/30.21 exact (zenon_H18f zenon_Hd2). % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.08/30.21 apply (zenon_L826_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.08/30.21 apply (zenon_L729_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.08/30.21 apply (zenon_L949_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.08/30.21 apply (zenon_L752_); trivial. % 30.08/30.21 apply (zenon_L733_); trivial. % 30.08/30.21 (* end of lemma zenon_L950_ *) % 30.08/30.21 assert (zenon_L951_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H16f zenon_Hf6 zenon_H10d zenon_H10e zenon_H8d zenon_H15a zenon_H18c zenon_H4a zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_Hd1 zenon_H4e zenon_He1 zenon_Hc9 zenon_H2d zenon_Hbd zenon_H27 zenon_H3c zenon_H1e zenon_H1a5 zenon_H89 zenon_H200 zenon_Hf4 zenon_H4c zenon_H14e zenon_H182 zenon_H6f. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.08/30.21 apply (zenon_L729_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.08/30.21 apply (zenon_L926_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.08/30.21 apply (zenon_L752_); trivial. % 30.08/30.21 apply (zenon_L758_); trivial. % 30.08/30.21 (* end of lemma zenon_L951_ *) % 30.08/30.21 assert (zenon_L952_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H35 zenon_H1e zenon_H1a5 zenon_H1a8 zenon_H6e zenon_H18f zenon_Hf6 zenon_Hf4 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_He1 zenon_H2a9 zenon_H19e zenon_H4c zenon_Hdc zenon_H18c zenon_H135 zenon_H20. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.08/30.21 apply (zenon_L740_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.08/30.21 apply (zenon_L42_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.08/30.21 apply (zenon_L764_); trivial. % 30.08/30.21 apply (zenon_L916_); trivial. % 30.08/30.21 (* end of lemma zenon_L952_ *) % 30.08/30.21 assert (zenon_L953_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.08/30.21 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H35 zenon_H1e zenon_H10e zenon_H1a5 zenon_H18c zenon_H4e zenon_H76. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.08/30.21 apply (zenon_L740_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.08/30.21 apply (zenon_L42_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.08/30.21 apply (zenon_L764_); trivial. % 30.08/30.21 apply (zenon_L864_); trivial. % 30.08/30.21 (* end of lemma zenon_L953_ *) % 30.08/30.21 assert (zenon_L954_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.08/30.21 do 0 intro. intros zenon_He4 zenon_H74 zenon_Hcd zenon_H68 zenon_Hdf zenon_Hde zenon_Hf4 zenon_H17d. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.21 exact (zenon_H74 zenon_H73). % 30.08/30.21 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.21 apply (zenon_L48_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.21 apply (zenon_L49_); trivial. % 30.08/30.21 apply (zenon_L847_); trivial. % 30.08/30.21 (* end of lemma zenon_L954_ *) % 30.08/30.21 assert (zenon_L955_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.08/30.21 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H6c zenon_H4a zenon_H10e zenon_H1a5 zenon_H18c zenon_H4e zenon_H76. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.08/30.21 apply (zenon_L740_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.08/30.21 apply (zenon_L763_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.08/30.21 apply (zenon_L764_); trivial. % 30.08/30.21 apply (zenon_L864_); trivial. % 30.08/30.21 (* end of lemma zenon_L955_ *) % 30.08/30.21 assert (zenon_L956_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H92 zenon_H17d zenon_H15a zenon_H35 zenon_He4 zenon_H74 zenon_H172 zenon_Hdf zenon_H4a zenon_Had zenon_H1a5 zenon_H18c zenon_H4e zenon_H1a8 zenon_H18f zenon_Hf6 zenon_H1fd zenon_H2d zenon_H2a9 zenon_H19e zenon_H4c zenon_H135 zenon_H20 zenon_H6f zenon_He1 zenon_H200 zenon_Hde zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_Hf4 zenon_H8d zenon_Hcd. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.21 exact (zenon_H74 zenon_H73). % 30.08/30.21 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.21 apply (zenon_L734_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.21 apply (zenon_L952_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.21 apply (zenon_L953_); trivial. % 30.08/30.21 apply (zenon_L938_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.21 apply (zenon_L49_); trivial. % 30.08/30.21 apply (zenon_L847_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.08/30.21 apply (zenon_L954_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.21 exact (zenon_H74 zenon_H73). % 30.08/30.21 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.21 apply (zenon_L925_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.21 apply (zenon_L952_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.21 apply (zenon_L955_); trivial. % 30.08/30.21 apply (zenon_L918_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.21 apply (zenon_L49_); trivial. % 30.08/30.21 apply (zenon_L847_); trivial. % 30.08/30.21 apply (zenon_L932_); trivial. % 30.08/30.21 (* end of lemma zenon_L956_ *) % 30.08/30.21 assert (zenon_L957_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.08/30.21 do 0 intro. intros zenon_He4 zenon_H74 zenon_Hcd zenon_H68 zenon_H8b zenon_H2d zenon_He1 zenon_H200 zenon_Hde zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_H172 zenon_Had zenon_H35 zenon_H4c zenon_H18c zenon_H4e zenon_H15a zenon_H8d zenon_Hf4 zenon_H17d. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.21 exact (zenon_H74 zenon_H73). % 30.08/30.21 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.21 apply (zenon_L48_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.21 apply (zenon_L789_); trivial. % 30.08/30.21 apply (zenon_L847_); trivial. % 30.08/30.21 (* end of lemma zenon_L957_ *) % 30.08/30.21 assert (zenon_L958_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H8d zenon_H117 zenon_Hd9 zenon_H6f zenon_H68 zenon_He1 zenon_Hc9 zenon_H40 zenon_H97. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.21 apply (zenon_L149_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.21 apply (zenon_L18_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.21 apply (zenon_L273_); trivial. % 30.08/30.21 apply (zenon_L862_); trivial. % 30.08/30.21 (* end of lemma zenon_L958_ *) % 30.08/30.21 assert (zenon_L959_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H8d zenon_H64 zenon_H10e zenon_H27 zenon_H3c zenon_H1e zenon_Hde zenon_Hc9 zenon_H200 zenon_H16a zenon_H16b zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.21 apply (zenon_L148_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.21 apply (zenon_L738_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.21 apply (zenon_L866_); trivial. % 30.08/30.21 apply (zenon_L862_); trivial. % 30.08/30.21 (* end of lemma zenon_L959_ *) % 30.08/30.21 assert (zenon_L960_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.08/30.21 do 0 intro. intros zenon_Hbd zenon_H15a zenon_H89 zenon_H4e zenon_H18c zenon_H4c zenon_Hc9 zenon_H4a zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_H1e zenon_H3f zenon_H10e zenon_H10d zenon_Hf6 zenon_H1e1. % 30.08/30.21 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.08/30.21 apply (zenon_L843_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.08/30.21 apply (zenon_L29_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.08/30.21 apply (zenon_L63_); trivial. % 30.08/30.21 apply (zenon_L690_); trivial. % 30.08/30.21 (* end of lemma zenon_L960_ *) % 30.08/30.21 assert (zenon_L961_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.08/30.21 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H40 zenon_Hcc zenon_He1 zenon_H156 zenon_H4e zenon_H16c. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.08/30.21 apply (zenon_L332_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.08/30.21 apply (zenon_L775_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.08/30.21 apply (zenon_L544_); trivial. % 30.08/30.21 apply (zenon_L779_); trivial. % 30.08/30.21 (* end of lemma zenon_L961_ *) % 30.08/30.21 assert (zenon_L962_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H200 zenon_H1a5 zenon_H2a9 zenon_H2d zenon_H14e zenon_Hf4 zenon_H1fd zenon_H135 zenon_Hf6 zenon_H10d zenon_H10e zenon_H3f zenon_H1e zenon_H172 zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_H4c zenon_H18c zenon_H15a zenon_Hbd zenon_H3c zenon_He9 zenon_H16c zenon_H4e zenon_H156 zenon_He1 zenon_H40 zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.21 apply (zenon_L925_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.21 apply (zenon_L207_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.21 apply (zenon_L939_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.21 apply (zenon_L960_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.21 apply (zenon_L88_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.21 apply (zenon_L961_); trivial. % 30.08/30.21 apply (zenon_L294_); trivial. % 30.08/30.21 (* end of lemma zenon_L962_ *) % 30.08/30.21 assert (zenon_L963_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H16f zenon_H100 zenon_H200 zenon_H1a5 zenon_H2a9 zenon_H2d zenon_H14e zenon_Hf4 zenon_H1fd zenon_H135 zenon_Hf6 zenon_H10d zenon_H10e zenon_H3f zenon_H1e zenon_H172 zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_H4c zenon_H18c zenon_H15a zenon_Hbd zenon_H3c zenon_He9 zenon_H4e zenon_H156 zenon_He1 zenon_H40 zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.08/30.21 apply (zenon_L241_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.08/30.21 apply (zenon_L150_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.08/30.21 apply (zenon_L752_); trivial. % 30.08/30.21 apply (zenon_L962_); trivial. % 30.08/30.21 (* end of lemma zenon_L963_ *) % 30.08/30.21 assert (zenon_L964_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H1d5 zenon_H4e zenon_H18c zenon_H1a5 zenon_H4a zenon_H6c zenon_H48 zenon_Hdf zenon_H172 zenon_H222 zenon_H40 zenon_Hcc zenon_He1 zenon_H1fd zenon_H2d zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.08/30.21 apply (zenon_L955_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.08/30.21 apply (zenon_L775_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.08/30.21 apply (zenon_L544_); trivial. % 30.08/30.21 apply (zenon_L845_); trivial. % 30.08/30.21 (* end of lemma zenon_L964_ *) % 30.08/30.21 assert (zenon_L965_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H135 zenon_Ha4 zenon_Hde zenon_H3c zenon_H74 zenon_H225 zenon_H2a9 zenon_H108 zenon_H14e zenon_H4c zenon_H10e zenon_H2d zenon_H1fd zenon_He1 zenon_H40 zenon_H222 zenon_H172 zenon_Hdf zenon_H48 zenon_H6c zenon_H4a zenon_H1a5 zenon_H18c zenon_H4e zenon_H1d5 zenon_Hf4 zenon_Hf6. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.21 apply (zenon_L49_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.21 apply (zenon_L820_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.21 apply (zenon_L964_); trivial. % 30.08/30.21 apply (zenon_L56_); trivial. % 30.08/30.21 (* end of lemma zenon_L965_ *) % 30.08/30.21 assert (zenon_L966_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((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 (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.08/30.21 do 0 intro. intros zenon_H200 zenon_Hf6 zenon_Hf4 zenon_H1d5 zenon_H4e zenon_H18c zenon_H1a5 zenon_H4a zenon_H6c zenon_H172 zenon_H222 zenon_H40 zenon_He1 zenon_H1fd zenon_H2d zenon_H4c zenon_H14e zenon_H108 zenon_H2a9 zenon_H225 zenon_H74 zenon_Hde zenon_Ha4 zenon_H135 zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_H6e. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.21 apply (zenon_L965_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.21 apply (zenon_L207_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.21 apply (zenon_L208_); trivial. % 30.08/30.21 apply (zenon_L737_); trivial. % 30.08/30.21 (* end of lemma zenon_L966_ *) % 30.08/30.21 assert (zenon_L967_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H97 zenon_H40 zenon_H16f zenon_H48 zenon_H156 zenon_H18c zenon_H2d zenon_H2b4 zenon_H100 zenon_H4c zenon_H14e zenon_H4e zenon_H16a zenon_H200 zenon_Hf6 zenon_H1d5 zenon_H1a5 zenon_H4a zenon_H6c zenon_H172 zenon_H222 zenon_He1 zenon_H1fd zenon_H108 zenon_H2a9 zenon_H225 zenon_H74 zenon_H135 zenon_H1e zenon_H3c zenon_H27 zenon_H10d zenon_H3f zenon_Had zenon_H15a zenon_Hbd zenon_Hc8 zenon_H8d zenon_H174 zenon_Hde zenon_H10e zenon_Hf4 zenon_Ha4. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.08/30.21 exact (zenon_H74 zenon_H73). % 30.08/30.21 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.21 apply (zenon_L963_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.21 apply (zenon_L4_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.21 apply (zenon_L87_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.21 apply (zenon_L963_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.21 apply (zenon_L966_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.21 apply (zenon_L866_); trivial. % 30.08/30.21 apply (zenon_L862_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.08/30.21 apply (zenon_L192_); trivial. % 30.08/30.21 apply (zenon_L819_); trivial. % 30.08/30.21 (* end of lemma zenon_L967_ *) % 30.08/30.21 assert (zenon_L968_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((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 (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H23b zenon_H20 zenon_H40 zenon_H6f zenon_H19a zenon_Hee zenon_H2b7 zenon_H8b zenon_Hb5 zenon_H110 zenon_Hf4 zenon_H2a9. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.08/30.21 apply (zenon_L27_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.08/30.21 apply (zenon_L80_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.08/30.21 apply (zenon_L337_); trivial. % 30.08/30.21 apply (zenon_L900_); trivial. % 30.08/30.21 (* end of lemma zenon_L968_ *) % 30.08/30.21 assert (zenon_L969_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.08/30.21 do 0 intro. intros zenon_H200 zenon_H69 zenon_H18c zenon_H3c zenon_H14e zenon_H1dc zenon_H3f zenon_H1e zenon_H23b zenon_H20 zenon_H40 zenon_H6f zenon_H19a zenon_Hee zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hf4 zenon_H2a9 zenon_Hbd zenon_H156 zenon_H48 zenon_H6e. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.21 apply (zenon_L740_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.21 apply (zenon_L207_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.08/30.21 apply (zenon_L968_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.08/30.21 apply (zenon_L29_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.08/30.21 apply (zenon_L177_); trivial. % 30.08/30.21 apply (zenon_L770_); trivial. % 30.08/30.21 apply (zenon_L737_); trivial. % 30.08/30.21 (* end of lemma zenon_L969_ *) % 30.08/30.21 assert (zenon_L970_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H1a8 zenon_H90 zenon_Had zenon_H18f zenon_H48 zenon_H156 zenon_Hbd zenon_H2a9 zenon_Hf4 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_Hee zenon_H6f zenon_H40 zenon_H20 zenon_H23b zenon_H1e zenon_H3f zenon_H1dc zenon_H14e zenon_H3c zenon_H18c zenon_H69 zenon_H200 zenon_H4e zenon_H6e zenon_Hd1. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.08/30.21 apply (zenon_L639_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.08/30.21 exact (zenon_H18f zenon_Hd2). % 30.08/30.21 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.08/30.21 apply (zenon_L969_); trivial. % 30.08/30.21 apply (zenon_L729_); trivial. % 30.08/30.21 (* end of lemma zenon_L970_ *) % 30.08/30.21 assert (zenon_L971_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.08/30.21 do 0 intro. intros zenon_H8d zenon_Hd1 zenon_H200 zenon_H69 zenon_H3c zenon_H1dc zenon_H3f zenon_H1e zenon_H23b zenon_H20 zenon_Hee zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H2a9 zenon_Hbd zenon_H18f zenon_Had zenon_H1a8 zenon_H16a zenon_H16b zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H40 zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H48 zenon_H16f zenon_H6f zenon_H90. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.21 apply (zenon_L538_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.21 apply (zenon_L970_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.21 apply (zenon_L866_); trivial. % 30.08/30.21 apply (zenon_L39_); trivial. % 30.08/30.21 (* end of lemma zenon_L971_ *) % 30.08/30.21 assert (zenon_L972_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((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 (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.08/30.21 do 0 intro. intros zenon_He4 zenon_Hf6 zenon_Hf4 zenon_H1d5 zenon_H222 zenon_H40 zenon_H1fd zenon_H14e zenon_H108 zenon_H2a9 zenon_H225 zenon_H74 zenon_Ha4 zenon_H135 zenon_H1a5 zenon_H2d zenon_He1 zenon_H200 zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_H172 zenon_Had zenon_H35 zenon_H4c zenon_H18c zenon_H4e zenon_H15a zenon_H8d zenon_H8b zenon_Hde. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.21 exact (zenon_H74 zenon_H73). % 30.08/30.21 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.08/30.21 apply (zenon_L749_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.08/30.21 apply (zenon_L42_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.08/30.21 apply (zenon_L764_); trivial. % 30.08/30.21 apply (zenon_L908_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.21 apply (zenon_L789_); trivial. % 30.08/30.21 apply (zenon_L288_); trivial. % 30.08/30.21 (* end of lemma zenon_L972_ *) % 30.08/30.21 assert (zenon_L973_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.08/30.21 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H3d zenon_H2a9 zenon_He1 zenon_H14e zenon_H4c zenon_H10e zenon_H2d zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.21 apply (zenon_L49_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.21 apply (zenon_L126_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.21 apply (zenon_L821_); trivial. % 30.08/30.21 apply (zenon_L56_); trivial. % 30.08/30.21 (* end of lemma zenon_L973_ *) % 30.08/30.21 assert (zenon_L974_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.08/30.21 do 0 intro. intros zenon_H200 zenon_Hf6 zenon_He1 zenon_H3d zenon_Hde zenon_H135 zenon_H1e zenon_H3c zenon_H2a9 zenon_H2d zenon_H14e zenon_H4c zenon_Hf4 zenon_H10e zenon_H1fd zenon_H156 zenon_H48 zenon_H6e. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.21 apply (zenon_L973_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.21 apply (zenon_L207_); trivial. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.21 apply (zenon_L939_); trivial. % 30.08/30.21 apply (zenon_L737_); trivial. % 30.08/30.21 (* end of lemma zenon_L974_ *) % 30.08/30.21 assert (zenon_L975_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((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 (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.08/30.21 do 0 intro. intros zenon_H200 zenon_Hf6 zenon_Hf4 zenon_H1d5 zenon_H4e zenon_H18c zenon_H222 zenon_H40 zenon_He1 zenon_H1fd zenon_H2d zenon_H4c zenon_H14e zenon_H108 zenon_H2a9 zenon_H225 zenon_H74 zenon_Hde zenon_Ha4 zenon_Hdc zenon_H135 zenon_H1a5 zenon_Hd2 zenon_H20 zenon_H172 zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_H6e. % 30.08/30.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.21 apply (zenon_L909_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.22 apply (zenon_L207_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.22 apply (zenon_L208_); trivial. % 30.08/30.22 apply (zenon_L737_); trivial. % 30.08/30.22 (* end of lemma zenon_L975_ *) % 30.08/30.22 assert (zenon_L976_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H174 zenon_H88 zenon_H3f zenon_H8d zenon_H6f zenon_H15a zenon_H10e zenon_H27 zenon_H3c zenon_H1e zenon_H172 zenon_H20 zenon_Hd2 zenon_H1a5 zenon_H135 zenon_Hdc zenon_Ha4 zenon_Hde zenon_H74 zenon_H225 zenon_H2a9 zenon_H108 zenon_H1fd zenon_He1 zenon_H222 zenon_H1d5 zenon_Hf6 zenon_H200 zenon_H16a zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.22 apply (zenon_L734_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.22 apply (zenon_L746_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.22 apply (zenon_L87_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.22 apply (zenon_L893_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.22 apply (zenon_L975_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.22 apply (zenon_L866_); trivial. % 30.08/30.22 apply (zenon_L862_); trivial. % 30.08/30.22 (* end of lemma zenon_L976_ *) % 30.08/30.22 assert (zenon_L977_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H42 zenon_H6e zenon_H174 zenon_H88 zenon_H3f zenon_H8d zenon_H6f zenon_H15a zenon_H10e zenon_H27 zenon_H3c zenon_H1e zenon_H172 zenon_H20 zenon_Hd2 zenon_H1a5 zenon_H135 zenon_Hdc zenon_Ha4 zenon_Hde zenon_H74 zenon_H225 zenon_H2a9 zenon_H108 zenon_H1fd zenon_He1 zenon_H222 zenon_H1d5 zenon_Hf6 zenon_H200 zenon_H16a zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H48 zenon_H16f zenon_H97. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.08/30.22 apply (zenon_L937_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.08/30.22 apply (zenon_L974_); trivial. % 30.08/30.22 apply (zenon_L976_); trivial. % 30.08/30.22 (* end of lemma zenon_L977_ *) % 30.08/30.22 assert (zenon_L978_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H8d zenon_H15a zenon_H48 zenon_H156 zenon_H10e zenon_H27 zenon_H3c zenon_H1e zenon_Hde zenon_H200 zenon_He1 zenon_Hc9 zenon_H16f zenon_Had zenon_Hd2 zenon_H6f zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.22 apply (zenon_L893_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.22 apply (zenon_L738_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.22 apply (zenon_L273_); trivial. % 30.08/30.22 apply (zenon_L895_); trivial. % 30.08/30.22 (* end of lemma zenon_L978_ *) % 30.08/30.22 assert (zenon_L979_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_He4 zenon_H18c zenon_H2b4 zenon_H42 zenon_H3f zenon_H172 zenon_H20 zenon_H1a5 zenon_H135 zenon_Ha4 zenon_H74 zenon_H225 zenon_H2a9 zenon_H108 zenon_H1fd zenon_H222 zenon_H1d5 zenon_Hf6 zenon_H100 zenon_H97 zenon_H16a zenon_H4e zenon_H14e zenon_H4c zenon_H6f zenon_Hd2 zenon_Had zenon_H16f zenon_He1 zenon_H200 zenon_Hde zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_H15a zenon_H8d zenon_H2d zenon_H88 zenon_H174 zenon_Hf4 zenon_H17d. % 30.08/30.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.22 exact (zenon_H74 zenon_H73). % 30.08/30.22 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.22 apply (zenon_L734_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.22 apply (zenon_L87_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.22 apply (zenon_L893_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.22 apply (zenon_L977_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.22 apply (zenon_L894_); trivial. % 30.08/30.22 apply (zenon_L895_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.22 apply (zenon_L734_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.22 apply (zenon_L87_); trivial. % 30.08/30.22 apply (zenon_L978_); trivial. % 30.08/30.22 apply (zenon_L847_); trivial. % 30.08/30.22 (* end of lemma zenon_L979_ *) % 30.08/30.22 assert (zenon_L980_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((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 (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.08/30.22 do 0 intro. intros zenon_H42 zenon_H6f zenon_H200 zenon_Hf6 zenon_Hf4 zenon_H1d5 zenon_H4e zenon_H18c zenon_H222 zenon_He1 zenon_H1fd zenon_H2d zenon_H4c zenon_H14e zenon_H108 zenon_H2a9 zenon_H225 zenon_H74 zenon_Hde zenon_Ha4 zenon_Hdc zenon_H135 zenon_H1a5 zenon_Hd2 zenon_H20 zenon_H172 zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_H6e. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.08/30.22 apply (zenon_L125_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.08/30.22 apply (zenon_L974_); trivial. % 30.08/30.22 apply (zenon_L975_); trivial. % 30.08/30.22 (* end of lemma zenon_L980_ *) % 30.08/30.22 assert (zenon_L981_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H200 zenon_Hf4 zenon_H1fd zenon_H2d zenon_H14e zenon_He1 zenon_H2a9 zenon_H3d zenon_Hde zenon_H135 zenon_H3c zenon_H27 zenon_Hbd zenon_H15a zenon_H89 zenon_H4e zenon_H18c zenon_H4c zenon_Hc9 zenon_H4a zenon_H6c zenon_Had zenon_H48 zenon_H172 zenon_H1e zenon_H3f zenon_H10e zenon_H10d zenon_Hf6. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.22 apply (zenon_L973_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.22 apply (zenon_L207_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.22 apply (zenon_L208_); trivial. % 30.08/30.22 apply (zenon_L960_); trivial. % 30.08/30.22 (* end of lemma zenon_L981_ *) % 30.08/30.22 assert (zenon_L982_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H8d zenon_H16a zenon_H16b zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H6f zenon_Hd2 zenon_H15a zenon_H16f zenon_H48 zenon_H156 zenon_H10e zenon_H27 zenon_H3c zenon_H1e zenon_Hde zenon_H200 zenon_He1 zenon_Hc9 zenon_H40 zenon_H97. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.22 apply (zenon_L893_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.22 apply (zenon_L738_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.22 apply (zenon_L273_); trivial. % 30.08/30.22 apply (zenon_L862_); trivial. % 30.08/30.22 (* end of lemma zenon_L982_ *) % 30.08/30.22 assert (zenon_L983_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H174 zenon_Hf6 zenon_H10d zenon_H3f zenon_H172 zenon_Had zenon_H6c zenon_H4a zenon_H18c zenon_Hbd zenon_H135 zenon_Ha4 zenon_H74 zenon_H225 zenon_H2a9 zenon_H108 zenon_H1fd zenon_H222 zenon_H1a5 zenon_H1d5 zenon_H2d zenon_H8d zenon_H16a zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H6f zenon_Hd2 zenon_H15a zenon_H16f zenon_H48 zenon_H156 zenon_H10e zenon_H27 zenon_H3c zenon_H1e zenon_Hde zenon_H200 zenon_He1 zenon_Hc9 zenon_H40 zenon_H97. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.22 apply (zenon_L965_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.22 apply (zenon_L207_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.22 apply (zenon_L208_); trivial. % 30.08/30.22 apply (zenon_L960_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.22 apply (zenon_L87_); trivial. % 30.08/30.22 apply (zenon_L982_); trivial. % 30.08/30.22 (* end of lemma zenon_L983_ *) % 30.08/30.22 assert (zenon_L984_ : (((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)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H92 zenon_Hd9 zenon_Hd1 zenon_Hc8 zenon_Had zenon_H10d zenon_H3f zenon_H4a zenon_Hbd zenon_H97 zenon_H17d zenon_He4 zenon_H16f zenon_H18c zenon_H2d zenon_H2b4 zenon_Hd2 zenon_H4c zenon_H14e zenon_H4e zenon_H16a zenon_H42 zenon_Hf6 zenon_H1d5 zenon_H222 zenon_H1fd zenon_H108 zenon_H2a9 zenon_H225 zenon_H74 zenon_Ha4 zenon_H135 zenon_H1a5 zenon_H20 zenon_H172 zenon_H15a zenon_H26 zenon_H174 zenon_H6f zenon_He1 zenon_H200 zenon_Hde zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_Hf4 zenon_H8d zenon_Hcd. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.08/30.22 apply (zenon_L797_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.08/30.22 apply (zenon_L45_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.08/30.22 exact (zenon_H74 zenon_H73). % 30.08/30.22 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.22 exact (zenon_H74 zenon_H73). % 30.08/30.22 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.08/30.22 apply (zenon_L241_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.08/30.22 apply (zenon_L125_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.08/30.22 apply (zenon_L752_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.08/30.22 apply (zenon_L125_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.22 apply (zenon_L973_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.22 apply (zenon_L207_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.22 apply (zenon_L208_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.22 apply (zenon_L960_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.22 apply (zenon_L126_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.22 apply (zenon_L821_); trivial. % 30.08/30.22 apply (zenon_L294_); trivial. % 30.08/30.22 apply (zenon_L962_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.22 apply (zenon_L598_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.22 apply (zenon_L893_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.22 apply (zenon_L980_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.22 apply (zenon_L157_); trivial. % 30.08/30.22 apply (zenon_L895_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.08/30.22 apply (zenon_L125_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.08/30.22 apply (zenon_L981_); trivial. % 30.08/30.22 apply (zenon_L983_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.22 apply (zenon_L87_); trivial. % 30.08/30.22 apply (zenon_L978_); trivial. % 30.08/30.22 apply (zenon_L847_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.08/30.22 apply (zenon_L192_); trivial. % 30.08/30.22 apply (zenon_L819_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.22 exact (zenon_H74 zenon_H73). % 30.08/30.22 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.22 apply (zenon_L538_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.22 apply (zenon_L598_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.22 apply (zenon_L893_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.22 apply (zenon_L980_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.22 apply (zenon_L894_); trivial. % 30.08/30.22 apply (zenon_L39_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.22 apply (zenon_L931_); trivial. % 30.08/30.22 apply (zenon_L386_); trivial. % 30.08/30.22 (* end of lemma zenon_L984_ *) % 30.08/30.22 assert (zenon_L985_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H42 zenon_H16a zenon_H33 zenon_Hc9 zenon_H27 zenon_H200 zenon_H1a5 zenon_H2a9 zenon_H2d zenon_H14e zenon_Hf4 zenon_H1fd zenon_H135 zenon_Hf6 zenon_H10d zenon_H10e zenon_H3f zenon_H1e zenon_H172 zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_H4c zenon_H18c zenon_H15a zenon_Hbd zenon_H3c zenon_He9 zenon_H16c zenon_H4e zenon_H156 zenon_He1 zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.08/30.22 apply (zenon_L839_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.08/30.22 apply (zenon_L981_); trivial. % 30.08/30.22 apply (zenon_L962_); trivial. % 30.08/30.22 (* end of lemma zenon_L985_ *) % 30.08/30.22 assert (zenon_L986_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.08/30.22 do 0 intro. intros zenon_Hbd zenon_H15a zenon_H89 zenon_H18c zenon_H4c zenon_Hc9 zenon_H1e zenon_H35 zenon_Had zenon_H48 zenon_H172 zenon_H40 zenon_H2d zenon_H10e zenon_H10d zenon_H1e6 zenon_H33 zenon_H218 zenon_Hf6 zenon_Hf4 zenon_H156 zenon_H4e zenon_H16c. % 30.08/30.22 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.08/30.22 apply (zenon_L788_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.08/30.22 apply (zenon_L766_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.08/30.22 apply (zenon_L63_); trivial. % 30.08/30.22 apply (zenon_L871_); trivial. % 30.08/30.22 (* end of lemma zenon_L986_ *) % 30.08/30.22 assert (zenon_L987_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H200 zenon_H108 zenon_H225 zenon_H74 zenon_Ha4 zenon_Hdc zenon_H1a5 zenon_Hd2 zenon_H20 zenon_H2a9 zenon_H14e zenon_H1fd zenon_H135 zenon_Hf4 zenon_Hf6 zenon_H218 zenon_H33 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2d zenon_H172 zenon_H48 zenon_Had zenon_H35 zenon_H1e zenon_H4c zenon_H18c zenon_H15a zenon_Hbd zenon_H3c zenon_He9 zenon_H16c zenon_H4e zenon_H156 zenon_He1 zenon_H40 zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.22 apply (zenon_L909_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.22 apply (zenon_L207_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.22 apply (zenon_L939_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.22 apply (zenon_L986_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.22 apply (zenon_L88_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.22 apply (zenon_L961_); trivial. % 30.08/30.22 apply (zenon_L294_); trivial. % 30.08/30.22 (* end of lemma zenon_L987_ *) % 30.08/30.22 assert (zenon_L988_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H16f zenon_H48 zenon_H156 zenon_H18c zenon_H76 zenon_H2d zenon_H2b4 zenon_H33 zenon_H4a zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.08/30.22 apply (zenon_L865_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.08/30.22 apply (zenon_L839_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.08/30.22 apply (zenon_L752_); trivial. % 30.08/30.22 apply (zenon_L859_); trivial. % 30.08/30.22 (* end of lemma zenon_L988_ *) % 30.08/30.22 assert (zenon_L989_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H16f zenon_H42 zenon_H16a zenon_H33 zenon_Hc9 zenon_H27 zenon_H200 zenon_H1a5 zenon_H2a9 zenon_H2d zenon_H14e zenon_Hf4 zenon_H1fd zenon_H135 zenon_Hf6 zenon_H10d zenon_H10e zenon_H3f zenon_H1e zenon_H172 zenon_H48 zenon_Had zenon_H6c zenon_H4a zenon_H4c zenon_H18c zenon_H15a zenon_Hbd zenon_H3c zenon_He9 zenon_H4e zenon_H156 zenon_He1 zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.08/30.22 apply (zenon_L241_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.08/30.22 apply (zenon_L839_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.08/30.22 apply (zenon_L752_); trivial. % 30.08/30.22 apply (zenon_L985_); trivial. % 30.08/30.22 (* end of lemma zenon_L989_ *) % 30.08/30.22 assert (zenon_L990_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_H17d zenon_H174 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_Hbd zenon_H18c zenon_H4a zenon_H6c zenon_H172 zenon_H3f zenon_H10d zenon_Hf6 zenon_H135 zenon_H1fd zenon_H2a9 zenon_H1a5 zenon_H33 zenon_H42 zenon_H2d zenon_H8d zenon_H15a zenon_H48 zenon_H156 zenon_H27 zenon_H3c zenon_H1e zenon_H200 zenon_He1 zenon_H16f zenon_Had zenon_Hd2 zenon_H6f zenon_H4c zenon_H14e zenon_H4e zenon_H16a zenon_H35 zenon_H1e6 zenon_H218 zenon_H20 zenon_H74 zenon_H225 zenon_H108 zenon_H2b4 zenon_He4 zenon_Hde zenon_H10e zenon_Hf4 zenon_Ha4. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.08/30.22 exact (zenon_H74 zenon_H73). % 30.08/30.22 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.22 exact (zenon_H74 zenon_H73). % 30.08/30.22 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.08/30.22 apply (zenon_L980_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.08/30.22 apply (zenon_L839_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.08/30.22 apply (zenon_L752_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.08/30.22 apply (zenon_L839_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.22 apply (zenon_L925_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.22 apply (zenon_L207_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.22 apply (zenon_L939_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.22 apply (zenon_L985_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.22 apply (zenon_L126_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.22 apply (zenon_L821_); trivial. % 30.08/30.22 apply (zenon_L294_); trivial. % 30.08/30.22 apply (zenon_L987_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.22 apply (zenon_L87_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.22 apply (zenon_L893_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.22 apply (zenon_L980_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.22 apply (zenon_L988_); trivial. % 30.08/30.22 apply (zenon_L895_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.22 apply (zenon_L989_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.22 apply (zenon_L87_); trivial. % 30.08/30.22 apply (zenon_L978_); trivial. % 30.08/30.22 apply (zenon_L847_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.08/30.22 apply (zenon_L192_); trivial. % 30.08/30.22 apply (zenon_L819_); trivial. % 30.08/30.22 (* end of lemma zenon_L990_ *) % 30.08/30.22 assert (zenon_L991_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.08/30.22 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H90 zenon_H1e zenon_H3f zenon_H142 zenon_H1dc zenon_H14e zenon_H48 zenon_H6e. % 30.08/30.22 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.08/30.22 apply (zenon_L27_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.08/30.22 apply (zenon_L29_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.08/30.22 apply (zenon_L177_); trivial. % 30.08/30.22 apply (zenon_L770_); trivial. % 30.08/30.22 (* end of lemma zenon_L991_ *) % 30.08/30.22 assert (zenon_L992_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (op (e1) (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 (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.08/30.22 do 0 intro. intros zenon_H200 zenon_Hf6 zenon_Hf4 zenon_H1d5 zenon_H4e zenon_H18c zenon_H222 zenon_H40 zenon_He1 zenon_H1fd zenon_H2d zenon_H10e zenon_H4c zenon_H108 zenon_H2a9 zenon_H225 zenon_H74 zenon_Hde zenon_Ha4 zenon_Hdc zenon_H135 zenon_H1a5 zenon_Hd2 zenon_H172 zenon_H3c zenon_H14e zenon_H1dc zenon_H3f zenon_H1e zenon_H90 zenon_H20 zenon_Hbd zenon_H156 zenon_H48 zenon_H6e. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.22 apply (zenon_L909_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.22 apply (zenon_L207_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.22 apply (zenon_L991_); trivial. % 30.08/30.22 apply (zenon_L737_); trivial. % 30.08/30.22 (* end of lemma zenon_L992_ *) % 30.08/30.22 assert (zenon_L993_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.08/30.22 do 0 intro. intros zenon_He4 zenon_H16f zenon_H18c zenon_H2d zenon_H2b4 zenon_H33 zenon_H4a zenon_H4c zenon_H14e zenon_H4e zenon_H16a zenon_H42 zenon_Hf6 zenon_H1d5 zenon_H222 zenon_H1fd zenon_H108 zenon_H2a9 zenon_H225 zenon_H74 zenon_Ha4 zenon_H135 zenon_H1a5 zenon_Hd2 zenon_H172 zenon_H1dc zenon_H3f zenon_H20 zenon_Hbd zenon_H15a zenon_H174 zenon_H6f zenon_He1 zenon_H200 zenon_Hde zenon_H1e zenon_H3c zenon_H27 zenon_H10e zenon_H156 zenon_H48 zenon_Hf4 zenon_H8d zenon_H90 zenon_Hcd. % 30.08/30.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.22 exact (zenon_H74 zenon_H73). % 30.08/30.22 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.22 apply (zenon_L538_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.22 apply (zenon_L87_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.22 apply (zenon_L893_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.08/30.22 apply (zenon_L4_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.08/30.22 apply (zenon_L839_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.08/30.22 apply (zenon_L974_); trivial. % 30.08/30.22 apply (zenon_L992_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.22 apply (zenon_L988_); trivial. % 30.08/30.22 apply (zenon_L39_); trivial. % 30.08/30.22 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.22 apply (zenon_L931_); trivial. % 30.08/30.22 apply (zenon_L386_); trivial. % 30.08/30.22 (* end of lemma zenon_L993_ *) % 30.08/30.22 assert (zenon_L994_ : (((op (e2) (op (e2) (e0))) = (e0))/\(((op (e2) (op (e2) (e1))) = (e1))/\(((op (e2) (op (e2) (e2))) = (e2))/\(((op (e2) (op (e2) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0)))/\(((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3)))))))))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 30.08/30.22 do 0 intro. intros zenon_H5a zenon_H2a9 zenon_Hf4. % 30.08/30.22 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.08/30.22 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.08/30.22 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.08/30.22 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.08/30.22 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.08/30.22 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.08/30.22 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.08/30.22 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.08/30.22 exact (zenon_H231 zenon_Hf4). % 30.08/30.22 exact (zenon_H2a9 zenon_Hb6). % 30.08/30.22 (* end of lemma zenon_L994_ *) % 30.08/30.22 assert (zenon_L995_ : ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_Hb3 zenon_Hf4 zenon_H15e zenon_Hee. % 30.08/30.22 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 30.08/30.22 intro zenon_D_pnotp. % 30.08/30.22 apply zenon_Hee. % 30.08/30.22 rewrite <- zenon_D_pnotp. % 30.08/30.22 exact zenon_Hef. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 30.08/30.22 congruence. % 30.08/30.22 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 30.08/30.22 intro zenon_D_pnotp. % 30.08/30.22 apply zenon_Hf1. % 30.08/30.22 rewrite <- zenon_D_pnotp. % 30.08/30.22 exact zenon_Hb3. % 30.08/30.22 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 30.08/30.22 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H11a]. % 30.08/30.22 congruence. % 30.08/30.22 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e2)))). % 30.08/30.22 intro zenon_D_pnotp. % 30.08/30.22 apply zenon_H11a. % 30.08/30.22 rewrite <- zenon_D_pnotp. % 30.08/30.22 exact zenon_Hef. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 30.08/30.22 congruence. % 30.08/30.22 apply (zenon_L67_); trivial. % 30.08/30.22 apply zenon_Hf0. apply refl_equal. % 30.08/30.22 apply zenon_Hf0. apply refl_equal. % 30.08/30.22 apply zenon_H1fb. apply sym_equal. exact zenon_H15e. % 30.08/30.22 apply zenon_Hf0. apply refl_equal. % 30.08/30.22 apply zenon_Hf0. apply refl_equal. % 30.08/30.22 (* end of lemma zenon_L995_ *) % 30.08/30.22 assert (zenon_L996_ : ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.08/30.22 do 0 intro. intros zenon_Hb3 zenon_Hf4 zenon_H1b9 zenon_H1dc. % 30.08/30.22 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e2) (e2)) = (op (e3) (e2)))). % 30.08/30.22 intro zenon_D_pnotp. % 30.08/30.22 apply zenon_H1dc. % 30.08/30.22 rewrite <- zenon_D_pnotp. % 30.08/30.22 exact zenon_Hef. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 30.08/30.22 congruence. % 30.08/30.22 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e2)) = (op (e2) (e2)))). % 30.08/30.22 intro zenon_D_pnotp. % 30.08/30.22 apply zenon_H1fa. % 30.08/30.22 rewrite <- zenon_D_pnotp. % 30.08/30.22 exact zenon_Hb3. % 30.08/30.22 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 30.08/30.22 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H11a]. % 30.08/30.22 congruence. % 30.08/30.22 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e2)))). % 30.08/30.22 intro zenon_D_pnotp. % 30.08/30.22 apply zenon_H11a. % 30.08/30.22 rewrite <- zenon_D_pnotp. % 30.08/30.22 exact zenon_Hef. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 30.08/30.22 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 30.08/30.22 congruence. % 30.08/30.22 apply (zenon_L67_); trivial. % 30.08/30.22 apply zenon_Hf0. apply refl_equal. % 30.08/30.22 apply zenon_Hf0. apply refl_equal. % 30.08/30.22 apply zenon_H1de. apply sym_equal. exact zenon_H1b9. % 30.08/30.22 apply zenon_Hf0. apply refl_equal. % 30.08/30.22 apply zenon_Hf0. apply refl_equal. % 30.08/30.22 (* end of lemma zenon_L996_ *) % 30.08/30.22 assert (zenon_L997_ : (((op (e3) (op (e3) (e0))) = (e0))/\(((op (e3) (op (e3) (e1))) = (e1))/\(((op (e3) (op (e3) (e2))) = (e2))/\(((op (e3) (op (e3) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0)))/\(((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1)))/\(((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3)))))))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H270 zenon_H1fd zenon_H10d zenon_Hee zenon_H1dc zenon_Hf4 zenon_H2a9. % 30.08/30.23 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.08/30.23 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.08/30.23 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.08/30.23 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.08/30.23 apply (zenon_L68_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.08/30.23 apply (zenon_L995_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.08/30.23 apply (zenon_L996_); trivial. % 30.08/30.23 exact (zenon_H2a9 zenon_Hb6). % 30.08/30.23 (* end of lemma zenon_L997_ *) % 30.08/30.23 assert (zenon_L998_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H88 zenon_H73 zenon_Hcd. % 30.08/30.23 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 30.08/30.23 cut (((e2) = (e2)) = ((e1) = (e2))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_Hcd. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_Hce. % 30.08/30.23 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 30.08/30.23 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 30.08/30.23 congruence. % 30.08/30.23 cut (((op (e0) (e0)) = (e1)) = ((e2) = (e1))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_Hcf. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H88. % 30.08/30.23 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.08/30.23 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 30.08/30.23 congruence. % 30.08/30.23 exact (zenon_H74 zenon_H73). % 30.08/30.23 apply zenon_H22. apply refl_equal. % 30.08/30.23 apply zenon_H57. apply refl_equal. % 30.08/30.23 apply zenon_H57. apply refl_equal. % 30.08/30.23 (* end of lemma zenon_L998_ *) % 30.08/30.23 assert (zenon_L999_ : (~((op (e0) (e0)) = (op (e0) (op (e0) (e3))))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H2c7 zenon_H185. % 30.08/30.23 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 30.08/30.23 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.08/30.23 congruence. % 30.08/30.23 apply zenon_H1d. apply refl_equal. % 30.08/30.23 apply zenon_H2c8. apply sym_equal. exact zenon_H185. % 30.08/30.23 (* end of lemma zenon_L999_ *) % 30.08/30.23 assert (zenon_L1000_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H15a zenon_H36 zenon_H185 zenon_H6e. % 30.08/30.23 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H15a. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H36. % 30.08/30.23 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 30.08/30.23 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2c9]. % 30.08/30.23 congruence. % 30.08/30.23 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H18b | zenon_intro zenon_Hcb ]. % 30.08/30.23 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e0)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H2c9. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H18b. % 30.08/30.23 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.08/30.23 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2c7]. % 30.08/30.23 congruence. % 30.08/30.23 apply (zenon_L999_); trivial. % 30.08/30.23 apply zenon_Hcb. apply refl_equal. % 30.08/30.23 apply zenon_Hcb. apply refl_equal. % 30.08/30.23 apply zenon_Haf. apply sym_equal. exact zenon_H6e. % 30.08/30.23 (* end of lemma zenon_L1000_ *) % 30.08/30.23 assert (zenon_L1001_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_Hc8 zenon_H36 zenon_H185 zenon_H76. % 30.08/30.23 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_Hc8. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H36. % 30.08/30.23 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 30.08/30.23 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2c9]. % 30.08/30.23 congruence. % 30.08/30.23 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H18b | zenon_intro zenon_Hcb ]. % 30.08/30.23 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e0)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H2c9. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H18b. % 30.08/30.23 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.08/30.23 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2c7]. % 30.08/30.23 congruence. % 30.08/30.23 apply (zenon_L999_); trivial. % 30.08/30.23 apply zenon_Hcb. apply refl_equal. % 30.08/30.23 apply zenon_Hcb. apply refl_equal. % 30.08/30.23 apply zenon_H1da. apply sym_equal. exact zenon_H76. % 30.08/30.23 (* end of lemma zenon_L1001_ *) % 30.08/30.23 assert (zenon_L1002_ : ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H37 zenon_H2c zenon_H35. % 30.08/30.23 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.08/30.23 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H35. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_Hc4. % 30.08/30.23 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.08/30.23 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 30.08/30.23 congruence. % 30.08/30.23 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_Hc6. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H37. % 30.08/30.23 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 30.08/30.23 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.08/30.23 congruence. % 30.08/30.23 apply zenon_Hc5. apply refl_equal. % 30.08/30.23 apply zenon_H191. apply sym_equal. exact zenon_H2c. % 30.08/30.23 apply zenon_Hc5. apply refl_equal. % 30.08/30.23 apply zenon_Hc5. apply refl_equal. % 30.08/30.23 (* end of lemma zenon_L1002_ *) % 30.08/30.23 assert (zenon_L1003_ : (~((op (e0) (e3)) = (op (e0) (op (e0) (e2))))) -> ((op (e0) (e2)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H2ca zenon_H117. % 30.08/30.23 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 30.08/30.23 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.08/30.23 congruence. % 30.08/30.23 apply zenon_H1d. apply refl_equal. % 30.08/30.23 apply zenon_H119. apply sym_equal. exact zenon_H117. % 30.08/30.23 (* end of lemma zenon_L1003_ *) % 30.08/30.23 assert (zenon_L1004_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H16a zenon_H198 zenon_H117 zenon_H155. % 30.08/30.23 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H16a. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H198. % 30.08/30.23 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 30.08/30.23 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2cb]. % 30.08/30.23 congruence. % 30.08/30.23 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H16e ]. % 30.08/30.23 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e3)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H2cb. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H194. % 30.08/30.23 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.08/30.23 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 30.08/30.23 congruence. % 30.08/30.23 apply (zenon_L1003_); trivial. % 30.08/30.23 apply zenon_H16e. apply refl_equal. % 30.08/30.23 apply zenon_H16e. apply refl_equal. % 30.08/30.23 apply zenon_H158. apply sym_equal. exact zenon_H155. % 30.08/30.23 (* end of lemma zenon_L1004_ *) % 30.08/30.23 assert (zenon_L1005_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hc9 zenon_H35 zenon_He9 zenon_Hcd zenon_H19a zenon_H16a zenon_H198 zenon_H117. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.08/30.23 apply (zenon_L142_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.08/30.23 apply (zenon_L95_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.08/30.23 apply (zenon_L159_); trivial. % 30.08/30.23 apply (zenon_L1004_); trivial. % 30.08/30.23 (* end of lemma zenon_L1005_ *) % 30.08/30.23 assert (zenon_L1006_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> False). % 30.08/30.23 do 0 intro. intros zenon_Ha4 zenon_H198 zenon_H117 zenon_Hf4. % 30.08/30.23 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_Ha4. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H198. % 30.08/30.23 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 30.08/30.23 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2cb]. % 30.08/30.23 congruence. % 30.08/30.23 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H16e ]. % 30.08/30.23 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e3)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H2cb. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H194. % 30.08/30.23 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.08/30.23 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 30.08/30.23 congruence. % 30.08/30.23 apply (zenon_L1003_); trivial. % 30.08/30.23 apply zenon_H16e. apply refl_equal. % 30.08/30.23 apply zenon_H16e. apply refl_equal. % 30.08/30.23 apply zenon_H116. apply sym_equal. exact zenon_Hf4. % 30.08/30.23 (* end of lemma zenon_L1006_ *) % 30.08/30.23 assert (zenon_L1007_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H267 zenon_Hde zenon_H185 zenon_H16a zenon_He1 zenon_H1c5 zenon_Ha4 zenon_H198 zenon_H117. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.08/30.23 apply (zenon_L817_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.08/30.23 apply (zenon_L1004_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.08/30.23 apply (zenon_L221_); trivial. % 30.08/30.23 apply (zenon_L1006_); trivial. % 30.08/30.23 (* end of lemma zenon_L1007_ *) % 30.08/30.23 assert (zenon_L1008_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H55 zenon_H27 zenon_H267 zenon_Hde zenon_H185 zenon_H16a zenon_He1 zenon_Ha4 zenon_H198 zenon_H117. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.08/30.23 apply (zenon_L174_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.08/30.23 apply (zenon_L126_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.08/30.23 apply (zenon_L160_); trivial. % 30.08/30.23 apply (zenon_L1007_); trivial. % 30.08/30.23 (* end of lemma zenon_L1008_ *) % 30.08/30.23 assert (zenon_L1009_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_Hcc zenon_H267 zenon_Hde zenon_H185 zenon_H16a zenon_He1 zenon_Ha4 zenon_H198 zenon_H117. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.08/30.23 apply (zenon_L174_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.08/30.23 apply (zenon_L131_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.08/30.23 apply (zenon_L544_); trivial. % 30.08/30.23 apply (zenon_L1007_); trivial. % 30.08/30.23 (* end of lemma zenon_L1009_ *) % 30.08/30.23 assert (zenon_L1010_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H1d5 zenon_H185 zenon_H36 zenon_Hc8 zenon_H37 zenon_H19e zenon_H27 zenon_H117 zenon_Hf5 zenon_He1. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.08/30.23 apply (zenon_L1001_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.08/30.23 apply (zenon_L131_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.08/30.23 apply (zenon_L160_); trivial. % 30.08/30.23 apply (zenon_L221_); trivial. % 30.08/30.23 (* end of lemma zenon_L1010_ *) % 30.08/30.23 assert (zenon_L1011_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H135 zenon_H19a zenon_Hcd zenon_He9 zenon_H35 zenon_H18c zenon_H173 zenon_H198 zenon_Ha4 zenon_H16a zenon_Hde zenon_H267 zenon_H8a zenon_H1d8 zenon_H1d5 zenon_H185 zenon_H36 zenon_Hc8 zenon_H37 zenon_H19e zenon_H27 zenon_H117 zenon_He1. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.23 apply (zenon_L1005_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.23 apply (zenon_L1008_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.23 apply (zenon_L1009_); trivial. % 30.08/30.23 apply (zenon_L1010_); trivial. % 30.08/30.23 (* end of lemma zenon_L1011_ *) % 30.08/30.23 assert (zenon_L1012_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H174 zenon_H85 zenon_H2cc zenon_H135 zenon_Hcd zenon_He9 zenon_H35 zenon_H18c zenon_H173 zenon_H198 zenon_Ha4 zenon_H16a zenon_Hde zenon_H267 zenon_H8a zenon_H1d8 zenon_H1d5 zenon_H36 zenon_Hc8 zenon_H37 zenon_H19e zenon_H27 zenon_He1 zenon_H6f zenon_Hdc zenon_H1a8 zenon_H185 zenon_H2d. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.23 apply (zenon_L1002_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.08/30.23 apply (zenon_L48_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.08/30.23 apply (zenon_L125_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.08/30.23 apply (zenon_L1011_); trivial. % 30.08/30.23 exact (zenon_H2cc zenon_H182). % 30.08/30.23 apply (zenon_L848_); trivial. % 30.08/30.23 (* end of lemma zenon_L1012_ *) % 30.08/30.23 assert (zenon_L1013_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H8d zenon_H15a zenon_H174 zenon_H85 zenon_H2cc zenon_H135 zenon_Hcd zenon_He9 zenon_H35 zenon_H18c zenon_H173 zenon_H198 zenon_Ha4 zenon_H16a zenon_Hde zenon_H267 zenon_H1d8 zenon_H1d5 zenon_H36 zenon_Hc8 zenon_H37 zenon_H19e zenon_H27 zenon_He1 zenon_H6f zenon_Hdc zenon_H1a8 zenon_H185 zenon_H2d. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.23 apply (zenon_L1000_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.23 apply (zenon_L1001_); trivial. % 30.08/30.23 apply (zenon_L1012_); trivial. % 30.08/30.23 (* end of lemma zenon_L1013_ *) % 30.08/30.23 assert (zenon_L1014_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H135 zenon_H73 zenon_Hd5 zenon_Hcd zenon_H198 zenon_Ha4 zenon_H16a zenon_Hde zenon_H267 zenon_H8a zenon_H1d8 zenon_H1d5 zenon_H185 zenon_H36 zenon_Hc8 zenon_H37 zenon_H19e zenon_H27 zenon_H117 zenon_He1. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.23 apply (zenon_L43_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.23 apply (zenon_L212_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.23 apply (zenon_L1009_); trivial. % 30.08/30.23 apply (zenon_L1010_); trivial. % 30.08/30.23 (* end of lemma zenon_L1014_ *) % 30.08/30.23 assert (zenon_L1015_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H246 zenon_H1b3 zenon_H68 zenon_H20 zenon_Hc9 zenon_Hde zenon_H2d zenon_H8a. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.08/30.23 exact (zenon_H1b3 zenon_H64). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.08/30.23 apply (zenon_L16_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.08/30.23 apply (zenon_L49_); trivial. % 30.08/30.23 apply (zenon_L25_); trivial. % 30.08/30.23 (* end of lemma zenon_L1015_ *) % 30.08/30.23 assert (zenon_L1016_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H8d zenon_H85 zenon_H15a zenon_H185 zenon_H36 zenon_Hc8 zenon_H246 zenon_H1b3 zenon_H68 zenon_H20 zenon_Hc9 zenon_Hde zenon_H2d. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.23 apply (zenon_L1000_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.23 apply (zenon_L1001_); trivial. % 30.08/30.23 apply (zenon_L1015_); trivial. % 30.08/30.23 (* end of lemma zenon_L1016_ *) % 30.08/30.23 assert (zenon_L1017_ : (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> False). % 30.08/30.23 do 0 intro. intros zenon_Hcd zenon_Hf5 zenon_H1e5. % 30.08/30.23 cut (((op (e2) (e3)) = (e2)) = ((e1) = (e2))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_Hcd. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_Hf5. % 30.08/30.23 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 30.08/30.23 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 30.08/30.23 congruence. % 30.08/30.23 exact (zenon_H2cd zenon_H1e5). % 30.08/30.23 apply zenon_H57. apply refl_equal. % 30.08/30.23 (* end of lemma zenon_L1017_ *) % 30.08/30.23 assert (zenon_L1018_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H172 zenon_Hcd zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H267 zenon_Hde zenon_He1 zenon_Ha4 zenon_H198 zenon_H117 zenon_He9 zenon_H3c zenon_H8d zenon_H85 zenon_H15a zenon_H36 zenon_Hc8 zenon_H246 zenon_H1b3 zenon_H68 zenon_H20 zenon_H2d zenon_H135 zenon_H73 zenon_H27 zenon_H18c zenon_H208 zenon_H16a zenon_H185. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.08/30.23 apply (zenon_L16_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.08/30.23 apply (zenon_L364_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.08/30.23 apply (zenon_L120_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.08/30.23 apply (zenon_L1014_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.08/30.23 apply (zenon_L170_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.23 apply (zenon_L1016_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.23 apply (zenon_L88_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.23 apply (zenon_L1009_); trivial. % 30.08/30.23 apply (zenon_L1017_); trivial. % 30.08/30.23 apply (zenon_L886_); trivial. % 30.08/30.23 (* end of lemma zenon_L1018_ *) % 30.08/30.23 assert (zenon_L1019_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H173 zenon_Hcd zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H267 zenon_Hde zenon_H185 zenon_He1 zenon_Ha4 zenon_H222 zenon_H8d zenon_H85 zenon_H15a zenon_H36 zenon_Hc8 zenon_H246 zenon_H1b3 zenon_H68 zenon_H20 zenon_H2d zenon_H135 zenon_Hfe zenon_H73 zenon_H27 zenon_H18c zenon_H208 zenon_Hfc zenon_H172 zenon_H3c zenon_H101 zenon_H16a zenon_H198 zenon_H117. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.08/30.23 apply (zenon_L48_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.08/30.23 apply (zenon_L158_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.08/30.23 apply (zenon_L1018_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.08/30.23 apply (zenon_L58_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.08/30.23 apply (zenon_L1008_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.08/30.23 apply (zenon_L120_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.08/30.23 apply (zenon_L1014_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.08/30.23 apply (zenon_L170_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.23 apply (zenon_L1016_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.23 apply (zenon_L264_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.23 apply (zenon_L1009_); trivial. % 30.08/30.23 apply (zenon_L1017_); trivial. % 30.08/30.23 apply (zenon_L1004_); trivial. % 30.08/30.23 (* end of lemma zenon_L1019_ *) % 30.08/30.23 assert (zenon_L1020_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H174 zenon_H35 zenon_H16a zenon_H173 zenon_Hcd zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H267 zenon_Hde zenon_He1 zenon_Ha4 zenon_H222 zenon_H8d zenon_H85 zenon_H15a zenon_H36 zenon_Hc8 zenon_H246 zenon_H1b3 zenon_H68 zenon_H20 zenon_H135 zenon_H73 zenon_H27 zenon_H18c zenon_H208 zenon_Hfc zenon_H172 zenon_H3c zenon_H101 zenon_H198 zenon_H185 zenon_H2d. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.23 apply (zenon_L1002_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.08/30.23 apply (zenon_L16_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.08/30.23 apply (zenon_L364_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.08/30.23 apply (zenon_L1019_); trivial. % 30.08/30.23 apply (zenon_L886_); trivial. % 30.08/30.23 apply (zenon_L848_); trivial. % 30.08/30.23 (* end of lemma zenon_L1020_ *) % 30.08/30.23 assert (zenon_L1021_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_He4 zenon_H2d zenon_H185 zenon_H172 zenon_H1d5 zenon_H1d8 zenon_H37 zenon_H19e zenon_H267 zenon_Ha4 zenon_H198 zenon_He9 zenon_H3c zenon_H8d zenon_H85 zenon_H15a zenon_H36 zenon_Hc8 zenon_H246 zenon_H1b3 zenon_H20 zenon_H135 zenon_H27 zenon_H18c zenon_H208 zenon_H16a zenon_H35 zenon_H174 zenon_Hcd zenon_H68 zenon_Hdf zenon_Hde zenon_He1 zenon_H8a. % 30.08/30.23 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.23 apply (zenon_L1002_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.23 apply (zenon_L1018_); trivial. % 30.08/30.23 apply (zenon_L848_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.23 apply (zenon_L48_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.23 apply (zenon_L49_); trivial. % 30.08/30.23 apply (zenon_L50_); trivial. % 30.08/30.23 (* end of lemma zenon_L1021_ *) % 30.08/30.23 assert (zenon_L1022_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H225 zenon_H101 zenon_Hfc zenon_H222 zenon_H173 zenon_H174 zenon_H35 zenon_H16a zenon_H208 zenon_H18c zenon_H27 zenon_H135 zenon_H20 zenon_H1b3 zenon_H246 zenon_Hc8 zenon_H36 zenon_H15a zenon_H85 zenon_H8d zenon_H3c zenon_H198 zenon_Ha4 zenon_H267 zenon_H19e zenon_H37 zenon_H1d8 zenon_H1d5 zenon_H172 zenon_H2d zenon_H8a zenon_He1 zenon_Hdf zenon_H68 zenon_Hcd zenon_Hd9 zenon_He4 zenon_H185 zenon_Hde. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.08/30.23 apply (zenon_L1020_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.08/30.23 apply (zenon_L1021_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.08/30.23 apply (zenon_L51_); trivial. % 30.08/30.23 apply (zenon_L817_); trivial. % 30.08/30.23 (* end of lemma zenon_L1022_ *) % 30.08/30.23 assert (zenon_L1023_ : (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H6f zenon_H225 zenon_H101 zenon_Hfc zenon_H222 zenon_H173 zenon_H174 zenon_H35 zenon_H16a zenon_H208 zenon_H18c zenon_H27 zenon_H135 zenon_H20 zenon_H1b3 zenon_H246 zenon_Hc8 zenon_H36 zenon_H15a zenon_H85 zenon_H8d zenon_H3c zenon_H198 zenon_Ha4 zenon_H267 zenon_H19e zenon_H37 zenon_H1d8 zenon_H1d5 zenon_H172 zenon_H2d zenon_He1 zenon_Hdf zenon_H68 zenon_Hcd zenon_Hd9 zenon_He4 zenon_H185 zenon_Hde. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.23 apply (zenon_L18_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.23 apply (zenon_L1001_); trivial. % 30.08/30.23 apply (zenon_L1022_); trivial. % 30.08/30.23 (* end of lemma zenon_L1023_ *) % 30.08/30.23 assert (zenon_L1024_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H8d zenon_He1 zenon_H73 zenon_H15a zenon_H185 zenon_H36 zenon_Hc8 zenon_H2d zenon_H8b. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.23 apply (zenon_L232_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.23 apply (zenon_L1000_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.23 apply (zenon_L1001_); trivial. % 30.08/30.23 apply (zenon_L25_); trivial. % 30.08/30.23 (* end of lemma zenon_L1024_ *) % 30.08/30.23 assert (zenon_L1025_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.08/30.23 do 0 intro. intros zenon_He4 zenon_He1 zenon_Hcd zenon_H2d zenon_H20 zenon_H68 zenon_H1b3 zenon_H246 zenon_Hc8 zenon_H36 zenon_H185 zenon_H15a zenon_H85 zenon_H8d zenon_H8b zenon_Hde. % 30.08/30.23 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.23 apply (zenon_L1024_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.23 apply (zenon_L48_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.23 apply (zenon_L1016_); trivial. % 30.08/30.23 apply (zenon_L288_); trivial. % 30.08/30.23 (* end of lemma zenon_L1025_ *) % 30.08/30.23 assert (zenon_L1026_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> False). % 30.08/30.23 do 0 intro. intros zenon_Hd9 zenon_H172 zenon_H1d5 zenon_H1d8 zenon_H37 zenon_H19e zenon_H267 zenon_Ha4 zenon_H198 zenon_H3c zenon_H135 zenon_H27 zenon_H18c zenon_H208 zenon_H16a zenon_H35 zenon_H174 zenon_H173 zenon_H222 zenon_Hfc zenon_H101 zenon_H225 zenon_H6f zenon_He4 zenon_He1 zenon_Hcd zenon_H2d zenon_H20 zenon_H68 zenon_H1b3 zenon_H246 zenon_Hc8 zenon_H36 zenon_H185 zenon_H15a zenon_H85 zenon_H8d zenon_Hde. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.08/30.23 exact (zenon_H1b3 zenon_H64). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.08/30.23 apply (zenon_L16_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.08/30.23 apply (zenon_L1023_); trivial. % 30.08/30.23 apply (zenon_L1025_); trivial. % 30.08/30.23 (* end of lemma zenon_L1026_ *) % 30.08/30.23 assert (zenon_L1027_ : (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H2cc zenon_H173 zenon_H18c zenon_Hc9 zenon_H35 zenon_He9 zenon_Hcd zenon_H16a zenon_H198 zenon_H6f zenon_H37 zenon_Hd9 zenon_H172 zenon_H1d5 zenon_H1d8 zenon_H19e zenon_H267 zenon_Ha4 zenon_H3c zenon_H135 zenon_H27 zenon_H208 zenon_H174 zenon_H222 zenon_Hfc zenon_H101 zenon_H225 zenon_He4 zenon_He1 zenon_H20 zenon_H1b3 zenon_H246 zenon_Hc8 zenon_H36 zenon_H15a zenon_H85 zenon_H8d zenon_Hde zenon_H1a8 zenon_H185 zenon_H2d. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.23 apply (zenon_L1002_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.08/30.23 apply (zenon_L1026_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.08/30.23 apply (zenon_L125_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.08/30.23 apply (zenon_L1005_); trivial. % 30.08/30.23 exact (zenon_H2cc zenon_H182). % 30.08/30.23 apply (zenon_L848_); trivial. % 30.08/30.23 (* end of lemma zenon_L1027_ *) % 30.08/30.23 assert (zenon_L1028_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H8d zenon_H85 zenon_H15a zenon_H185 zenon_H36 zenon_Hc8 zenon_He1 zenon_He2. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.23 apply (zenon_L1000_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.23 apply (zenon_L1001_); trivial. % 30.08/30.23 apply (zenon_L50_); trivial. % 30.08/30.23 (* end of lemma zenon_L1028_ *) % 30.08/30.23 assert (zenon_L1029_ : (~((op (e0) (e2)) = (op (e0) (op (e0) (e2))))) -> ((op (e0) (e2)) = (e2)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H2ce zenon_Hda. % 30.08/30.23 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 30.08/30.23 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.08/30.23 congruence. % 30.08/30.23 apply zenon_H1d. apply refl_equal. % 30.08/30.23 apply zenon_Hdb. apply sym_equal. exact zenon_Hda. % 30.08/30.23 (* end of lemma zenon_L1029_ *) % 30.08/30.23 assert (zenon_L1030_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H1a5 zenon_H198 zenon_Hda zenon_Hed. % 30.08/30.23 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H1a5. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H198. % 30.08/30.23 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 30.08/30.23 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2cf]. % 30.08/30.23 congruence. % 30.08/30.23 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H10f ]. % 30.08/30.23 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e2)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H2cf. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H211. % 30.08/30.23 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.08/30.23 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 30.08/30.23 congruence. % 30.08/30.23 apply (zenon_L1029_); trivial. % 30.08/30.23 apply zenon_H10f. apply refl_equal. % 30.08/30.23 apply zenon_H10f. apply refl_equal. % 30.08/30.23 apply zenon_Hf2. apply sym_equal. exact zenon_Hed. % 30.08/30.23 (* end of lemma zenon_L1030_ *) % 30.08/30.23 assert (zenon_L1031_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hc9 zenon_Ha4 zenon_H10d zenon_H100 zenon_He1 zenon_H8a zenon_Hf9 zenon_Hda zenon_H1a5 zenon_H16a zenon_H198 zenon_H117. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.08/30.23 apply (zenon_L142_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.08/30.23 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.08/30.23 apply (zenon_L50_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.08/30.23 apply (zenon_L60_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.08/30.23 apply (zenon_L64_); trivial. % 30.08/30.23 apply (zenon_L1006_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.08/30.23 apply (zenon_L1030_); trivial. % 30.08/30.23 apply (zenon_L1004_); trivial. % 30.08/30.23 (* end of lemma zenon_L1031_ *) % 30.08/30.23 assert (zenon_L1032_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H174 zenon_H35 zenon_H37 zenon_H198 zenon_H16a zenon_H1a5 zenon_Hda zenon_Hf9 zenon_He1 zenon_H100 zenon_H10d zenon_Ha4 zenon_Hc9 zenon_H18c zenon_H173 zenon_Hc8 zenon_H36 zenon_H15a zenon_H85 zenon_H8d zenon_H185 zenon_H2d. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.23 apply (zenon_L1002_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.23 apply (zenon_L1000_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.23 apply (zenon_L1001_); trivial. % 30.08/30.23 apply (zenon_L1031_); trivial. % 30.08/30.23 apply (zenon_L848_); trivial. % 30.08/30.23 (* end of lemma zenon_L1032_ *) % 30.08/30.23 assert (zenon_L1033_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> False). % 30.08/30.23 do 0 intro. intros zenon_He4 zenon_Hcd zenon_H88 zenon_H2d zenon_H173 zenon_H18c zenon_Ha4 zenon_H10d zenon_H100 zenon_Hf9 zenon_Hda zenon_H1a5 zenon_H16a zenon_H198 zenon_H37 zenon_H35 zenon_H174 zenon_H8d zenon_H85 zenon_H15a zenon_H185 zenon_H36 zenon_Hc8 zenon_He1. % 30.08/30.23 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.23 apply (zenon_L998_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.23 apply (zenon_L937_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.23 apply (zenon_L1032_); trivial. % 30.08/30.23 apply (zenon_L1028_); trivial. % 30.08/30.23 (* end of lemma zenon_L1033_ *) % 30.08/30.23 assert (zenon_L1034_ : (~((op (e0) (e1)) = (op (e0) (op (e0) (e1))))) -> ((op (e0) (e1)) = (e1)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H2d0 zenon_H1f. % 30.08/30.23 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 30.08/30.23 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.08/30.23 congruence. % 30.08/30.23 apply zenon_H1d. apply refl_equal. % 30.08/30.23 apply zenon_H20b. apply sym_equal. exact zenon_H1f. % 30.08/30.23 (* end of lemma zenon_L1034_ *) % 30.08/30.23 assert (zenon_L1035_ : ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 30.08/30.23 do 0 intro. intros zenon_H188 zenon_H1f zenon_H88 zenon_H65. % 30.08/30.23 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 30.08/30.23 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (e0)) = (op (e0) (e1)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H65. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H3a. % 30.08/30.23 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 30.08/30.23 cut (((op (e0) (e1)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 30.08/30.23 congruence. % 30.08/30.23 cut (((op (e0) (op (e0) (e1))) = (e1)) = ((op (e0) (e1)) = (op (e0) (e0)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H66. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H188. % 30.08/30.23 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2a3]. % 30.08/30.23 cut (((op (e0) (op (e0) (e1))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 30.08/30.23 congruence. % 30.08/30.23 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 30.08/30.23 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (op (e0) (e1))) = (op (e0) (e1)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H2d1. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H3a. % 30.08/30.23 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 30.08/30.23 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2d0]. % 30.08/30.23 congruence. % 30.08/30.23 apply (zenon_L1034_); trivial. % 30.08/30.23 apply zenon_H3b. apply refl_equal. % 30.08/30.23 apply zenon_H3b. apply refl_equal. % 30.08/30.23 apply zenon_H2a3. apply sym_equal. exact zenon_H88. % 30.08/30.23 apply zenon_H3b. apply refl_equal. % 30.08/30.23 apply zenon_H3b. apply refl_equal. % 30.08/30.23 (* end of lemma zenon_L1035_ *) % 30.08/30.23 assert (zenon_L1036_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H173 zenon_H73 zenon_H15a zenon_He1 zenon_H37 zenon_Hcd zenon_H19a zenon_H16a zenon_H198 zenon_H117. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.08/30.23 apply (zenon_L94_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.08/30.23 apply (zenon_L158_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.08/30.23 apply (zenon_L159_); trivial. % 30.08/30.23 apply (zenon_L1004_); trivial. % 30.08/30.23 (* end of lemma zenon_L1036_ *) % 30.08/30.23 assert (zenon_L1037_ : (~((op (e0) (e3)) = (op (e0) (op (e0) (e3))))) -> ((op (e0) (e3)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H2d2 zenon_H16b. % 30.08/30.23 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 30.08/30.23 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.08/30.23 congruence. % 30.08/30.23 apply zenon_H1d. apply refl_equal. % 30.08/30.23 apply zenon_H21a. apply sym_equal. exact zenon_H16b. % 30.08/30.23 (* end of lemma zenon_L1037_ *) % 30.08/30.23 assert (zenon_L1038_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H218 zenon_H36 zenon_H16b zenon_H1c5. % 30.08/30.23 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H218. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H36. % 30.08/30.23 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 30.08/30.23 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d3]. % 30.08/30.23 congruence. % 30.08/30.23 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H16e ]. % 30.08/30.23 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e3)))). % 30.08/30.23 intro zenon_D_pnotp. % 30.08/30.23 apply zenon_H2d3. % 30.08/30.23 rewrite <- zenon_D_pnotp. % 30.08/30.23 exact zenon_H194. % 30.08/30.23 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.08/30.23 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2d2]. % 30.08/30.23 congruence. % 30.08/30.23 apply (zenon_L1037_); trivial. % 30.08/30.23 apply zenon_H16e. apply refl_equal. % 30.08/30.23 apply zenon_H16e. apply refl_equal. % 30.08/30.23 apply zenon_H1c6. apply sym_equal. exact zenon_H1c5. % 30.08/30.23 (* end of lemma zenon_L1038_ *) % 30.08/30.23 assert (zenon_L1039_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H73 zenon_H6c zenon_H218 zenon_H36 zenon_H16b. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.08/30.23 apply (zenon_L174_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.08/30.23 apply (zenon_L131_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.08/30.23 apply (zenon_L244_); trivial. % 30.08/30.23 apply (zenon_L1038_); trivial. % 30.08/30.23 (* end of lemma zenon_L1039_ *) % 30.08/30.23 assert (zenon_L1040_ : (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.08/30.23 do 0 intro. intros zenon_H2cc zenon_H173 zenon_H15a zenon_He1 zenon_Hcd zenon_H16a zenon_H198 zenon_H6f zenon_H174 zenon_H35 zenon_H267 zenon_Hde zenon_Ha4 zenon_H222 zenon_H8d zenon_H85 zenon_Hc8 zenon_H246 zenon_H1b3 zenon_H20 zenon_H135 zenon_H27 zenon_H18c zenon_H208 zenon_Hfc zenon_H172 zenon_H3c zenon_H101 zenon_H185 zenon_H2d zenon_H1a8 zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H73 zenon_H6c zenon_H218 zenon_H36. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.23 exact (zenon_H85 zenon_H89). % 30.08/30.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.23 apply (zenon_L1002_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.08/30.23 apply (zenon_L1020_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.08/30.23 apply (zenon_L125_); trivial. % 30.08/30.23 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.08/30.24 apply (zenon_L1036_); trivial. % 30.08/30.24 exact (zenon_H2cc zenon_H182). % 30.08/30.24 apply (zenon_L1039_); trivial. % 30.08/30.24 (* end of lemma zenon_L1040_ *) % 30.08/30.24 assert (zenon_L1041_ : ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H198 zenon_Hda zenon_He9 zenon_H138. % 30.08/30.24 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H10f ]. % 30.08/30.24 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))). % 30.08/30.24 intro zenon_D_pnotp. % 30.08/30.24 apply zenon_H138. % 30.08/30.24 rewrite <- zenon_D_pnotp. % 30.08/30.24 exact zenon_H211. % 30.08/30.24 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.08/30.24 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2d4]. % 30.08/30.24 congruence. % 30.08/30.24 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e2)) = (op (e0) (e1)))). % 30.08/30.24 intro zenon_D_pnotp. % 30.08/30.24 apply zenon_H2d4. % 30.08/30.24 rewrite <- zenon_D_pnotp. % 30.08/30.24 exact zenon_H198. % 30.08/30.24 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 30.08/30.24 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2cf]. % 30.08/30.24 congruence. % 30.08/30.24 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H10f ]. % 30.08/30.24 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e2)))). % 30.08/30.24 intro zenon_D_pnotp. % 30.08/30.24 apply zenon_H2cf. % 30.08/30.24 rewrite <- zenon_D_pnotp. % 30.08/30.24 exact zenon_H211. % 30.08/30.24 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.08/30.24 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 30.08/30.24 congruence. % 30.08/30.24 apply (zenon_L1029_); trivial. % 30.08/30.24 apply zenon_H10f. apply refl_equal. % 30.08/30.24 apply zenon_H10f. apply refl_equal. % 30.08/30.24 apply zenon_H153. apply sym_equal. exact zenon_He9. % 30.08/30.24 apply zenon_H10f. apply refl_equal. % 30.08/30.24 apply zenon_H10f. apply refl_equal. % 30.08/30.24 (* end of lemma zenon_L1041_ *) % 30.08/30.24 assert (zenon_L1042_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H101 zenon_H138 zenon_Hdc zenon_Hd1 zenon_H135 zenon_H1a5 zenon_Hda zenon_Hf9 zenon_H100 zenon_H10d zenon_H18c zenon_H173 zenon_H222 zenon_H198 zenon_Ha4 zenon_H16a zenon_Hde zenon_H267 zenon_H8a zenon_H1d8 zenon_H1d5 zenon_H185 zenon_H36 zenon_Hc8 zenon_H37 zenon_H19e zenon_H27 zenon_H117 zenon_He1. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.08/30.24 apply (zenon_L1041_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.08/30.24 apply (zenon_L154_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.08/30.24 apply (zenon_L1008_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.24 apply (zenon_L1031_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.24 apply (zenon_L264_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.24 apply (zenon_L1009_); trivial. % 30.08/30.24 apply (zenon_L1010_); trivial. % 30.08/30.24 (* end of lemma zenon_L1042_ *) % 30.08/30.24 assert (zenon_L1043_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.08/30.24 do 0 intro. intros zenon_He4 zenon_Hd9 zenon_H101 zenon_H138 zenon_Hd1 zenon_H135 zenon_H222 zenon_Hde zenon_H267 zenon_H1d8 zenon_H1d5 zenon_H19e zenon_H27 zenon_H2d zenon_H185 zenon_H8d zenon_H85 zenon_H15a zenon_H36 zenon_Hc8 zenon_H173 zenon_H18c zenon_Ha4 zenon_H10d zenon_H100 zenon_Hf9 zenon_Hda zenon_H1a5 zenon_H16a zenon_H198 zenon_H37 zenon_H35 zenon_H174 zenon_He1 zenon_H8a. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.24 apply (zenon_L47_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.24 apply (zenon_L1002_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.24 apply (zenon_L1042_); trivial. % 30.08/30.24 apply (zenon_L848_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.24 apply (zenon_L1032_); trivial. % 30.08/30.24 apply (zenon_L50_); trivial. % 30.08/30.24 (* end of lemma zenon_L1043_ *) % 30.08/30.24 assert (zenon_L1044_ : (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H2cc zenon_Hcd zenon_H6f zenon_H172 zenon_H3c zenon_H208 zenon_Hfc zenon_H225 zenon_H20 zenon_H1b3 zenon_H246 zenon_H1a8 zenon_H6c zenon_H218 zenon_H8a zenon_He1 zenon_H174 zenon_H35 zenon_H37 zenon_H198 zenon_H16a zenon_H1a5 zenon_Hf9 zenon_H100 zenon_H10d zenon_Ha4 zenon_H18c zenon_H173 zenon_Hc8 zenon_H36 zenon_H15a zenon_H85 zenon_H8d zenon_H2d zenon_H27 zenon_H19e zenon_H1d5 zenon_H1d8 zenon_H267 zenon_H222 zenon_H135 zenon_Hd1 zenon_H138 zenon_H101 zenon_Hd9 zenon_He4 zenon_H185 zenon_Hde. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.08/30.24 apply (zenon_L1040_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.24 apply (zenon_L1040_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.24 apply (zenon_L1012_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.24 apply (zenon_L1027_); trivial. % 30.08/30.24 apply (zenon_L50_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.08/30.24 apply (zenon_L1043_); trivial. % 30.08/30.24 apply (zenon_L817_); trivial. % 30.08/30.24 (* end of lemma zenon_L1044_ *) % 30.08/30.24 assert (zenon_L1045_ : (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H2cc zenon_Hcd zenon_H6f zenon_H172 zenon_H3c zenon_H208 zenon_Hfc zenon_H225 zenon_H20 zenon_H1b3 zenon_H246 zenon_H1a8 zenon_H6c zenon_H218 zenon_He1 zenon_H174 zenon_H35 zenon_H37 zenon_H198 zenon_H16a zenon_H1a5 zenon_Hf9 zenon_H100 zenon_H10d zenon_Ha4 zenon_H18c zenon_H173 zenon_Hc8 zenon_H36 zenon_H15a zenon_H85 zenon_H8d zenon_H2d zenon_H27 zenon_H19e zenon_H1d5 zenon_H1d8 zenon_H267 zenon_H222 zenon_H135 zenon_Hd1 zenon_H138 zenon_H101 zenon_Hd9 zenon_He4 zenon_H185 zenon_Hde. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.24 apply (zenon_L1000_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.24 apply (zenon_L157_); trivial. % 30.08/30.24 apply (zenon_L1044_); trivial. % 30.08/30.24 (* end of lemma zenon_L1045_ *) % 30.08/30.24 assert (zenon_L1046_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.08/30.24 do 0 intro. intros zenon_H8d zenon_H85 zenon_H15a zenon_H185 zenon_H36 zenon_Hc8 zenon_H6f zenon_H90. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.24 apply (zenon_L1000_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.24 apply (zenon_L1001_); trivial. % 30.08/30.24 apply (zenon_L39_); trivial. % 30.08/30.24 (* end of lemma zenon_L1046_ *) % 30.08/30.24 assert (zenon_L1047_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H174 zenon_H85 zenon_H35 zenon_H37 zenon_H6f zenon_H26 zenon_H185 zenon_H2d. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.24 apply (zenon_L1002_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.24 apply (zenon_L598_); trivial. % 30.08/30.24 apply (zenon_L848_); trivial. % 30.08/30.24 (* end of lemma zenon_L1047_ *) % 30.08/30.24 assert (zenon_L1048_ : (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H2d zenon_H185 zenon_H1a8 zenon_H8d zenon_H85 zenon_H15a zenon_H36 zenon_Hc8 zenon_H246 zenon_H1b3 zenon_H20 zenon_He1 zenon_He4 zenon_H225 zenon_H101 zenon_Hfc zenon_H222 zenon_H174 zenon_H208 zenon_H27 zenon_H135 zenon_H3c zenon_Ha4 zenon_H267 zenon_H19e zenon_H1d8 zenon_H1d5 zenon_H172 zenon_Hd9 zenon_H37 zenon_H6f zenon_H198 zenon_H16a zenon_Hcd zenon_He9 zenon_H35 zenon_H18c zenon_H173 zenon_H2cc zenon_H8b zenon_Hde. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.24 apply (zenon_L1024_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.24 apply (zenon_L1013_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.24 apply (zenon_L1027_); trivial. % 30.08/30.24 apply (zenon_L288_); trivial. % 30.08/30.24 (* end of lemma zenon_L1048_ *) % 30.08/30.24 assert (zenon_L1049_ : (~((op (e0) (e0)) = (op (e0) (op (e0) (e0))))) -> ((op (e0) (e0)) = (e0)) -> False). % 30.08/30.24 do 0 intro. intros zenon_H2d5 zenon_H64. % 30.08/30.24 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 30.08/30.24 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.08/30.24 congruence. % 30.08/30.24 apply zenon_H1d. apply refl_equal. % 30.08/30.24 apply zenon_H67. apply sym_equal. exact zenon_H64. % 30.08/30.24 (* end of lemma zenon_L1049_ *) % 30.08/30.24 assert (zenon_L1050_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 30.08/30.24 do 0 intro. intros zenon_H2c1 zenon_H2d6 zenon_H64 zenon_H185. % 30.08/30.24 cut (((op (e0) (op (e0) (e0))) = (e0)) = ((op (e0) (e0)) = (op (e0) (e3)))). % 30.08/30.24 intro zenon_D_pnotp. % 30.08/30.24 apply zenon_H2c1. % 30.08/30.24 rewrite <- zenon_D_pnotp. % 30.08/30.24 exact zenon_H2d6. % 30.08/30.24 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 30.08/30.24 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2d7]. % 30.08/30.24 congruence. % 30.08/30.24 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H18b | zenon_intro zenon_Hcb ]. % 30.08/30.24 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (e0) (op (e0) (e0))) = (op (e0) (e0)))). % 30.08/30.24 intro zenon_D_pnotp. % 30.08/30.24 apply zenon_H2d7. % 30.08/30.24 rewrite <- zenon_D_pnotp. % 30.08/30.24 exact zenon_H18b. % 30.08/30.24 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.08/30.24 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2d5]. % 30.08/30.24 congruence. % 30.08/30.24 apply (zenon_L1049_); trivial. % 30.08/30.24 apply zenon_Hcb. apply refl_equal. % 30.08/30.24 apply zenon_Hcb. apply refl_equal. % 30.08/30.24 apply zenon_H2c8. apply sym_equal. exact zenon_H185. % 30.08/30.24 (* end of lemma zenon_L1050_ *) % 30.08/30.24 assert (zenon_L1051_ : (((op (e1) (op (e1) (e0))) = (e0))/\(((op (e1) (op (e1) (e1))) = (e1))/\(((op (e1) (op (e1) (e2))) = (e2))/\(((op (e1) (op (e1) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2)))/\((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3)))))))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H45 zenon_H100 zenon_H16a zenon_H37 zenon_H2cc zenon_H156 zenon_H2b1. % 30.08/30.24 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.08/30.24 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.08/30.24 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.08/30.24 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.08/30.24 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.08/30.24 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.08/30.24 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.08/30.24 apply (zenon_L839_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.08/30.24 exact (zenon_H2cc zenon_H182). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.08/30.24 apply (zenon_L841_); trivial. % 30.08/30.24 exact (zenon_H1ab zenon_H112). % 30.08/30.24 apply (zenon_L150_); trivial. % 30.08/30.24 (* end of lemma zenon_L1051_ *) % 30.08/30.24 assert (zenon_L1052_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H2b1 zenon_H20 zenon_H185 zenon_H2cc zenon_H19e zenon_H1af zenon_Hb8 zenon_Had zenon_H6e zenon_H100 zenon_H37 zenon_H10d zenon_H117 zenon_H6f. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.08/30.24 apply (zenon_L117_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.08/30.24 exact (zenon_H2cc zenon_H182). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.08/30.24 apply (zenon_L214_); trivial. % 30.08/30.24 apply (zenon_L153_); trivial. % 30.08/30.24 (* end of lemma zenon_L1052_ *) % 30.08/30.24 assert (zenon_L1053_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 30.08/30.24 do 0 intro. intros zenon_He7 zenon_H88 zenon_H90. % 30.08/30.24 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 30.08/30.24 intro zenon_D_pnotp. % 30.08/30.24 apply zenon_He7. % 30.08/30.24 rewrite <- zenon_D_pnotp. % 30.08/30.24 exact zenon_H88. % 30.08/30.24 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H26a]. % 30.08/30.24 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.08/30.24 congruence. % 30.08/30.24 apply zenon_Hcb. apply refl_equal. % 30.08/30.24 apply zenon_H26a. apply sym_equal. exact zenon_H90. % 30.08/30.24 (* end of lemma zenon_L1053_ *) % 30.08/30.24 assert (zenon_L1054_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H208 zenon_H88 zenon_Hc8 zenon_H98 zenon_H5e zenon_H222 zenon_H3c zenon_He9 zenon_H60 zenon_H1af zenon_H37 zenon_H19e. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.08/30.24 apply (zenon_L809_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.08/30.24 apply (zenon_L514_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.08/30.24 apply (zenon_L219_); trivial. % 30.08/30.24 apply (zenon_L214_); trivial. % 30.08/30.24 (* end of lemma zenon_L1054_ *) % 30.08/30.24 assert (zenon_L1055_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H208 zenon_H88 zenon_Hc8 zenon_H98 zenon_H5e zenon_H9d zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.08/30.24 apply (zenon_L809_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.08/30.24 apply (zenon_L514_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.08/30.24 apply (zenon_L256_); trivial. % 30.08/30.24 apply (zenon_L214_); trivial. % 30.08/30.24 (* end of lemma zenon_L1055_ *) % 30.08/30.24 assert (zenon_L1056_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H101 zenon_H3c zenon_H6e zenon_H1bd zenon_Hc9 zenon_H208 zenon_H88 zenon_Hc8 zenon_H98 zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.08/30.24 apply (zenon_L1054_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.08/30.24 apply (zenon_L795_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.08/30.24 apply (zenon_L282_); trivial. % 30.08/30.24 apply (zenon_L1055_); trivial. % 30.08/30.24 (* end of lemma zenon_L1056_ *) % 30.08/30.24 assert (zenon_L1057_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H23b zenon_He7 zenon_H19e zenon_H1af zenon_H222 zenon_H60 zenon_H5e zenon_Hc8 zenon_H88 zenon_H208 zenon_Hc9 zenon_H1bd zenon_H3c zenon_H101 zenon_H19a zenon_Hee zenon_Hb8 zenon_Had zenon_H6e zenon_H100 zenon_H37 zenon_H10d zenon_H117 zenon_H6f. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.08/30.24 apply (zenon_L1053_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.08/30.24 apply (zenon_L1056_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.08/30.24 apply (zenon_L337_); trivial. % 30.08/30.24 apply (zenon_L153_); trivial. % 30.08/30.24 (* end of lemma zenon_L1057_ *) % 30.08/30.24 assert (zenon_L1058_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> False). % 30.08/30.24 do 0 intro. intros zenon_H23b zenon_H88 zenon_He7 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hf6 zenon_H1e5. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.08/30.24 apply (zenon_L1053_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.08/30.24 apply (zenon_L336_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.08/30.24 apply (zenon_L337_); trivial. % 30.08/30.24 apply (zenon_L187_); trivial. % 30.08/30.24 (* end of lemma zenon_L1058_ *) % 30.08/30.24 assert (zenon_L1059_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H173 zenon_He1 zenon_Hcd zenon_H208 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H1dc zenon_H1d2 zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H2d zenon_H1ca zenon_Hd6 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H6f zenon_H27 zenon_H117 zenon_H108 zenon_H14b zenon_H3c zenon_H5e zenon_H20e zenon_H23b zenon_H88 zenon_He7 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hf6. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.08/30.24 apply (zenon_L937_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.08/30.24 apply (zenon_L158_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.08/30.24 apply (zenon_L159_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.08/30.24 apply (zenon_L181_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.08/30.24 apply (zenon_L218_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.08/30.24 apply (zenon_L225_); trivial. % 30.08/30.24 apply (zenon_L1058_); trivial. % 30.08/30.24 (* end of lemma zenon_L1059_ *) % 30.08/30.24 assert (zenon_L1060_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H174 zenon_H35 zenon_Hf6 zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_He7 zenon_H88 zenon_H23b zenon_H20e zenon_H5e zenon_H3c zenon_H14b zenon_H108 zenon_H27 zenon_H6f zenon_H1c7 zenon_H1af zenon_H1bd zenon_Hd6 zenon_H1ca zenon_H19e zenon_H37 zenon_H1d8 zenon_H1d5 zenon_H1d2 zenon_H1dc zenon_H6b zenon_Hd0 zenon_H60 zenon_H156 zenon_H208 zenon_Hcd zenon_He1 zenon_H173 zenon_Hd1 zenon_H101 zenon_H159 zenon_H222 zenon_Hc8 zenon_Hc9 zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H85 zenon_H8d zenon_H185 zenon_H2d. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.24 apply (zenon_L1002_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.24 apply (zenon_L1057_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.24 apply (zenon_L263_); trivial. % 30.08/30.24 apply (zenon_L1059_); trivial. % 30.08/30.24 apply (zenon_L848_); trivial. % 30.08/30.24 (* end of lemma zenon_L1060_ *) % 30.08/30.24 assert (zenon_L1061_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.24 do 0 intro. intros zenon_He4 zenon_H74 zenon_Hc8 zenon_H156 zenon_Hd0 zenon_H6b zenon_H1dc zenon_H1d2 zenon_H1d5 zenon_H1d8 zenon_H1ca zenon_Hd6 zenon_H1bd zenon_H1c7 zenon_H27 zenon_H108 zenon_H14b zenon_H23b zenon_H88 zenon_He7 zenon_H3f zenon_Hee zenon_Hf6 zenon_H174 zenon_H35 zenon_He1 zenon_H173 zenon_Hd1 zenon_H101 zenon_H159 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H6f zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e zenon_H2b1 zenon_H20 zenon_H2cc zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H85 zenon_H8d zenon_H185 zenon_H2d. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.24 exact (zenon_H74 zenon_H73). % 30.08/30.24 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.24 apply (zenon_L937_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.24 apply (zenon_L1060_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.24 apply (zenon_L1002_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.24 apply (zenon_L1052_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.24 apply (zenon_L263_); trivial. % 30.08/30.24 apply (zenon_L50_); trivial. % 30.08/30.24 apply (zenon_L848_); trivial. % 30.08/30.24 (* end of lemma zenon_L1061_ *) % 30.08/30.24 assert (zenon_L1062_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H174 zenon_H35 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H6c zenon_H1dc zenon_H1d2 zenon_H1d5 zenon_H1d8 zenon_H37 zenon_H19e zenon_H1ca zenon_Hd6 zenon_H5e zenon_H1bd zenon_H1af zenon_H1c7 zenon_H6f zenon_H27 zenon_H108 zenon_H14b zenon_H19a zenon_Hcd zenon_He1 zenon_Hc9 zenon_H18c zenon_H173 zenon_H2b1 zenon_H20 zenon_H2cc zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H85 zenon_H8d zenon_H185 zenon_H2d. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.24 apply (zenon_L1002_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.24 apply (zenon_L1052_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.24 apply (zenon_L157_); trivial. % 30.08/30.24 apply (zenon_L182_); trivial. % 30.08/30.24 apply (zenon_L848_); trivial. % 30.08/30.24 (* end of lemma zenon_L1062_ *) % 30.08/30.24 assert (zenon_L1063_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H174 zenon_H35 zenon_He2 zenon_He1 zenon_H6c zenon_H6f zenon_H2b1 zenon_H20 zenon_H2cc zenon_H19e zenon_H1af zenon_Hb8 zenon_Had zenon_H100 zenon_H37 zenon_H10d zenon_H85 zenon_H8d zenon_H185 zenon_H2d. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.24 apply (zenon_L1002_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.24 apply (zenon_L1052_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.24 apply (zenon_L157_); trivial. % 30.08/30.24 apply (zenon_L50_); trivial. % 30.08/30.24 apply (zenon_L848_); trivial. % 30.08/30.24 (* end of lemma zenon_L1063_ *) % 30.08/30.24 assert (zenon_L1064_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H174 zenon_H35 zenon_H90 zenon_H6f zenon_H101 zenon_Hdc zenon_Hd1 zenon_H19a zenon_H20e zenon_Hcd zenon_H208 zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e zenon_H2b1 zenon_H20 zenon_H2cc zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H85 zenon_H8d zenon_H185 zenon_H2d. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.24 apply (zenon_L1002_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.24 apply (zenon_L1052_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.24 apply (zenon_L258_); trivial. % 30.08/30.24 apply (zenon_L39_); trivial. % 30.08/30.24 apply (zenon_L848_); trivial. % 30.08/30.24 (* end of lemma zenon_L1064_ *) % 30.08/30.24 assert (zenon_L1065_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H174 zenon_H35 zenon_H90 zenon_H6f zenon_Hc9 zenon_He1 zenon_H2b1 zenon_H20 zenon_H2cc zenon_H19e zenon_H1af zenon_Hb8 zenon_Had zenon_H100 zenon_H37 zenon_H10d zenon_H85 zenon_H8d zenon_H185 zenon_H2d. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.24 apply (zenon_L1002_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.24 exact (zenon_H85 zenon_H89). % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.24 apply (zenon_L1052_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.24 apply (zenon_L273_); trivial. % 30.08/30.24 apply (zenon_L39_); trivial. % 30.08/30.24 apply (zenon_L848_); trivial. % 30.08/30.24 (* end of lemma zenon_L1065_ *) % 30.08/30.24 assert (zenon_L1066_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.08/30.24 do 0 intro. intros zenon_He4 zenon_H74 zenon_H222 zenon_H60 zenon_H5e zenon_H1f zenon_H3c zenon_H208 zenon_H20e zenon_H19a zenon_Hd1 zenon_H101 zenon_H2d zenon_H185 zenon_H8d zenon_H85 zenon_H10d zenon_H37 zenon_H100 zenon_Had zenon_Hb8 zenon_H1af zenon_H19e zenon_H2cc zenon_H20 zenon_H2b1 zenon_He1 zenon_H6f zenon_H35 zenon_H174 zenon_H90 zenon_Hcd. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.24 exact (zenon_H74 zenon_H73). % 30.08/30.24 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.24 apply (zenon_L1064_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.24 apply (zenon_L1065_); trivial. % 30.08/30.24 apply (zenon_L386_); trivial. % 30.08/30.24 (* end of lemma zenon_L1066_ *) % 30.08/30.24 assert (zenon_L1067_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H23b zenon_Hcd zenon_H174 zenon_H35 zenon_H2b1 zenon_H20 zenon_H2cc zenon_H19e zenon_H1af zenon_Had zenon_H85 zenon_H8d zenon_H185 zenon_H101 zenon_Hd1 zenon_H20e zenon_H208 zenon_H3c zenon_H5e zenon_H60 zenon_H74 zenon_He4 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hf9 zenon_H6f zenon_H2d zenon_H9c zenon_H37 zenon_H100 zenon_He1 zenon_Hb8 zenon_H55 zenon_H222 zenon_Hda zenon_H10d zenon_H231. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.08/30.24 apply (zenon_L1066_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.08/30.24 apply (zenon_L336_); trivial. % 30.08/30.24 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.08/30.24 apply (zenon_L337_); trivial. % 30.08/30.24 apply (zenon_L356_); trivial. % 30.08/30.24 (* end of lemma zenon_L1067_ *) % 30.08/30.24 assert (zenon_L1068_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 30.08/30.24 do 0 intro. intros zenon_H135 zenon_H156 zenon_H6b zenon_H6c zenon_H1dc zenon_H1d2 zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H1ca zenon_Hd6 zenon_H1bd zenon_H1c7 zenon_H108 zenon_H14b zenon_H18c zenon_H173 zenon_H231 zenon_H10d zenon_Hda zenon_H222 zenon_Hb8 zenon_He1 zenon_H100 zenon_H37 zenon_H9c zenon_H2d zenon_H6f zenon_Hf9 zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_He4 zenon_H74 zenon_H60 zenon_H5e zenon_H3c zenon_H208 zenon_H20e zenon_Hd1 zenon_H101 zenon_H185 zenon_H8d zenon_H85 zenon_Had zenon_H19e zenon_H2cc zenon_H20 zenon_H2b1 zenon_H35 zenon_H174 zenon_Hcd zenon_H23b zenon_Hd0 zenon_H1af zenon_H117 zenon_H27. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.08/30.25 apply (zenon_L182_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.08/30.25 apply (zenon_L1067_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.08/30.25 exact (zenon_Hd0 zenon_Hcc). % 30.08/30.25 apply (zenon_L183_); trivial. % 30.08/30.25 (* end of lemma zenon_L1068_ *) % 30.08/30.25 assert (zenon_L1069_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H225 zenon_H2d zenon_H8d zenon_H85 zenon_H10d zenon_H37 zenon_H100 zenon_Had zenon_Hb8 zenon_H1af zenon_H19e zenon_H2cc zenon_H20 zenon_H2b1 zenon_H6f zenon_H6c zenon_He1 zenon_H35 zenon_H174 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H1dc zenon_H1d2 zenon_H1d5 zenon_H1d8 zenon_H1ca zenon_Hd6 zenon_H5e zenon_H1bd zenon_H1c7 zenon_H27 zenon_H108 zenon_H14b zenon_H19a zenon_Hcd zenon_H18c zenon_H173 zenon_H23b zenon_H101 zenon_Hd1 zenon_H20e zenon_H208 zenon_H3c zenon_H74 zenon_He4 zenon_H1f zenon_H3f zenon_Hee zenon_Hf9 zenon_H222 zenon_H231 zenon_H135 zenon_H185 zenon_Hde. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.08/30.25 exact (zenon_H74 zenon_H73). % 30.08/30.25 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.08/30.25 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.25 exact (zenon_H74 zenon_H73). % 30.08/30.25 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.25 exact (zenon_H85 zenon_H89). % 30.08/30.25 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.25 apply (zenon_L1002_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.25 exact (zenon_H85 zenon_H89). % 30.08/30.25 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.25 apply (zenon_L1052_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.25 apply (zenon_L258_); trivial. % 30.08/30.25 apply (zenon_L184_); trivial. % 30.08/30.25 apply (zenon_L848_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.25 apply (zenon_L1062_); trivial. % 30.08/30.25 apply (zenon_L1063_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.08/30.25 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.08/30.25 exact (zenon_H74 zenon_H73). % 30.08/30.25 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.08/30.25 exact (zenon_H85 zenon_H89). % 30.08/30.25 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.08/30.25 apply (zenon_L1002_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.08/30.25 exact (zenon_H85 zenon_H89). % 30.08/30.25 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.08/30.25 apply (zenon_L1052_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.08/30.25 apply (zenon_L258_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.08/30.25 apply (zenon_L192_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.08/30.25 apply (zenon_L173_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.08/30.25 apply (zenon_L176_); trivial. % 30.08/30.25 apply (zenon_L1068_); trivial. % 30.08/30.25 apply (zenon_L848_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.08/30.25 apply (zenon_L1062_); trivial. % 30.08/30.25 apply (zenon_L1063_); trivial. % 30.08/30.25 apply (zenon_L817_); trivial. % 30.08/30.25 (* end of lemma zenon_L1069_ *) % 30.08/30.25 assert (zenon_L1070_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H92 zenon_H159 zenon_Hf6 zenon_He7 zenon_Hc8 zenon_H69 zenon_Hde zenon_H135 zenon_H231 zenon_Hf9 zenon_Hee zenon_H3f zenon_H23b zenon_H173 zenon_H18c zenon_H14b zenon_H108 zenon_H27 zenon_H1c7 zenon_H1bd zenon_Hd6 zenon_H1ca zenon_H1d8 zenon_H1d5 zenon_H1d2 zenon_H1dc zenon_H6b zenon_Hd0 zenon_H156 zenon_H225 zenon_He4 zenon_H74 zenon_H222 zenon_H60 zenon_H5e zenon_H1f zenon_H3c zenon_H208 zenon_H20e zenon_H19a zenon_Hd1 zenon_H101 zenon_H2d zenon_H185 zenon_H8d zenon_H85 zenon_H10d zenon_H37 zenon_H100 zenon_Had zenon_Hb8 zenon_H1af zenon_H19e zenon_H2cc zenon_H20 zenon_H2b1 zenon_He1 zenon_H6f zenon_H35 zenon_H174 zenon_Hcd. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.08/30.25 apply (zenon_L1061_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.08/30.25 apply (zenon_L16_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.08/30.25 apply (zenon_L1069_); trivial. % 30.08/30.25 apply (zenon_L1066_); trivial. % 30.08/30.25 (* end of lemma zenon_L1070_ *) % 30.08/30.25 assert (zenon_L1071_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H1a8 zenon_Hcd zenon_H174 zenon_H35 zenon_H6f zenon_He1 zenon_H2b1 zenon_H20 zenon_H19e zenon_H1af zenon_Hb8 zenon_Had zenon_H100 zenon_H37 zenon_H10d zenon_H85 zenon_H8d zenon_H185 zenon_H2d zenon_H101 zenon_Hd1 zenon_H20e zenon_H208 zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H74 zenon_He4 zenon_H225 zenon_H156 zenon_Hd0 zenon_H6b zenon_H1dc zenon_H1d2 zenon_H1d5 zenon_H1d8 zenon_H1ca zenon_Hd6 zenon_H1bd zenon_H1c7 zenon_H27 zenon_H108 zenon_H14b zenon_H18c zenon_H173 zenon_H23b zenon_H3f zenon_Hee zenon_Hf9 zenon_H231 zenon_H135 zenon_Hde zenon_H69 zenon_Hc8 zenon_He7 zenon_Hf6 zenon_H159 zenon_H92 zenon_H2cc. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.08/30.25 apply (zenon_L16_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.08/30.25 apply (zenon_L125_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.08/30.25 apply (zenon_L1070_); trivial. % 30.08/30.25 exact (zenon_H2cc zenon_H182). % 30.08/30.25 (* end of lemma zenon_L1071_ *) % 30.08/30.25 assert (zenon_L1072_ : ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((e3) = (op (op (e2) (e2)) (e2)))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H117 zenon_H142 zenon_H15f. % 30.08/30.25 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 30.08/30.25 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e3) = (op (op (e2) (e2)) (e2)))). % 30.08/30.25 intro zenon_D_pnotp. % 30.08/30.25 apply zenon_H15f. % 30.08/30.25 rewrite <- zenon_D_pnotp. % 30.08/30.25 exact zenon_H160. % 30.08/30.25 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 30.08/30.25 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 30.08/30.25 congruence. % 30.08/30.25 cut (((op (e0) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 30.08/30.25 intro zenon_D_pnotp. % 30.08/30.25 apply zenon_H162. % 30.08/30.25 rewrite <- zenon_D_pnotp. % 30.08/30.25 exact zenon_H117. % 30.08/30.25 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.08/30.25 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 30.08/30.25 congruence. % 30.08/30.25 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H160 | zenon_intro zenon_H161 ]. % 30.08/30.25 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 30.08/30.25 intro zenon_D_pnotp. % 30.08/30.25 apply zenon_H264. % 30.08/30.25 rewrite <- zenon_D_pnotp. % 30.08/30.25 exact zenon_H160. % 30.08/30.25 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 30.08/30.25 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H261]. % 30.08/30.25 congruence. % 30.08/30.25 apply (zenon_L624_); trivial. % 30.08/30.25 apply zenon_H161. apply refl_equal. % 30.08/30.25 apply zenon_H161. apply refl_equal. % 30.08/30.25 apply zenon_H2f. apply refl_equal. % 30.08/30.25 apply zenon_H161. apply refl_equal. % 30.08/30.25 apply zenon_H161. apply refl_equal. % 30.08/30.25 (* end of lemma zenon_L1072_ *) % 30.08/30.25 assert (zenon_L1073_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.08/30.25 do 0 intro. intros zenon_H200 zenon_H27 zenon_Hd0 zenon_He9 zenon_H3c zenon_Hde zenon_H135 zenon_Hd5 zenon_H5e zenon_H1bd zenon_H117 zenon_H88 zenon_H1d8 zenon_H1af zenon_H8a. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.08/30.25 apply (zenon_L378_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.08/30.25 apply (zenon_L608_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.08/30.25 apply (zenon_notand_s _ _ ax21); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H2d8 ]. % 30.08/30.25 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 30.08/30.25 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e1) = (op (op (e2) (e2)) (op (e2) (e2))))). % 30.08/30.25 intro zenon_D_pnotp. % 30.08/30.25 apply zenon_H1f5. % 30.08/30.25 rewrite <- zenon_D_pnotp. % 30.08/30.25 exact zenon_H166. % 30.08/30.25 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 30.08/30.25 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 30.08/30.25 congruence. % 30.08/30.25 cut (((op (e0) (e0)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 30.08/30.25 intro zenon_D_pnotp. % 30.08/30.25 apply zenon_H1f6. % 30.08/30.25 rewrite <- zenon_D_pnotp. % 30.08/30.25 exact zenon_H88. % 30.08/30.25 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.08/30.25 cut (((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H266]. % 30.08/30.25 congruence. % 30.08/30.25 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 30.08/30.25 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 30.08/30.25 intro zenon_D_pnotp. % 30.08/30.25 apply zenon_H266. % 30.08/30.25 rewrite <- zenon_D_pnotp. % 30.08/30.25 exact zenon_H166. % 30.08/30.25 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 30.08/30.25 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H25f]. % 30.08/30.25 congruence. % 30.08/30.25 apply (zenon_L623_); trivial. % 30.08/30.25 apply zenon_H167. apply refl_equal. % 30.08/30.25 apply zenon_H167. apply refl_equal. % 30.08/30.25 apply zenon_H22. apply refl_equal. % 30.08/30.25 apply zenon_H167. apply refl_equal. % 30.08/30.25 apply zenon_H167. apply refl_equal. % 30.08/30.25 apply (zenon_notand_s _ _ zenon_H2d8); [ zenon_intro zenon_H15f | zenon_intro zenon_H1c1 ]. % 30.08/30.25 apply (zenon_L1072_); trivial. % 30.08/30.25 apply zenon_H1c1. apply sym_equal. exact zenon_H142. % 30.08/30.25 apply (zenon_L186_); trivial. % 30.08/30.25 (* end of lemma zenon_L1073_ *) % 30.08/30.25 assert (zenon_L1074_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H173 zenon_He1 zenon_Hcd zenon_H19a zenon_H101 zenon_H3c zenon_H159 zenon_H1bd zenon_Hc9 zenon_H208 zenon_H88 zenon_Hc8 zenon_H98 zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.08/30.25 apply (zenon_L937_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.08/30.25 apply (zenon_L158_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.08/30.25 apply (zenon_L159_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.08/30.25 apply (zenon_L1054_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.08/30.25 apply (zenon_L93_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.08/30.25 apply (zenon_L282_); trivial. % 30.08/30.25 apply (zenon_L1055_); trivial. % 30.08/30.25 (* end of lemma zenon_L1074_ *) % 30.08/30.25 assert (zenon_L1075_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H23b zenon_H88 zenon_He7 zenon_Hd5 zenon_H5e zenon_H222 zenon_H19a zenon_Hee zenon_Hb8 zenon_He2 zenon_He1 zenon_H100 zenon_H37 zenon_H9c zenon_H2d zenon_H6f. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.08/30.25 apply (zenon_L1053_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.08/30.25 apply (zenon_L514_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.08/30.25 apply (zenon_L337_); trivial. % 30.08/30.25 apply (zenon_L355_); trivial. % 30.08/30.25 (* end of lemma zenon_L1075_ *) % 30.08/30.25 assert (zenon_L1076_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.08/30.25 do 0 intro. intros zenon_Hbd zenon_Hde zenon_H1e zenon_H3f zenon_H6f zenon_H2d zenon_H37 zenon_H100 zenon_He1 zenon_He2 zenon_Hb8 zenon_Hee zenon_H19a zenon_H222 zenon_H5e zenon_Hd5 zenon_He7 zenon_H88 zenon_H23b zenon_Ha4 zenon_H185. % 30.08/30.25 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.08/30.25 apply (zenon_L288_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.08/30.25 apply (zenon_L29_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.08/30.25 apply (zenon_L1075_); trivial. % 30.08/30.25 apply (zenon_L869_); trivial. % 30.08/30.25 (* end of lemma zenon_L1076_ *) % 30.08/30.25 assert (zenon_L1077_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H173 zenon_He1 zenon_H101 zenon_H3c zenon_H159 zenon_H19a zenon_H20e zenon_Hcd zenon_H76 zenon_H6f zenon_H208 zenon_H88 zenon_Hc8 zenon_H98 zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.08/30.25 apply (zenon_L937_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.08/30.25 apply (zenon_L158_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.08/30.25 apply (zenon_L159_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.08/30.25 apply (zenon_L1054_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.08/30.25 apply (zenon_L93_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.08/30.25 apply (zenon_L255_); trivial. % 30.08/30.25 apply (zenon_L1055_); trivial. % 30.08/30.25 (* end of lemma zenon_L1077_ *) % 30.08/30.25 assert (zenon_L1078_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H124 zenon_Hd1 zenon_H185 zenon_Ha4 zenon_H23b zenon_He7 zenon_Hee zenon_Hb8 zenon_He2 zenon_H100 zenon_H2d zenon_H3f zenon_H1e zenon_Hde zenon_Hbd zenon_H173 zenon_He1 zenon_H101 zenon_H3c zenon_H159 zenon_H19a zenon_H20e zenon_Hcd zenon_H76 zenon_H6f zenon_H208 zenon_H88 zenon_Hc8 zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.08/30.25 apply (zenon_L263_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.08/30.25 apply (zenon_L125_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.08/30.25 apply (zenon_L1076_); trivial. % 30.08/30.25 apply (zenon_L1077_); trivial. % 30.08/30.25 (* end of lemma zenon_L1078_ *) % 30.08/30.25 assert (zenon_L1079_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H124 zenon_H174 zenon_H35 zenon_H2b1 zenon_H20 zenon_H2cc zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H85 zenon_H8d zenon_H185 zenon_H2d zenon_Hd1 zenon_H74 zenon_He4 zenon_H225 zenon_H156 zenon_Hd0 zenon_H6b zenon_H1dc zenon_H1d2 zenon_H1d5 zenon_H1d8 zenon_H1ca zenon_Hd6 zenon_H1c7 zenon_H27 zenon_H108 zenon_H14b zenon_H18c zenon_H23b zenon_H3f zenon_Hee zenon_Hf9 zenon_H231 zenon_H135 zenon_Hde zenon_H69 zenon_He7 zenon_Hf6 zenon_H92 zenon_Hfc zenon_H1ba zenon_H1bd zenon_H173 zenon_He1 zenon_H101 zenon_H3c zenon_H159 zenon_H19a zenon_H20e zenon_Hcd zenon_H76 zenon_H6f zenon_H208 zenon_H88 zenon_Hc8 zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.08/30.25 apply (zenon_L1070_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.08/30.25 apply (zenon_L130_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.08/30.25 apply (zenon_L608_); trivial. % 30.08/30.25 apply (zenon_L1077_); trivial. % 30.08/30.25 (* end of lemma zenon_L1079_ *) % 30.08/30.25 assert (zenon_L1080_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_Hd5 zenon_H5e zenon_H222 zenon_H19a zenon_Hee zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H95 zenon_H2d zenon_H10d zenon_H117 zenon_H6f. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.08/30.25 apply (zenon_L386_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.08/30.25 apply (zenon_L514_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.08/30.25 apply (zenon_L337_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.08/30.25 apply (zenon_L174_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.08/30.25 apply (zenon_L766_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.08/30.25 apply (zenon_L151_); trivial. % 30.08/30.25 apply (zenon_L152_); trivial. % 30.08/30.25 (* end of lemma zenon_L1080_ *) % 30.08/30.25 assert (zenon_L1081_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H2d9 zenon_H95 zenon_H98 zenon_H3f zenon_H3c zenon_H55 zenon_H37 zenon_H35. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H1e | zenon_intro zenon_H2da ]. % 30.08/30.25 apply (zenon_L29_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H1f | zenon_intro zenon_H2db ]. % 30.08/30.25 apply (zenon_L336_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_He9 | zenon_intro zenon_H2c ]. % 30.08/30.25 apply (zenon_L88_); trivial. % 30.08/30.25 apply (zenon_L1002_); trivial. % 30.08/30.25 (* end of lemma zenon_L1081_ *) % 30.08/30.25 assert (zenon_L1082_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.08/30.25 do 0 intro. intros zenon_H173 zenon_He1 zenon_Hcd zenon_H19a zenon_H101 zenon_H159 zenon_H35 zenon_H3c zenon_H3f zenon_H95 zenon_H2d9 zenon_H208 zenon_H88 zenon_Hc8 zenon_H98 zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.08/30.25 apply (zenon_L937_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.08/30.25 apply (zenon_L158_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.08/30.25 apply (zenon_L159_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.08/30.25 apply (zenon_L1054_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.08/30.25 apply (zenon_L93_); trivial. % 30.08/30.25 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.08/30.25 apply (zenon_L1081_); trivial. % 30.08/30.25 apply (zenon_L1055_); trivial. % 30.08/30.25 (* end of lemma zenon_L1082_ *) % 30.08/30.25 assert (zenon_L1083_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H124 zenon_H20e zenon_Hd1 zenon_H6f zenon_H117 zenon_H10d zenon_H2d zenon_H76 zenon_H1d8 zenon_Hb8 zenon_Hee zenon_He2 zenon_H23b zenon_H173 zenon_He1 zenon_Hcd zenon_H19a zenon_H101 zenon_H159 zenon_H35 zenon_H3c zenon_H3f zenon_H95 zenon_H2d9 zenon_H208 zenon_H88 zenon_Hc8 zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.25 apply (zenon_L263_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.25 apply (zenon_L125_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.25 apply (zenon_L1080_); trivial. % 30.13/30.25 apply (zenon_L1082_); trivial. % 30.13/30.25 (* end of lemma zenon_L1083_ *) % 30.13/30.25 assert (zenon_L1084_ : ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.25 do 0 intro. intros zenon_He2 zenon_He1 zenon_H296 zenon_Hbd zenon_Ha4 zenon_H1bd zenon_Hfc zenon_H92 zenon_Hf6 zenon_He7 zenon_H69 zenon_Hde zenon_H135 zenon_H231 zenon_Hf9 zenon_H18c zenon_H14b zenon_H108 zenon_H27 zenon_H1c7 zenon_Hd6 zenon_H1ca zenon_H1d5 zenon_H1d2 zenon_H1dc zenon_H6b zenon_Hd0 zenon_H156 zenon_H225 zenon_He4 zenon_H74 zenon_H8d zenon_H85 zenon_H100 zenon_Had zenon_H2cc zenon_H20 zenon_H2b1 zenon_H174 zenon_H124 zenon_H20e zenon_Hd1 zenon_H6f zenon_H10d zenon_H1d8 zenon_Hb8 zenon_Hee zenon_H23b zenon_H173 zenon_Hcd zenon_H19a zenon_H101 zenon_H159 zenon_H35 zenon_H3c zenon_H3f zenon_H2d9 zenon_H208 zenon_H88 zenon_Hc8 zenon_H5e zenon_H60 zenon_H222 zenon_H1af zenon_H37 zenon_H19e zenon_H185 zenon_H2d. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.25 exact (zenon_H85 zenon_H89). % 30.13/30.25 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.25 apply (zenon_L1002_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.25 exact (zenon_H85 zenon_H89). % 30.13/30.25 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.25 apply (zenon_L1052_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.25 apply (zenon_L1078_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.25 apply (zenon_L364_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.25 apply (zenon_L1079_); trivial. % 30.13/30.25 apply (zenon_L1083_); trivial. % 30.13/30.25 apply (zenon_L50_); trivial. % 30.13/30.25 apply (zenon_L848_); trivial. % 30.13/30.25 (* end of lemma zenon_L1084_ *) % 30.13/30.25 assert (zenon_L1085_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H174 zenon_H35 zenon_H8b zenon_Hc9 zenon_He1 zenon_H23b zenon_He7 zenon_H19e zenon_H1af zenon_H222 zenon_H60 zenon_H5e zenon_Hc8 zenon_H88 zenon_H208 zenon_H1bd zenon_H3c zenon_H101 zenon_H19a zenon_Hee zenon_Hb8 zenon_Had zenon_H100 zenon_H37 zenon_H10d zenon_H6f zenon_H85 zenon_H8d zenon_H185 zenon_H2d. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.25 exact (zenon_H85 zenon_H89). % 30.13/30.25 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.25 apply (zenon_L1002_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.25 exact (zenon_H85 zenon_H89). % 30.13/30.25 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.25 apply (zenon_L1057_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.25 apply (zenon_L273_); trivial. % 30.13/30.25 apply (zenon_L25_); trivial. % 30.13/30.25 apply (zenon_L848_); trivial. % 30.13/30.25 (* end of lemma zenon_L1085_ *) % 30.13/30.25 assert (zenon_L1086_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H208 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H60 zenon_H142 zenon_Hd6 zenon_H1ca zenon_H2d zenon_H19e zenon_H37 zenon_H8a zenon_H1d8 zenon_H1d5 zenon_H3c zenon_H5e zenon_H20e zenon_H23b zenon_H88 zenon_He7 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hf6. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.25 apply (zenon_L176_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.25 apply (zenon_L218_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.25 apply (zenon_L225_); trivial. % 30.13/30.25 apply (zenon_L1058_); trivial. % 30.13/30.25 (* end of lemma zenon_L1086_ *) % 30.13/30.25 assert (zenon_L1087_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H2d9 zenon_H95 zenon_Hf6 zenon_Hee zenon_H19a zenon_He7 zenon_H88 zenon_H23b zenon_H20e zenon_H5e zenon_H3c zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H19e zenon_H2d zenon_H1ca zenon_Hd6 zenon_H142 zenon_H60 zenon_H1bd zenon_H1af zenon_H1c7 zenon_H208 zenon_H9d zenon_H3f zenon_H37 zenon_H35. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H1e | zenon_intro zenon_H2da ]. % 30.13/30.25 apply (zenon_L29_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H1f | zenon_intro zenon_H2db ]. % 30.13/30.25 apply (zenon_L1086_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_He9 | zenon_intro zenon_H2c ]. % 30.13/30.25 apply (zenon_L53_); trivial. % 30.13/30.25 apply (zenon_L1002_); trivial. % 30.13/30.25 (* end of lemma zenon_L1087_ *) % 30.13/30.25 assert (zenon_L1088_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 30.13/30.25 do 0 intro. intros zenon_H218 zenon_H185 zenon_H1e1. % 30.13/30.25 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 30.13/30.25 intro zenon_D_pnotp. % 30.13/30.25 apply zenon_H218. % 30.13/30.25 rewrite <- zenon_D_pnotp. % 30.13/30.25 exact zenon_H185. % 30.13/30.25 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 30.13/30.25 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.13/30.25 congruence. % 30.13/30.25 apply zenon_H16e. apply refl_equal. % 30.13/30.25 apply zenon_H1e2. apply sym_equal. exact zenon_H1e1. % 30.13/30.25 (* end of lemma zenon_L1088_ *) % 30.13/30.25 assert (zenon_L1089_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H174 zenon_H85 zenon_H35 zenon_H37 zenon_H27 zenon_H1af zenon_Hd0 zenon_He9 zenon_H3c zenon_Hde zenon_Hdf zenon_H135 zenon_H185 zenon_H2d. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.25 exact (zenon_H85 zenon_H89). % 30.13/30.25 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.25 apply (zenon_L1002_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.25 apply (zenon_L378_); trivial. % 30.13/30.25 apply (zenon_L848_); trivial. % 30.13/30.25 (* end of lemma zenon_L1089_ *) % 30.13/30.25 assert (zenon_L1090_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_Hd5 zenon_H5e zenon_H222 zenon_H19a zenon_Hee zenon_Hb8 zenon_Had zenon_H6e zenon_H100 zenon_H37 zenon_H10d zenon_H117 zenon_H6f. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.25 apply (zenon_L386_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.25 apply (zenon_L514_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.25 apply (zenon_L337_); trivial. % 30.13/30.25 apply (zenon_L153_); trivial. % 30.13/30.25 (* end of lemma zenon_L1090_ *) % 30.13/30.25 assert (zenon_L1091_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H174 zenon_H85 zenon_H35 zenon_H37 zenon_H10e zenon_H185 zenon_H2d. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.25 exact (zenon_H85 zenon_H89). % 30.13/30.25 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.25 apply (zenon_L1002_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.25 apply (zenon_L87_); trivial. % 30.13/30.25 apply (zenon_L848_); trivial. % 30.13/30.25 (* end of lemma zenon_L1091_ *) % 30.13/30.25 assert (zenon_L1092_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H208 zenon_H88 zenon_Hc8 zenon_H98 zenon_H5e zenon_H222 zenon_Hfe zenon_H1af zenon_H37 zenon_H19e. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.25 apply (zenon_L809_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.25 apply (zenon_L514_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.25 apply (zenon_L170_); trivial. % 30.13/30.25 apply (zenon_L214_); trivial. % 30.13/30.25 (* end of lemma zenon_L1092_ *) % 30.13/30.25 assert (zenon_L1093_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H208 zenon_Hc8 zenon_H6f zenon_H2d zenon_H9c zenon_H100 zenon_He1 zenon_He2 zenon_Hb8 zenon_Hee zenon_H222 zenon_H5e zenon_He7 zenon_H88 zenon_H23b zenon_H20e zenon_H19a zenon_H1af zenon_H37 zenon_H19e. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.25 apply (zenon_L809_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.25 apply (zenon_L1075_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.25 apply (zenon_L225_); trivial. % 30.13/30.25 apply (zenon_L214_); trivial. % 30.13/30.25 (* end of lemma zenon_L1093_ *) % 30.13/30.25 assert (zenon_L1094_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H124 zenon_H3f zenon_H117 zenon_H10d zenon_H6e zenon_Had zenon_Hcd zenon_H14b zenon_H185 zenon_H35 zenon_H85 zenon_H174 zenon_H6b zenon_Hdf zenon_H208 zenon_Hc8 zenon_H6f zenon_H2d zenon_H100 zenon_He1 zenon_He2 zenon_Hb8 zenon_Hee zenon_H222 zenon_H5e zenon_He7 zenon_H88 zenon_H23b zenon_H20e zenon_H19a zenon_H1af zenon_H37 zenon_H19e. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.25 apply (zenon_L571_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.25 apply (zenon_L125_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.25 apply (zenon_L1090_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.13/30.25 apply (zenon_L1091_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.13/30.25 apply (zenon_L1092_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.13/30.25 apply (zenon_L303_); trivial. % 30.13/30.25 apply (zenon_L1093_); trivial. % 30.13/30.25 (* end of lemma zenon_L1094_ *) % 30.13/30.25 assert (zenon_L1095_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 30.13/30.25 do 0 intro. intros zenon_H173 zenon_H88 zenon_He1 zenon_H101 zenon_H2d zenon_H185 zenon_H3c zenon_H35 zenon_H85 zenon_H174 zenon_H159 zenon_H19e zenon_H37 zenon_H19a zenon_H20e zenon_Hcd zenon_H76 zenon_H6f zenon_H208 zenon_H135 zenon_Hdf zenon_Hde zenon_H222 zenon_Hd0 zenon_H1af zenon_H117 zenon_H27. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.25 apply (zenon_L937_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.25 apply (zenon_L158_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.25 apply (zenon_L159_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.25 apply (zenon_L1089_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.25 apply (zenon_L93_); trivial. % 30.13/30.25 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.25 apply (zenon_L255_); trivial. % 30.13/30.25 apply (zenon_L444_); trivial. % 30.13/30.25 (* end of lemma zenon_L1095_ *) % 30.13/30.25 assert (zenon_L1096_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.13/30.26 do 0 intro. intros zenon_Hf9 zenon_H8a zenon_He1 zenon_H27 zenon_H117 zenon_H1af zenon_Hd0 zenon_H222 zenon_Hde zenon_Hdf zenon_H135 zenon_Hda zenon_H10d zenon_H231. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.13/30.26 apply (zenon_L50_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.13/30.26 apply (zenon_L444_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.13/30.26 apply (zenon_L64_); trivial. % 30.13/30.26 exact (zenon_H231 zenon_Hf4). % 30.13/30.26 (* end of lemma zenon_L1096_ *) % 30.13/30.26 assert (zenon_L1097_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.26 do 0 intro. intros zenon_He4 zenon_H74 zenon_H231 zenon_H10d zenon_Hda zenon_H135 zenon_Hdf zenon_Hde zenon_H222 zenon_Hd0 zenon_H1af zenon_H27 zenon_He1 zenon_Hf9 zenon_H173 zenon_H88 zenon_H101 zenon_H3c zenon_H35 zenon_H85 zenon_H174 zenon_H159 zenon_H19e zenon_H37 zenon_H19a zenon_H20e zenon_Hcd zenon_H6f zenon_H208 zenon_H124 zenon_H3f zenon_Had zenon_H14b zenon_H6b zenon_Hc8 zenon_H100 zenon_Hb8 zenon_Hee zenon_H5e zenon_He7 zenon_H23b zenon_H8d zenon_H185 zenon_H2d. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.26 apply (zenon_L937_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.26 apply (zenon_L49_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.26 apply (zenon_L1094_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.26 apply (zenon_L1095_); trivial. % 30.13/30.26 apply (zenon_L1096_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 (* end of lemma zenon_L1097_ *) % 30.13/30.26 assert (zenon_L1098_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H225 zenon_H2d zenon_H8d zenon_H23b zenon_He7 zenon_H5e zenon_Hee zenon_Hb8 zenon_H100 zenon_Hc8 zenon_H6b zenon_H14b zenon_Had zenon_H3f zenon_H124 zenon_H208 zenon_H6f zenon_Hcd zenon_H20e zenon_H19a zenon_H37 zenon_H19e zenon_H159 zenon_H174 zenon_H85 zenon_H35 zenon_H3c zenon_H101 zenon_H88 zenon_H173 zenon_Hf9 zenon_He1 zenon_H27 zenon_H1af zenon_Hd0 zenon_H222 zenon_Hdf zenon_H135 zenon_H10d zenon_H231 zenon_H74 zenon_He4 zenon_H185 zenon_Hde. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.26 apply (zenon_L1089_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.26 apply (zenon_L1097_); trivial. % 30.13/30.26 apply (zenon_L817_); trivial. % 30.13/30.26 (* end of lemma zenon_L1098_ *) % 30.13/30.26 assert (zenon_L1099_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H8d zenon_H85 zenon_H37 zenon_H100 zenon_Had zenon_Hb8 zenon_H19e zenon_H2cc zenon_H185 zenon_H20 zenon_H2b1 zenon_H6f zenon_H6c zenon_Hf9 zenon_He1 zenon_H27 zenon_H117 zenon_H1af zenon_Hd0 zenon_H222 zenon_Hde zenon_Hdf zenon_H135 zenon_Hda zenon_H10d zenon_H231. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.26 apply (zenon_L1052_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.26 apply (zenon_L157_); trivial. % 30.13/30.26 apply (zenon_L1096_); trivial. % 30.13/30.26 (* end of lemma zenon_L1099_ *) % 30.13/30.26 assert (zenon_L1100_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H225 zenon_H74 zenon_H3c zenon_H2d zenon_H8d zenon_H85 zenon_H37 zenon_H100 zenon_Had zenon_Hb8 zenon_H19e zenon_H2cc zenon_H20 zenon_H2b1 zenon_H6f zenon_H6c zenon_Hf9 zenon_He1 zenon_H27 zenon_H1af zenon_Hd0 zenon_H222 zenon_Hdf zenon_H135 zenon_H10d zenon_H231 zenon_H35 zenon_H174 zenon_H185 zenon_Hde. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.26 apply (zenon_L1089_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_L1099_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 apply (zenon_L817_); trivial. % 30.13/30.26 (* end of lemma zenon_L1100_ *) % 30.13/30.26 assert (zenon_L1101_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.13/30.26 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_H90 zenon_He9 zenon_H3f zenon_Hda zenon_H10d zenon_H231. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.13/30.26 apply (zenon_L386_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.13/30.26 apply (zenon_L53_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.13/30.26 apply (zenon_L64_); trivial. % 30.13/30.26 exact (zenon_H231 zenon_Hf4). % 30.13/30.26 (* end of lemma zenon_L1101_ *) % 30.13/30.26 assert (zenon_L1102_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H92 zenon_Hde zenon_He1 zenon_H74 zenon_He4 zenon_H1b1 zenon_H2d zenon_H185 zenon_H8d zenon_H85 zenon_H10d zenon_H37 zenon_H100 zenon_Had zenon_Hb8 zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_H23b zenon_H6f zenon_H35 zenon_H174 zenon_H8b zenon_H20. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.26 apply (zenon_L937_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.26 apply (zenon_L338_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.26 apply (zenon_L273_); trivial. % 30.13/30.26 apply (zenon_L25_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 apply (zenon_L288_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.26 apply (zenon_L147_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.26 apply (zenon_L338_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.26 apply (zenon_L157_); trivial. % 30.13/30.26 apply (zenon_L25_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 apply (zenon_L27_); trivial. % 30.13/30.26 (* end of lemma zenon_L1102_ *) % 30.13/30.26 assert (zenon_L1103_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H246 zenon_Hf6 zenon_H18c zenon_H108 zenon_H1c7 zenon_Hd6 zenon_H1ca zenon_H1d8 zenon_H1d5 zenon_H1d2 zenon_H1dc zenon_H156 zenon_Hd1 zenon_H2d9 zenon_Hfc zenon_Ha4 zenon_Hbd zenon_H296 zenon_H200 zenon_H218 zenon_H173 zenon_H159 zenon_H124 zenon_H14b zenon_H6b zenon_H225 zenon_H2cc zenon_H2b1 zenon_H27 zenon_Hd0 zenon_H135 zenon_Hcd zenon_H20e zenon_Hf9 zenon_H231 zenon_Hc0 zenon_He7 zenon_H19e zenon_H1af zenon_H222 zenon_H60 zenon_H5e zenon_Hc8 zenon_H208 zenon_H1bd zenon_H3c zenon_H101 zenon_H174 zenon_H35 zenon_H6f zenon_H23b zenon_H3f zenon_Hee zenon_Hb8 zenon_Had zenon_H100 zenon_H37 zenon_H10d zenon_H85 zenon_H8d zenon_H2d zenon_H1b1 zenon_He4 zenon_H74 zenon_He1 zenon_Hde zenon_H92 zenon_H1a5 zenon_H19a zenon_H185 zenon_H20. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.26 apply (zenon_L912_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.26 apply (zenon_L1061_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.26 apply (zenon_L147_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.26 apply (zenon_L1069_); trivial. % 30.13/30.26 apply (zenon_L1066_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.26 apply (zenon_L136_); trivial. % 30.13/30.26 apply (zenon_L117_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.26 apply (zenon_L937_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.26 apply (zenon_L1052_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.26 apply (zenon_L273_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.26 apply (zenon_L1061_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.26 apply (zenon_L130_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.26 apply (zenon_L1073_); trivial. % 30.13/30.26 apply (zenon_L1074_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 apply (zenon_L1084_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.26 apply (zenon_L937_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.26 apply (zenon_L1057_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.26 apply (zenon_L273_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.26 apply (zenon_L1060_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.26 apply (zenon_L130_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.26 apply (zenon_L142_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.26 apply (zenon_L158_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.26 apply (zenon_L159_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.26 apply (zenon_L300_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.26 apply (zenon_L93_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.26 apply (zenon_L282_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.13/30.26 apply (zenon_L444_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.13/30.26 apply (zenon_L608_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.13/30.26 apply (zenon_L1085_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.13/30.26 apply (zenon_L1087_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.13/30.26 apply (zenon_L177_); trivial. % 30.13/30.26 apply (zenon_L320_); trivial. % 30.13/30.26 apply (zenon_L1088_); trivial. % 30.13/30.26 apply (zenon_L1074_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 apply (zenon_L1084_); trivial. % 30.13/30.26 apply (zenon_L817_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.26 apply (zenon_L1070_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.26 apply (zenon_L136_); trivial. % 30.13/30.26 apply (zenon_L117_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.26 apply (zenon_L1098_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.26 apply (zenon_L1098_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.26 apply (zenon_L147_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.26 apply (zenon_L1100_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.26 apply (zenon_L1052_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.26 apply (zenon_L220_); trivial. % 30.13/30.26 apply (zenon_L39_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.26 apply (zenon_L1052_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.26 apply (zenon_L1101_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.26 apply (zenon_L158_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.26 apply (zenon_L255_); trivial. % 30.13/30.26 apply (zenon_L444_); trivial. % 30.13/30.26 apply (zenon_L39_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 apply (zenon_L817_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.26 apply (zenon_L136_); trivial. % 30.13/30.26 apply (zenon_L117_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.26 apply (zenon_L937_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.26 apply (zenon_L1085_); trivial. % 30.13/30.26 apply (zenon_L288_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.26 apply (zenon_L1102_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.26 apply (zenon_L136_); trivial. % 30.13/30.26 apply (zenon_L117_); trivial. % 30.13/30.26 (* end of lemma zenon_L1103_ *) % 30.13/30.26 assert (zenon_L1104_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H174 zenon_H85 zenon_H35 zenon_H37 zenon_H10d zenon_Hb6 zenon_H185 zenon_H2d. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_L151_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 (* end of lemma zenon_L1104_ *) % 30.13/30.26 assert (zenon_L1105_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.13/30.26 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_H90 zenon_He9 zenon_H3f zenon_Hcc zenon_H60 zenon_H1dc zenon_H231. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.13/30.26 apply (zenon_L386_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.13/30.26 apply (zenon_L53_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.13/30.26 apply (zenon_L567_); trivial. % 30.13/30.26 exact (zenon_H231 zenon_Hf4). % 30.13/30.26 (* end of lemma zenon_L1105_ *) % 30.13/30.26 assert (zenon_L1106_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H225 zenon_H74 zenon_H231 zenon_H1dc zenon_H3f zenon_H90 zenon_Hcd zenon_Hf9 zenon_H27 zenon_Hcc zenon_H60 zenon_H185 zenon_Hde. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.26 apply (zenon_L1105_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.26 apply (zenon_L554_); trivial. % 30.13/30.26 apply (zenon_L817_); trivial. % 30.13/30.26 (* end of lemma zenon_L1106_ *) % 30.13/30.26 assert (zenon_L1107_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H23b zenon_Hde zenon_H185 zenon_H60 zenon_Hcc zenon_H27 zenon_Hf9 zenon_Hcd zenon_H1dc zenon_H231 zenon_H74 zenon_H225 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hb8 zenon_Had zenon_H6e zenon_H100 zenon_H37 zenon_H10d zenon_H117 zenon_H6f. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.26 apply (zenon_L1106_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.26 apply (zenon_L336_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.26 apply (zenon_L337_); trivial. % 30.13/30.26 apply (zenon_L153_); trivial. % 30.13/30.26 (* end of lemma zenon_L1107_ *) % 30.13/30.26 assert (zenon_L1108_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H8d zenon_H85 zenon_H117 zenon_H10d zenon_H100 zenon_Had zenon_Hb8 zenon_Hee zenon_H19a zenon_H225 zenon_H74 zenon_Hcd zenon_H27 zenon_H185 zenon_Hde zenon_H23b zenon_H19e zenon_H37 zenon_H1af zenon_H3c zenon_H5e zenon_H1f zenon_H6f zenon_H208 zenon_Hf9 zenon_He1 zenon_He9 zenon_H3f zenon_Hcc zenon_H60 zenon_H1dc zenon_H231. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.26 apply (zenon_L1107_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.26 apply (zenon_L220_); trivial. % 30.13/30.26 apply (zenon_L568_); trivial. % 30.13/30.26 (* end of lemma zenon_L1108_ *) % 30.13/30.26 assert (zenon_L1109_ : (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H2d zenon_H8d zenon_H85 zenon_H10d zenon_H100 zenon_Had zenon_Hb8 zenon_Hee zenon_H19a zenon_H225 zenon_H74 zenon_Hcd zenon_H23b zenon_H19e zenon_H37 zenon_H1af zenon_H3c zenon_H5e zenon_H1f zenon_H6f zenon_H208 zenon_Hf9 zenon_He1 zenon_H3f zenon_H1dc zenon_H231 zenon_H35 zenon_H174 zenon_H27 zenon_Hcc zenon_H60 zenon_H185 zenon_Hde. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_L1108_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.26 apply (zenon_L554_); trivial. % 30.13/30.26 apply (zenon_L817_); trivial. % 30.13/30.26 (* end of lemma zenon_L1109_ *) % 30.13/30.26 assert (zenon_L1110_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H14b zenon_H117 zenon_H98 zenon_H76 zenon_Hde zenon_Hcc zenon_H208 zenon_Hc8 zenon_H6f zenon_H2d zenon_H100 zenon_He1 zenon_He2 zenon_Hb8 zenon_Hee zenon_H222 zenon_H5e zenon_He7 zenon_H88 zenon_H23b zenon_H20e zenon_H19a zenon_H1af zenon_H37 zenon_H19e. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.13/30.26 apply (zenon_L87_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.13/30.26 apply (zenon_L718_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.13/30.26 apply (zenon_L89_); trivial. % 30.13/30.26 apply (zenon_L1093_); trivial. % 30.13/30.26 (* end of lemma zenon_L1110_ *) % 30.13/30.26 assert (zenon_L1111_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H124 zenon_H185 zenon_H60 zenon_H27 zenon_H174 zenon_H35 zenon_H231 zenon_H1dc zenon_H3f zenon_Hf9 zenon_H3c zenon_H74 zenon_H225 zenon_Had zenon_H85 zenon_H8d zenon_H10d zenon_H95 zenon_H1d8 zenon_Hcd zenon_H14b zenon_H117 zenon_H76 zenon_Hde zenon_Hcc zenon_H208 zenon_Hc8 zenon_H6f zenon_H2d zenon_H100 zenon_He1 zenon_He2 zenon_Hb8 zenon_Hee zenon_H222 zenon_H5e zenon_He7 zenon_H88 zenon_H23b zenon_H20e zenon_H19a zenon_H1af zenon_H37 zenon_H19e. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.26 apply (zenon_L1109_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.26 apply (zenon_L125_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.26 apply (zenon_L1080_); trivial. % 30.13/30.26 apply (zenon_L1110_); trivial. % 30.13/30.26 (* end of lemma zenon_L1111_ *) % 30.13/30.26 assert (zenon_L1112_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H296 zenon_Hbd zenon_Ha4 zenon_H1bd zenon_Hfc zenon_He9 zenon_H124 zenon_H185 zenon_H60 zenon_H27 zenon_H174 zenon_H35 zenon_H231 zenon_H1dc zenon_H3f zenon_Hf9 zenon_H3c zenon_H74 zenon_H225 zenon_Had zenon_H85 zenon_H8d zenon_H10d zenon_H1d8 zenon_Hcd zenon_H14b zenon_H117 zenon_H76 zenon_Hde zenon_Hcc zenon_H208 zenon_Hc8 zenon_H6f zenon_H2d zenon_H100 zenon_He1 zenon_He2 zenon_Hb8 zenon_Hee zenon_H222 zenon_H5e zenon_He7 zenon_H88 zenon_H23b zenon_H20e zenon_H19a zenon_H1af zenon_H37 zenon_H19e. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.26 apply (zenon_L1109_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.26 apply (zenon_L125_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.26 apply (zenon_L1076_); trivial. % 30.13/30.26 apply (zenon_L1110_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.26 apply (zenon_L364_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.26 apply (zenon_L220_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.26 apply (zenon_L130_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.26 apply (zenon_L608_); trivial. % 30.13/30.26 apply (zenon_L1110_); trivial. % 30.13/30.26 apply (zenon_L1111_); trivial. % 30.13/30.26 (* end of lemma zenon_L1112_ *) % 30.13/30.26 assert (zenon_L1113_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H19e zenon_H37 zenon_H1af zenon_H19a zenon_H20e zenon_H23b zenon_H88 zenon_He7 zenon_H5e zenon_H222 zenon_Hee zenon_Hb8 zenon_He2 zenon_H100 zenon_H2d zenon_H6f zenon_Hc8 zenon_H208 zenon_Hde zenon_H117 zenon_H14b zenon_Hcd zenon_H1d8 zenon_H10d zenon_H8d zenon_H85 zenon_Had zenon_H225 zenon_H74 zenon_H3c zenon_H35 zenon_H174 zenon_H27 zenon_H185 zenon_H124 zenon_Hfc zenon_H1bd zenon_Ha4 zenon_Hbd zenon_H296 zenon_Hf9 zenon_He1 zenon_He9 zenon_H3f zenon_Hcc zenon_H60 zenon_H1dc zenon_H231. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.26 apply (zenon_L1107_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.26 apply (zenon_L130_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.26 apply (zenon_L1090_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.13/30.26 apply (zenon_L87_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.13/30.26 apply (zenon_L1092_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.13/30.26 apply (zenon_L89_); trivial. % 30.13/30.26 apply (zenon_L1093_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.26 apply (zenon_L1112_); trivial. % 30.13/30.26 apply (zenon_L568_); trivial. % 30.13/30.26 (* end of lemma zenon_L1113_ *) % 30.13/30.26 assert (zenon_L1114_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 30.13/30.26 do 0 intro. intros zenon_H25c zenon_H246 zenon_H218 zenon_H124 zenon_H200 zenon_Hfc zenon_H296 zenon_H2d9 zenon_Hbd zenon_Ha4 zenon_H20 zenon_H92 zenon_H18c zenon_H135 zenon_Hde zenon_Hf9 zenon_H225 zenon_H1b1 zenon_H74 zenon_H37 zenon_H174 zenon_H185 zenon_H23b zenon_Had zenon_H100 zenon_H10d zenon_H6f zenon_Hb8 zenon_H19a zenon_Hee zenon_H208 zenon_H1af zenon_H19e zenon_H60 zenon_H3c zenon_H5e zenon_H222 zenon_Hc8 zenon_H1bd zenon_H101 zenon_He7 zenon_H173 zenon_H159 zenon_He1 zenon_Hd1 zenon_H20e zenon_Hcd zenon_H14b zenon_H1dc zenon_H6b zenon_H156 zenon_H1d8 zenon_H27 zenon_H1d2 zenon_H108 zenon_Hd6 zenon_H1c7 zenon_H1ca zenon_H1d5 zenon_H2d zenon_Hf6 zenon_H3f zenon_H8d zenon_H35 zenon_H85 zenon_H2b1 zenon_H2cc zenon_He4 zenon_H1a5 zenon_Hc0 zenon_H25b. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.13/30.26 apply (zenon_L1103_); trivial. % 30.13/30.26 apply (zenon_L1104_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.26 exact (zenon_H74 zenon_H73). % 30.13/30.26 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.26 apply (zenon_L937_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.26 apply (zenon_L552_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.26 exact (zenon_H85 zenon_H89). % 30.13/30.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.26 apply (zenon_L1002_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.26 apply (zenon_L1113_); trivial. % 30.13/30.26 apply (zenon_L848_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.26 apply (zenon_L554_); trivial. % 30.13/30.26 apply (zenon_L817_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.26 apply (zenon_L1109_); trivial. % 30.13/30.26 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.26 apply (zenon_L136_); trivial. % 30.13/30.26 apply (zenon_L117_); trivial. % 30.13/30.26 apply (zenon_L1104_); trivial. % 30.13/30.26 (* end of lemma zenon_L1114_ *) % 30.13/30.26 assert (zenon_L1115_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H1a8 zenon_H69 zenon_H25b zenon_Hc0 zenon_H1a5 zenon_He4 zenon_H2b1 zenon_H85 zenon_H35 zenon_H8d zenon_H3f zenon_Hf6 zenon_H2d zenon_H1d5 zenon_H1ca zenon_H1c7 zenon_Hd6 zenon_H108 zenon_H1d2 zenon_H27 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_H20e zenon_Hd1 zenon_He1 zenon_H159 zenon_H173 zenon_He7 zenon_H101 zenon_H1bd zenon_Hc8 zenon_H222 zenon_H5e zenon_H3c zenon_H60 zenon_H19e zenon_H1af zenon_H208 zenon_Hee zenon_Hb8 zenon_H6f zenon_H10d zenon_H100 zenon_Had zenon_H23b zenon_H185 zenon_H174 zenon_H37 zenon_H74 zenon_H1b1 zenon_H225 zenon_Hf9 zenon_Hde zenon_H135 zenon_H18c zenon_H92 zenon_H20 zenon_Ha4 zenon_Hbd zenon_H2d9 zenon_H296 zenon_Hfc zenon_H200 zenon_H124 zenon_H218 zenon_H246 zenon_H25c zenon_H2cc. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.27 apply (zenon_L16_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.27 apply (zenon_L125_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.27 apply (zenon_L1114_); trivial. % 30.13/30.27 exact (zenon_H2cc zenon_H182). % 30.13/30.27 (* end of lemma zenon_L1115_ *) % 30.13/30.27 assert (zenon_L1116_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H8d zenon_H85 zenon_H117 zenon_H10d zenon_H100 zenon_Had zenon_Hb8 zenon_H2cc zenon_H185 zenon_H20 zenon_H2b1 zenon_H19e zenon_H37 zenon_H1af zenon_H60 zenon_He9 zenon_H3c zenon_H5e zenon_H1f zenon_H6f zenon_H208 zenon_He1 zenon_He2. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.27 exact (zenon_H85 zenon_H89). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.27 apply (zenon_L1052_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.27 apply (zenon_L220_); trivial. % 30.13/30.27 apply (zenon_L50_); trivial. % 30.13/30.27 (* end of lemma zenon_L1116_ *) % 30.13/30.27 assert (zenon_L1117_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H101 zenon_H60 zenon_H3c zenon_H5e zenon_H1f zenon_H13b zenon_H19e zenon_H37 zenon_Hfe zenon_Hcd zenon_H76 zenon_H6f zenon_H208 zenon_H135 zenon_Hdf zenon_Hde zenon_H222 zenon_Hd0 zenon_H1af zenon_H117 zenon_H27. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.27 apply (zenon_L220_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.27 exact (zenon_H13b zenon_Hfd). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.27 apply (zenon_L215_); trivial. % 30.13/30.27 apply (zenon_L444_); trivial. % 30.13/30.27 (* end of lemma zenon_L1117_ *) % 30.13/30.27 assert (zenon_L1118_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.27 do 0 intro. intros zenon_He4 zenon_H74 zenon_H174 zenon_H35 zenon_He1 zenon_H172 zenon_H68 zenon_H20 zenon_H27 zenon_H1af zenon_Hd0 zenon_H222 zenon_Hde zenon_Hdf zenon_H135 zenon_H208 zenon_H6f zenon_Hcd zenon_H37 zenon_H19e zenon_H13b zenon_H1f zenon_H5e zenon_H3c zenon_H60 zenon_H101 zenon_H16a zenon_H2b1 zenon_H2cc zenon_Hb8 zenon_Had zenon_H100 zenon_H10d zenon_H85 zenon_H8d zenon_H185 zenon_H2d. % 30.13/30.27 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.27 exact (zenon_H74 zenon_H73). % 30.13/30.27 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.27 apply (zenon_L48_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.27 apply (zenon_L49_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.27 exact (zenon_H85 zenon_H89). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.27 apply (zenon_L1002_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.27 exact (zenon_H85 zenon_H89). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.27 apply (zenon_L1052_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.27 apply (zenon_L16_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.27 apply (zenon_L364_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.27 apply (zenon_L1117_); trivial. % 30.13/30.27 apply (zenon_L886_); trivial. % 30.13/30.27 apply (zenon_L50_); trivial. % 30.13/30.27 apply (zenon_L848_); trivial. % 30.13/30.27 (* end of lemma zenon_L1118_ *) % 30.13/30.27 assert (zenon_L1119_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H174 zenon_H85 zenon_H1e zenon_H6f zenon_H26 zenon_H185 zenon_H2d. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.27 exact (zenon_H85 zenon_H89). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.27 apply (zenon_L4_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.27 apply (zenon_L598_); trivial. % 30.13/30.27 apply (zenon_L848_); trivial. % 30.13/30.27 (* end of lemma zenon_L1119_ *) % 30.13/30.27 assert (zenon_L1120_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H2b1 zenon_H88 zenon_H2c1 zenon_H2cc zenon_H19e zenon_H37 zenon_H1af zenon_H1a0 zenon_H110. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.13/30.27 apply (zenon_L940_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.13/30.27 exact (zenon_H2cc zenon_H182). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.13/30.27 apply (zenon_L214_); trivial. % 30.13/30.27 apply (zenon_L133_); trivial. % 30.13/30.27 (* end of lemma zenon_L1120_ *) % 30.13/30.27 assert (zenon_L1121_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H1a2 zenon_H85 zenon_H174 zenon_H185 zenon_Ha4 zenon_H23b zenon_He7 zenon_H5e zenon_H222 zenon_Hee zenon_Hb8 zenon_He2 zenon_He1 zenon_H100 zenon_H2d zenon_H6f zenon_H3f zenon_H1e zenon_Hde zenon_Hbd zenon_Hd6 zenon_Hd5 zenon_H2b1 zenon_H88 zenon_H2c1 zenon_H2cc zenon_H19e zenon_H37 zenon_H1af zenon_H110. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.27 apply (zenon_L1119_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.27 apply (zenon_L1076_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.27 apply (zenon_L46_); trivial. % 30.13/30.27 apply (zenon_L1120_); trivial. % 30.13/30.27 (* end of lemma zenon_L1121_ *) % 30.13/30.27 assert (zenon_L1122_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H1a2 zenon_Hd9 zenon_H6f zenon_H117 zenon_H10d zenon_H2d zenon_H95 zenon_H76 zenon_H1d8 zenon_Hb8 zenon_Hee zenon_H222 zenon_H5e zenon_Hd5 zenon_He2 zenon_Hcd zenon_H23b zenon_Hfe zenon_H2b1 zenon_H88 zenon_H2c1 zenon_H2cc zenon_H19e zenon_H37 zenon_H1af zenon_H110. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.27 apply (zenon_L797_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.27 apply (zenon_L1080_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.27 apply (zenon_L170_); trivial. % 30.13/30.27 apply (zenon_L1120_); trivial. % 30.13/30.27 (* end of lemma zenon_L1122_ *) % 30.13/30.27 assert (zenon_L1123_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H174 zenon_H35 zenon_H8b zenon_Hc9 zenon_He1 zenon_H2b1 zenon_H20 zenon_H2cc zenon_H19e zenon_H1af zenon_Hb8 zenon_Had zenon_H100 zenon_H37 zenon_H10d zenon_H6f zenon_H85 zenon_H8d zenon_H185 zenon_H2d. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.27 exact (zenon_H85 zenon_H89). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.27 apply (zenon_L1002_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.27 exact (zenon_H85 zenon_H89). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.27 apply (zenon_L1052_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.27 apply (zenon_L273_); trivial. % 30.13/30.27 apply (zenon_L25_); trivial. % 30.13/30.27 apply (zenon_L848_); trivial. % 30.13/30.27 (* end of lemma zenon_L1123_ *) % 30.13/30.27 assert (zenon_L1124_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H225 zenon_H74 zenon_H19e zenon_H37 zenon_H1af zenon_H3c zenon_H5e zenon_H1f zenon_H18c zenon_H68 zenon_H208 zenon_H27 zenon_Hcc zenon_H60 zenon_H185 zenon_Hde. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.27 exact (zenon_H74 zenon_H73). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.27 apply (zenon_L454_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.27 apply (zenon_L554_); trivial. % 30.13/30.27 apply (zenon_L817_); trivial. % 30.13/30.27 (* end of lemma zenon_L1124_ *) % 30.13/30.27 assert (zenon_L1125_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H1a8 zenon_He9 zenon_H88 zenon_H1a2 zenon_He2 zenon_H1e zenon_H2c1 zenon_H110 zenon_Hcc zenon_H25b zenon_Hc0 zenon_H1a5 zenon_He4 zenon_H2b1 zenon_H85 zenon_H35 zenon_H8d zenon_H3f zenon_Hf6 zenon_H2d zenon_H1d5 zenon_H1ca zenon_H1c7 zenon_Hd6 zenon_H108 zenon_H1d2 zenon_H27 zenon_H1d8 zenon_H156 zenon_H6b zenon_H1dc zenon_H14b zenon_Hcd zenon_H20e zenon_Hd1 zenon_He1 zenon_H159 zenon_H173 zenon_He7 zenon_H101 zenon_H1bd zenon_Hc8 zenon_H222 zenon_H5e zenon_H3c zenon_H60 zenon_H19e zenon_H1af zenon_H208 zenon_Hee zenon_Hb8 zenon_H6f zenon_H10d zenon_H100 zenon_Had zenon_H23b zenon_H185 zenon_H174 zenon_H37 zenon_H74 zenon_H1b1 zenon_H225 zenon_Hf9 zenon_Hde zenon_H135 zenon_H18c zenon_H92 zenon_H20 zenon_Ha4 zenon_Hbd zenon_H2d9 zenon_H296 zenon_Hfc zenon_H200 zenon_H124 zenon_H218 zenon_H246 zenon_H25c zenon_H2cc. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.27 apply (zenon_L1124_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.27 apply (zenon_L45_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.27 apply (zenon_L1121_); trivial. % 30.13/30.27 apply (zenon_L1054_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.27 apply (zenon_L125_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.27 apply (zenon_L1114_); trivial. % 30.13/30.27 exact (zenon_H2cc zenon_H182). % 30.13/30.27 (* end of lemma zenon_L1125_ *) % 30.13/30.27 assert (zenon_L1126_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H1ba zenon_H5e zenon_H1bd zenon_Hcd zenon_Hcc zenon_H1af zenon_H37 zenon_H19e. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.27 apply (zenon_L120_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.27 apply (zenon_L608_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.27 apply (zenon_L44_); trivial. % 30.13/30.27 apply (zenon_L214_); trivial. % 30.13/30.27 (* end of lemma zenon_L1126_ *) % 30.13/30.27 assert (zenon_L1127_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H1a8 zenon_H1ba zenon_H18c zenon_H231 zenon_H1dc zenon_H60 zenon_Hcc zenon_H3f zenon_He9 zenon_He1 zenon_Hf9 zenon_H296 zenon_Hbd zenon_Ha4 zenon_H1bd zenon_Hfc zenon_H124 zenon_H185 zenon_H27 zenon_H174 zenon_H35 zenon_H3c zenon_H74 zenon_H225 zenon_Had zenon_H85 zenon_H8d zenon_H10d zenon_H1d8 zenon_Hcd zenon_H14b zenon_H117 zenon_Hde zenon_H208 zenon_Hc8 zenon_H6f zenon_H2d zenon_H100 zenon_He2 zenon_Hb8 zenon_Hee zenon_H222 zenon_H5e zenon_He7 zenon_H88 zenon_H23b zenon_H20e zenon_H1af zenon_H37 zenon_H19e zenon_H2cc. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.27 apply (zenon_L1126_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.27 apply (zenon_L125_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.27 apply (zenon_L1113_); trivial. % 30.13/30.27 exact (zenon_H2cc zenon_H182). % 30.13/30.27 (* end of lemma zenon_L1127_ *) % 30.13/30.27 assert (zenon_L1128_ : (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H2d zenon_H16a zenon_H25c zenon_H246 zenon_H218 zenon_H200 zenon_H20 zenon_H92 zenon_H135 zenon_H1b1 zenon_H6b zenon_H156 zenon_H1d2 zenon_H108 zenon_Hd6 zenon_H1c7 zenon_H1ca zenon_H1d5 zenon_Hf6 zenon_He4 zenon_H1a5 zenon_Hc0 zenon_H25b zenon_He7 zenon_H100 zenon_H14b zenon_H8d zenon_H85 zenon_Had zenon_H174 zenon_Hfc zenon_H1bd zenon_Ha4 zenon_Hbd zenon_H296 zenon_Hf9 zenon_H1dc zenon_H231 zenon_H1a8 zenon_H1a2 zenon_Hd9 zenon_H2b1 zenon_H2c1 zenon_H110 zenon_H225 zenon_H74 zenon_H18c zenon_H19e zenon_H37 zenon_H1af zenon_H222 zenon_H5e zenon_Hc8 zenon_H88 zenon_H208 zenon_H2d9 zenon_H3f zenon_H3c zenon_H35 zenon_H159 zenon_H101 zenon_Hcd zenon_H173 zenon_H23b zenon_Hee zenon_Hb8 zenon_H1d8 zenon_H10d zenon_H6f zenon_Hd1 zenon_H20e zenon_H124 zenon_H2cc zenon_H172 zenon_He1 zenon_H27 zenon_Hcc zenon_H60 zenon_H185 zenon_Hde. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.27 exact (zenon_H74 zenon_H73). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.27 exact (zenon_H74 zenon_H73). % 30.13/30.27 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.27 apply (zenon_L937_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.27 apply (zenon_L552_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.27 exact (zenon_H85 zenon_H89). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.27 apply (zenon_L1002_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.27 exact (zenon_H85 zenon_H89). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.27 apply (zenon_L1052_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.27 apply (zenon_L1125_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.27 apply (zenon_L364_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.27 apply (zenon_L1127_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.27 apply (zenon_L16_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.27 apply (zenon_L125_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.27 apply (zenon_L1111_); trivial. % 30.13/30.27 exact (zenon_H2cc zenon_H182). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.27 apply (zenon_L364_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.27 apply (zenon_L1125_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.27 apply (zenon_L59_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.27 apply (zenon_L1127_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.27 apply (zenon_L1124_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.27 apply (zenon_L125_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.27 apply (zenon_L1122_); trivial. % 30.13/30.27 apply (zenon_L718_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.27 apply (zenon_L125_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.27 apply (zenon_L1083_); trivial. % 30.13/30.27 exact (zenon_H2cc zenon_H182). % 30.13/30.27 apply (zenon_L886_); trivial. % 30.13/30.27 apply (zenon_L50_); trivial. % 30.13/30.27 apply (zenon_L848_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.27 apply (zenon_L554_); trivial. % 30.13/30.27 apply (zenon_L817_); trivial. % 30.13/30.27 (* end of lemma zenon_L1128_ *) % 30.13/30.27 assert (zenon_L1129_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H225 zenon_H74 zenon_H2d zenon_H8d zenon_H85 zenon_H10d zenon_H37 zenon_H100 zenon_Had zenon_Hb8 zenon_H1af zenon_H19e zenon_H2cc zenon_H20 zenon_H2b1 zenon_H6f zenon_H6c zenon_Hf9 zenon_He1 zenon_H3f zenon_H1dc zenon_H231 zenon_H35 zenon_H174 zenon_H27 zenon_Hcc zenon_H60 zenon_H185 zenon_Hde. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.27 exact (zenon_H74 zenon_H73). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.27 exact (zenon_H85 zenon_H89). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.27 apply (zenon_L1002_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.27 exact (zenon_H85 zenon_H89). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.27 apply (zenon_L1052_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.27 apply (zenon_L157_); trivial. % 30.13/30.27 apply (zenon_L568_); trivial. % 30.13/30.27 apply (zenon_L848_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.27 apply (zenon_L554_); trivial. % 30.13/30.27 apply (zenon_L817_); trivial. % 30.13/30.27 (* end of lemma zenon_L1129_ *) % 30.13/30.27 assert (zenon_L1130_ : (((op (e3) (op (e3) (e0))) = (e0))/\(((op (e3) (op (e3) (e1))) = (e1))/\(((op (e3) (op (e3) (e2))) = (e2))/\(((op (e3) (op (e3) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0)))/\(((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1)))/\(((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3)))))))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e1) (e1)) = (e3)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H270 zenon_H2cc zenon_H37. % 30.13/30.27 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.13/30.27 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.13/30.27 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.13/30.27 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.13/30.27 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.13/30.27 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H103 | zenon_intro zenon_H182 ]. % 30.13/30.27 exact (zenon_H103 zenon_H37). % 30.13/30.27 exact (zenon_H2cc zenon_H182). % 30.13/30.27 (* end of lemma zenon_L1130_ *) % 30.13/30.27 assert (zenon_L1131_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H182 zenon_Hd2 zenon_H159. % 30.13/30.27 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H183 | zenon_intro zenon_H150 ]. % 30.13/30.27 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e1)) = (op (e1) (e3)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H159. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H183. % 30.13/30.27 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.13/30.27 cut (((op (e1) (e3)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e0]. % 30.13/30.27 congruence. % 30.13/30.27 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e1)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H2e0. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H182. % 30.13/30.27 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 30.13/30.27 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 30.13/30.27 congruence. % 30.13/30.27 apply zenon_H150. apply refl_equal. % 30.13/30.27 apply zenon_Hd3. apply sym_equal. exact zenon_Hd2. % 30.13/30.27 apply zenon_H150. apply refl_equal. % 30.13/30.27 apply zenon_H150. apply refl_equal. % 30.13/30.27 (* end of lemma zenon_L1131_ *) % 30.13/30.27 assert (zenon_L1132_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H218 zenon_H188 zenon_H2c zenon_H1e5. % 30.13/30.27 cut (((op (e0) (op (e0) (e1))) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H218. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H188. % 30.13/30.27 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 30.13/30.27 cut (((op (e0) (op (e0) (e1))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 30.13/30.27 congruence. % 30.13/30.27 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H16e ]. % 30.13/30.27 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (op (e0) (e1))) = (op (e0) (e3)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H193. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H194. % 30.13/30.27 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.13/30.27 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 30.13/30.27 congruence. % 30.13/30.27 apply (zenon_L123_); trivial. % 30.13/30.27 apply zenon_H16e. apply refl_equal. % 30.13/30.27 apply zenon_H16e. apply refl_equal. % 30.13/30.27 apply zenon_H205. apply sym_equal. exact zenon_H1e5. % 30.13/30.27 (* end of lemma zenon_L1132_ *) % 30.13/30.27 assert (zenon_L1133_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e3)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H2b1 zenon_H20 zenon_H185 zenon_H159 zenon_Hd2 zenon_H218 zenon_Ha4 zenon_H188 zenon_H2c. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.13/30.27 apply (zenon_L117_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.13/30.27 apply (zenon_L1131_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.13/30.27 apply (zenon_L1132_); trivial. % 30.13/30.27 apply (zenon_L124_); trivial. % 30.13/30.27 (* end of lemma zenon_L1133_ *) % 30.13/30.27 assert (zenon_L1134_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H3f zenon_H2d6 zenon_H88 zenon_H95. % 30.13/30.27 cut (((op (e0) (op (e0) (e0))) = (e0)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H3f. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H2d6. % 30.13/30.27 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 30.13/30.27 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e1]. % 30.13/30.27 congruence. % 30.13/30.27 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 30.13/30.27 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (op (e0) (e0))) = (op (e0) (e1)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H2e1. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H3a. % 30.13/30.27 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 30.13/30.27 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2e2]. % 30.13/30.27 congruence. % 30.13/30.27 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2a3]. % 30.13/30.27 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.13/30.27 congruence. % 30.13/30.27 apply zenon_H1d. apply refl_equal. % 30.13/30.27 apply zenon_H2a3. apply sym_equal. exact zenon_H88. % 30.13/30.27 apply zenon_H3b. apply refl_equal. % 30.13/30.27 apply zenon_H3b. apply refl_equal. % 30.13/30.27 apply zenon_H96. apply sym_equal. exact zenon_H95. % 30.13/30.27 (* end of lemma zenon_L1134_ *) % 30.13/30.27 assert (zenon_L1135_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H182 zenon_H155 zenon_Hcd. % 30.13/30.27 elim (classic ((e2) = (e2))); [ zenon_intro zenon_Hce | zenon_intro zenon_H57 ]. % 30.13/30.27 cut (((e2) = (e2)) = ((e1) = (e2))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_Hcd. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_Hce. % 30.13/30.27 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 30.13/30.27 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 30.13/30.27 congruence. % 30.13/30.27 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_Hcf. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H182. % 30.13/30.27 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.13/30.27 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2e3]. % 30.13/30.27 congruence. % 30.13/30.27 exact (zenon_H2e3 zenon_H155). % 30.13/30.27 apply zenon_H22. apply refl_equal. % 30.13/30.27 apply zenon_H57. apply refl_equal. % 30.13/30.27 apply zenon_H57. apply refl_equal. % 30.13/30.27 (* end of lemma zenon_L1135_ *) % 30.13/30.27 assert (zenon_L1136_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H2b1 zenon_H20 zenon_H185 zenon_Hcd zenon_H155 zenon_H2c zenon_H188 zenon_H218 zenon_H9c zenon_H1b9. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.13/30.27 apply (zenon_L117_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.13/30.27 apply (zenon_L1135_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.13/30.27 apply (zenon_L1132_); trivial. % 30.13/30.27 apply (zenon_L198_); trivial. % 30.13/30.27 (* end of lemma zenon_L1136_ *) % 30.13/30.27 assert (zenon_L1137_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hc9 zenon_H1ba zenon_H19a zenon_Hbd zenon_H8a zenon_H2d zenon_H88 zenon_H2d6 zenon_H3f zenon_H1b9 zenon_H218 zenon_H188 zenon_H2c zenon_Hcd zenon_H20 zenon_H2b1 zenon_Ha4 zenon_H185. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.27 apply (zenon_L142_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.27 apply (zenon_L777_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.27 apply (zenon_L159_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.13/30.27 apply (zenon_L25_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.13/30.27 apply (zenon_L1134_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.13/30.27 apply (zenon_L1136_); trivial. % 30.13/30.27 apply (zenon_L869_); trivial. % 30.13/30.27 (* end of lemma zenon_L1137_ *) % 30.13/30.27 assert (zenon_L1138_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H25 zenon_H1b9 zenon_H6f. % 30.13/30.27 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 30.13/30.27 cut (((e3) = (e3)) = ((e1) = (e3))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H6f. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H2e. % 30.13/30.27 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.13/30.27 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 30.13/30.27 congruence. % 30.13/30.27 cut (((op (e2) (e2)) = (e1)) = ((e3) = (e1))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H70. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H25. % 30.13/30.27 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.13/30.27 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 30.13/30.27 congruence. % 30.13/30.27 exact (zenon_H1db zenon_H1b9). % 30.13/30.27 apply zenon_H22. apply refl_equal. % 30.13/30.27 apply zenon_H2f. apply refl_equal. % 30.13/30.27 apply zenon_H2f. apply refl_equal. % 30.13/30.27 (* end of lemma zenon_L1138_ *) % 30.13/30.27 assert (zenon_L1139_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e3)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H208 zenon_H88 zenon_Hc8 zenon_H55 zenon_Hcd zenon_H6f zenon_H1b9 zenon_H218 zenon_H188 zenon_H2c. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.27 apply (zenon_L809_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.27 apply (zenon_L212_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.27 apply (zenon_L1138_); trivial. % 30.13/30.27 apply (zenon_L1132_); trivial. % 30.13/30.27 (* end of lemma zenon_L1139_ *) % 30.13/30.27 assert (zenon_L1140_ : (~((op (e0) (e2)) = (op (e0) (op (e0) (e3))))) -> ((op (e0) (e3)) = (e2)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H2e4 zenon_H17b. % 30.13/30.27 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 30.13/30.27 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.13/30.27 congruence. % 30.13/30.27 apply zenon_H1d. apply refl_equal. % 30.13/30.27 apply zenon_H223. apply sym_equal. exact zenon_H17b. % 30.13/30.27 (* end of lemma zenon_L1140_ *) % 30.13/30.27 assert (zenon_L1141_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H27 zenon_H36 zenon_H17b zenon_H1b9. % 30.13/30.27 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H27. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H36. % 30.13/30.27 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 30.13/30.27 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e5]. % 30.13/30.27 congruence. % 30.13/30.27 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H10f ]. % 30.13/30.27 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e2)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H2e5. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H211. % 30.13/30.27 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.13/30.27 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2e4]. % 30.13/30.27 congruence. % 30.13/30.27 apply (zenon_L1140_); trivial. % 30.13/30.27 apply zenon_H10f. apply refl_equal. % 30.13/30.27 apply zenon_H10f. apply refl_equal. % 30.13/30.27 apply zenon_H1de. apply sym_equal. exact zenon_H1b9. % 30.13/30.27 (* end of lemma zenon_L1141_ *) % 30.13/30.27 assert (zenon_L1142_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 30.13/30.27 do 0 intro. intros zenon_Ha4 zenon_H36 zenon_H16b zenon_Hbc. % 30.13/30.27 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_Ha4. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H36. % 30.13/30.27 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 30.13/30.27 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d3]. % 30.13/30.27 congruence. % 30.13/30.27 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H16e ]. % 30.13/30.27 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e3)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H2d3. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H194. % 30.13/30.27 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.13/30.27 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2d2]. % 30.13/30.27 congruence. % 30.13/30.27 apply (zenon_L1037_); trivial. % 30.13/30.27 apply zenon_H16e. apply refl_equal. % 30.13/30.27 apply zenon_H16e. apply refl_equal. % 30.13/30.27 apply zenon_H17e. apply sym_equal. exact zenon_Hbc. % 30.13/30.27 (* end of lemma zenon_L1142_ *) % 30.13/30.27 assert (zenon_L1143_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H2bd zenon_H6e zenon_H15a zenon_H16a zenon_H182 zenon_H1b9 zenon_H27 zenon_Ha4 zenon_H36 zenon_Hbc. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H185 | zenon_intro zenon_H2be ]. % 30.13/30.27 apply (zenon_L1000_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H33 | zenon_intro zenon_H2bf ]. % 30.13/30.27 apply (zenon_L115_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H17b | zenon_intro zenon_H16b ]. % 30.13/30.27 apply (zenon_L1141_); trivial. % 30.13/30.27 apply (zenon_L1142_); trivial. % 30.13/30.27 (* end of lemma zenon_L1143_ *) % 30.13/30.27 assert (zenon_L1144_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.13/30.27 do 0 intro. intros zenon_Hb8 zenon_Had zenon_H3f zenon_H2c zenon_H1dc zenon_H2bd zenon_H6e zenon_H15a zenon_H16a zenon_H182 zenon_H1b9 zenon_H27 zenon_Ha4 zenon_H36. % 30.13/30.27 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.13/30.27 apply (zenon_L34_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.13/30.27 apply (zenon_L746_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.13/30.27 apply (zenon_L200_); trivial. % 30.13/30.27 apply (zenon_L1143_); trivial. % 30.13/30.27 (* end of lemma zenon_L1144_ *) % 30.13/30.27 assert (zenon_L1145_ : ((op (e2) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H1b9 zenon_H15e zenon_H20e. % 30.13/30.27 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 30.13/30.27 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H20e. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H28. % 30.13/30.27 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 30.13/30.27 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 30.13/30.27 congruence. % 30.13/30.27 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 30.13/30.27 intro zenon_D_pnotp. % 30.13/30.27 apply zenon_H20f. % 30.13/30.27 rewrite <- zenon_D_pnotp. % 30.13/30.27 exact zenon_H1b9. % 30.13/30.27 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 30.13/30.27 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 30.13/30.27 congruence. % 30.13/30.27 apply zenon_H29. apply refl_equal. % 30.13/30.27 apply zenon_H1fb. apply sym_equal. exact zenon_H15e. % 30.13/30.27 apply zenon_H29. apply refl_equal. % 30.13/30.27 apply zenon_H29. apply refl_equal. % 30.13/30.27 (* end of lemma zenon_L1145_ *) % 30.13/30.27 assert (zenon_L1146_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.13/30.27 do 0 intro. intros zenon_H16f zenon_H36 zenon_Ha4 zenon_H27 zenon_H16a zenon_H15a zenon_H2bd zenon_H1dc zenon_H3f zenon_Had zenon_Hb8 zenon_H35 zenon_H2c zenon_H20e zenon_H1b9 zenon_H182 zenon_H6f. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.13/30.27 apply (zenon_L1144_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.13/30.27 apply (zenon_L1002_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.13/30.27 apply (zenon_L1145_); trivial. % 30.13/30.27 apply (zenon_L758_); trivial. % 30.13/30.27 (* end of lemma zenon_L1146_ *) % 30.13/30.27 assert (zenon_L1147_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e1)) -> False). % 30.13/30.27 do 0 intro. intros zenon_H296 zenon_H19f zenon_H6f zenon_H1b9 zenon_H20e zenon_H2c zenon_H35 zenon_Hb8 zenon_Had zenon_H1dc zenon_H2bd zenon_H15a zenon_H16a zenon_H27 zenon_Ha4 zenon_H36 zenon_H16f zenon_H135 zenon_H185 zenon_H2b1 zenon_H20 zenon_H2d zenon_H8a zenon_Hbd zenon_H18c zenon_H173 zenon_H188 zenon_H218 zenon_Hcd zenon_Hc8 zenon_H208 zenon_He1 zenon_H2e6 zenon_H159 zenon_Hdc zenon_H1a8 zenon_H3f zenon_H2d6 zenon_H88. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.27 apply (zenon_L4_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.27 exact (zenon_H19f zenon_Hc3). % 30.13/30.27 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.27 apply (zenon_L48_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.27 apply (zenon_L1133_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.27 apply (zenon_L1137_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.27 apply (zenon_L1139_); trivial. % 30.13/30.27 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.27 apply (zenon_L544_); trivial. % 30.13/30.27 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.27 apply (zenon_L1146_); trivial. % 30.13/30.27 apply (zenon_L1134_); trivial. % 30.13/30.27 (* end of lemma zenon_L1147_ *) % 30.13/30.27 assert (zenon_L1148_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H174 zenon_H88 zenon_H2d6 zenon_H3f zenon_H1a8 zenon_Hdc zenon_H159 zenon_H2e6 zenon_He1 zenon_H208 zenon_Hc8 zenon_Hcd zenon_H218 zenon_H188 zenon_H173 zenon_H18c zenon_Hbd zenon_H20 zenon_H2b1 zenon_H135 zenon_H16f zenon_H36 zenon_Ha4 zenon_H16a zenon_H15a zenon_H2bd zenon_H1dc zenon_Had zenon_Hb8 zenon_H35 zenon_H20e zenon_H6f zenon_H19f zenon_H296 zenon_H85 zenon_H8d zenon_H27 zenon_H1b9 zenon_H185 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.28 apply (zenon_L1000_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.28 apply (zenon_L1001_); trivial. % 30.13/30.28 apply (zenon_L1147_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L160_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 (* end of lemma zenon_L1148_ *) % 30.13/30.28 assert (zenon_L1149_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H1b9 zenon_H76 zenon_H6b. % 30.13/30.28 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ]. % 30.13/30.28 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H6b. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H28. % 30.13/30.28 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 30.13/30.28 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 30.13/30.28 congruence. % 30.13/30.28 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H1ec. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H1b9. % 30.13/30.28 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 30.13/30.28 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 30.13/30.28 congruence. % 30.13/30.28 apply zenon_H29. apply refl_equal. % 30.13/30.28 apply zenon_H1da. apply sym_equal. exact zenon_H76. % 30.13/30.28 apply zenon_H29. apply refl_equal. % 30.13/30.28 apply zenon_H29. apply refl_equal. % 30.13/30.28 (* end of lemma zenon_L1149_ *) % 30.13/30.28 assert (zenon_L1150_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H8d zenon_H85 zenon_H6f zenon_H68 zenon_H6b zenon_H1b9 zenon_H2d zenon_H8b. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.28 apply (zenon_L18_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.28 apply (zenon_L1149_); trivial. % 30.13/30.28 apply (zenon_L25_); trivial. % 30.13/30.28 (* end of lemma zenon_L1150_ *) % 30.13/30.28 assert (zenon_L1151_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H246 zenon_H1b3 zenon_H20 zenon_Hc9 zenon_Hde zenon_H8d zenon_H85 zenon_H6f zenon_H68 zenon_H6b zenon_H1b9 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.13/30.28 exact (zenon_H1b3 zenon_H64). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.13/30.28 apply (zenon_L16_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.13/30.28 apply (zenon_L49_); trivial. % 30.13/30.28 apply (zenon_L1150_); trivial. % 30.13/30.28 (* end of lemma zenon_L1151_ *) % 30.13/30.28 assert (zenon_L1152_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H208 zenon_H73 zenon_H2e6 zenon_He1 zenon_Hcd zenon_H246 zenon_H1b3 zenon_H20 zenon_Hde zenon_H8d zenon_H85 zenon_H68 zenon_H6b zenon_H2d zenon_H135 zenon_H6f zenon_H1b9 zenon_H218 zenon_H188 zenon_H2c. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.28 apply (zenon_L244_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.28 apply (zenon_L1151_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.28 apply (zenon_L212_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.28 apply (zenon_L544_); trivial. % 30.13/30.28 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.28 apply (zenon_L1138_); trivial. % 30.13/30.28 apply (zenon_L1132_); trivial. % 30.13/30.28 (* end of lemma zenon_L1152_ *) % 30.13/30.28 assert (zenon_L1153_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H8d zenon_H85 zenon_H6f zenon_H68 zenon_H6b zenon_H1b9 zenon_He1 zenon_He2. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.28 apply (zenon_L18_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.28 apply (zenon_L1149_); trivial. % 30.13/30.28 apply (zenon_L50_); trivial. % 30.13/30.28 (* end of lemma zenon_L1153_ *) % 30.13/30.28 assert (zenon_L1154_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_He4 zenon_H2d zenon_H185 zenon_H27 zenon_H208 zenon_H2e6 zenon_H246 zenon_H1b3 zenon_H20 zenon_H135 zenon_H218 zenon_H188 zenon_H174 zenon_Hcd zenon_Hdf zenon_Hde zenon_H8d zenon_H85 zenon_H6f zenon_H68 zenon_H6b zenon_H1b9 zenon_He1. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_L1152_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L160_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.28 apply (zenon_L48_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.28 apply (zenon_L49_); trivial. % 30.13/30.28 apply (zenon_L1153_); trivial. % 30.13/30.28 (* end of lemma zenon_L1154_ *) % 30.13/30.28 assert (zenon_L1155_ : (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_He1 zenon_H1b9 zenon_H6b zenon_H68 zenon_H6f zenon_H85 zenon_H8d zenon_Hde zenon_Hcd zenon_H174 zenon_H188 zenon_H218 zenon_H135 zenon_H20 zenon_H1b3 zenon_H246 zenon_H2e6 zenon_H208 zenon_H27 zenon_H185 zenon_He4 zenon_H2d zenon_H8a. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.13/30.28 exact (zenon_H1b3 zenon_H64). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.13/30.28 apply (zenon_L16_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.13/30.28 apply (zenon_L1154_); trivial. % 30.13/30.28 apply (zenon_L25_); trivial. % 30.13/30.28 (* end of lemma zenon_L1155_ *) % 30.13/30.28 assert (zenon_L1156_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e1)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H296 zenon_H19f zenon_H6f zenon_H1b9 zenon_H20e zenon_H2c zenon_H35 zenon_Hb8 zenon_Had zenon_H1dc zenon_H2bd zenon_H15a zenon_H16a zenon_H27 zenon_Ha4 zenon_H36 zenon_H16f zenon_H173 zenon_H18c zenon_Hc9 zenon_Hbd zenon_H8a zenon_H2d zenon_H218 zenon_H188 zenon_Hcd zenon_H20 zenon_H2b1 zenon_H185 zenon_H159 zenon_He1 zenon_H6b zenon_H85 zenon_H8d zenon_Hde zenon_H174 zenon_H135 zenon_H1b3 zenon_H246 zenon_H2e6 zenon_H208 zenon_He4 zenon_H1a8 zenon_H3f zenon_H2d6 zenon_H88. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.28 apply (zenon_L4_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.28 exact (zenon_H19f zenon_Hc3). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.28 apply (zenon_L1155_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.28 apply (zenon_L1133_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.28 apply (zenon_L1137_); trivial. % 30.13/30.28 apply (zenon_L1146_); trivial. % 30.13/30.28 apply (zenon_L1134_); trivial. % 30.13/30.28 (* end of lemma zenon_L1156_ *) % 30.13/30.28 assert (zenon_L1157_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H267 zenon_H1b9 zenon_H36 zenon_H27 zenon_H16a zenon_H2e6 zenon_Ha4 zenon_H198 zenon_H117. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.13/30.28 apply (zenon_L1141_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.13/30.28 apply (zenon_L1004_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.13/30.28 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.28 apply (zenon_L1006_); trivial. % 30.13/30.28 (* end of lemma zenon_L1157_ *) % 30.13/30.28 assert (zenon_L1158_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H88 zenon_H2d6 zenon_H3f zenon_H1a8 zenon_He4 zenon_H208 zenon_H246 zenon_H1b3 zenon_H135 zenon_H174 zenon_Hde zenon_H8d zenon_H85 zenon_H6b zenon_He1 zenon_H159 zenon_H2b1 zenon_H20 zenon_Hcd zenon_H188 zenon_H218 zenon_Hbd zenon_Hc9 zenon_H18c zenon_H173 zenon_H16f zenon_H15a zenon_H2bd zenon_H1dc zenon_Had zenon_Hb8 zenon_H35 zenon_H20e zenon_H6f zenon_H19f zenon_H296 zenon_H198 zenon_Ha4 zenon_H2e6 zenon_H16a zenon_H27 zenon_H36 zenon_H1b9 zenon_H267 zenon_H185 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.28 apply (zenon_L1000_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.28 apply (zenon_L1149_); trivial. % 30.13/30.28 apply (zenon_L1156_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L1157_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 (* end of lemma zenon_L1158_ *) % 30.13/30.28 assert (zenon_L1159_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H3f zenon_H188 zenon_H1f zenon_H98. % 30.13/30.28 cut (((op (e0) (op (e0) (e1))) = (e1)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H3f. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H188. % 30.13/30.28 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 30.13/30.28 cut (((op (e0) (op (e0) (e1))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 30.13/30.28 congruence. % 30.13/30.28 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 30.13/30.28 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (op (e0) (e1))) = (op (e0) (e1)))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H2d1. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H3a. % 30.13/30.28 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 30.13/30.28 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2d0]. % 30.13/30.28 congruence. % 30.13/30.28 apply (zenon_L1034_); trivial. % 30.13/30.28 apply zenon_H3b. apply refl_equal. % 30.13/30.28 apply zenon_H3b. apply refl_equal. % 30.13/30.28 apply zenon_H99. apply sym_equal. exact zenon_H98. % 30.13/30.28 (* end of lemma zenon_L1159_ *) % 30.13/30.28 assert (zenon_L1160_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H23b zenon_H8a zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Ha4 zenon_H188 zenon_H2c. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.28 apply (zenon_L39_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.28 apply (zenon_L1159_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.28 apply (zenon_L337_); trivial. % 30.13/30.28 apply (zenon_L124_); trivial. % 30.13/30.28 (* end of lemma zenon_L1160_ *) % 30.13/30.28 assert (zenon_L1161_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H1a8 zenon_H6c zenon_H18c zenon_H218 zenon_H159 zenon_H185 zenon_H20 zenon_H2b1 zenon_H188 zenon_Hee zenon_H1f zenon_H8a zenon_H23b zenon_H16f zenon_H36 zenon_Ha4 zenon_H27 zenon_H16a zenon_H15a zenon_H2bd zenon_H1dc zenon_H3f zenon_Had zenon_Hb8 zenon_H35 zenon_H2c zenon_H20e zenon_H1b9 zenon_H6f. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.28 apply (zenon_L120_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.28 apply (zenon_L1133_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.28 apply (zenon_L1160_); trivial. % 30.13/30.28 apply (zenon_L1146_); trivial. % 30.13/30.28 (* end of lemma zenon_L1161_ *) % 30.13/30.28 assert (zenon_L1162_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H174 zenon_H85 zenon_H6f zenon_H20e zenon_H35 zenon_Hb8 zenon_Had zenon_H3f zenon_H1dc zenon_H2bd zenon_H15a zenon_H16f zenon_H23b zenon_H8a zenon_H1f zenon_Hee zenon_H188 zenon_H2b1 zenon_H20 zenon_H159 zenon_H218 zenon_H18c zenon_H6c zenon_H1a8 zenon_H198 zenon_Ha4 zenon_H2e6 zenon_H16a zenon_H27 zenon_H36 zenon_H1b9 zenon_H267 zenon_H185 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_L1161_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L1157_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 (* end of lemma zenon_L1162_ *) % 30.13/30.28 assert (zenon_L1163_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H8d zenon_H174 zenon_H85 zenon_H6f zenon_H20e zenon_H35 zenon_Hb8 zenon_Had zenon_H3f zenon_H1dc zenon_H2bd zenon_H15a zenon_H16f zenon_H23b zenon_H1f zenon_Hee zenon_H188 zenon_H2b1 zenon_H20 zenon_H159 zenon_H218 zenon_H18c zenon_H6c zenon_H1a8 zenon_H198 zenon_Ha4 zenon_H2e6 zenon_H16a zenon_H27 zenon_H36 zenon_H1b9 zenon_H267 zenon_H185 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.28 apply (zenon_L1000_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.28 apply (zenon_L157_); trivial. % 30.13/30.28 apply (zenon_L1162_); trivial. % 30.13/30.28 (* end of lemma zenon_L1163_ *) % 30.13/30.28 assert (zenon_L1164_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H174 zenon_H85 zenon_H1b9 zenon_H20e zenon_H35 zenon_Hb8 zenon_Had zenon_H3f zenon_H1dc zenon_H2bd zenon_H15a zenon_H16a zenon_H27 zenon_Ha4 zenon_H36 zenon_H16f zenon_H1a5 zenon_H2b1 zenon_H20 zenon_H159 zenon_H218 zenon_H188 zenon_H18c zenon_H6c zenon_H1a8 zenon_H6f zenon_H26 zenon_H185 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.28 apply (zenon_L120_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.28 apply (zenon_L1133_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.28 apply (zenon_L136_); trivial. % 30.13/30.28 apply (zenon_L1146_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L598_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 (* end of lemma zenon_L1164_ *) % 30.13/30.28 assert (zenon_L1165_ : (((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)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H92 zenon_Hd9 zenon_H69 zenon_H2d zenon_H26 zenon_H1a8 zenon_H18c zenon_H188 zenon_H218 zenon_H159 zenon_H20 zenon_H2b1 zenon_H1a5 zenon_H16f zenon_Ha4 zenon_H27 zenon_H16a zenon_H2bd zenon_H1dc zenon_H3f zenon_Had zenon_Hb8 zenon_H35 zenon_H20e zenon_H1b9 zenon_H174 zenon_H8d zenon_H85 zenon_H15a zenon_H185 zenon_H36 zenon_Hc8 zenon_H6f. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.28 apply (zenon_L797_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.28 apply (zenon_L16_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.28 apply (zenon_L1164_); trivial. % 30.13/30.28 apply (zenon_L1046_); trivial. % 30.13/30.28 (* end of lemma zenon_L1165_ *) % 30.13/30.28 assert (zenon_L1166_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H92 zenon_Hd9 zenon_H6b zenon_H8d zenon_H2d zenon_H185 zenon_H26 zenon_H6f zenon_H1a8 zenon_H18c zenon_H188 zenon_H218 zenon_H159 zenon_H2b1 zenon_H1a5 zenon_H16f zenon_H36 zenon_Ha4 zenon_H27 zenon_H16a zenon_H15a zenon_H2bd zenon_H1dc zenon_H3f zenon_Had zenon_Hb8 zenon_H35 zenon_H20e zenon_H1b9 zenon_H85 zenon_H174 zenon_H8b zenon_H20. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.28 apply (zenon_L797_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.28 apply (zenon_L1150_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.28 apply (zenon_L1164_); trivial. % 30.13/30.28 apply (zenon_L27_); trivial. % 30.13/30.28 (* end of lemma zenon_L1166_ *) % 30.13/30.28 assert (zenon_L1167_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.13/30.28 do 0 intro. intros zenon_Hc8 zenon_Hc0 zenon_H296 zenon_H19f zenon_H173 zenon_Hbd zenon_Hcd zenon_He1 zenon_H135 zenon_H208 zenon_He4 zenon_H2d6 zenon_H23b zenon_Hee zenon_H198 zenon_H2e6 zenon_H267 zenon_H246 zenon_H1b3 zenon_Hc9 zenon_Hde zenon_H65 zenon_H174 zenon_H85 zenon_H1b9 zenon_H20e zenon_H35 zenon_Hb8 zenon_Had zenon_H3f zenon_H1dc zenon_H2bd zenon_H15a zenon_H16a zenon_H27 zenon_Ha4 zenon_H36 zenon_H16f zenon_H1a5 zenon_H2b1 zenon_H159 zenon_H218 zenon_H188 zenon_H18c zenon_H1a8 zenon_H6f zenon_H2d zenon_H8d zenon_H6b zenon_Hd9 zenon_H92 zenon_H185 zenon_H20. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.13/30.28 exact (zenon_H1b3 zenon_H64). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.28 apply (zenon_L1158_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.28 apply (zenon_L1158_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.28 apply (zenon_L1151_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.28 apply (zenon_L1163_); trivial. % 30.13/30.28 apply (zenon_L1046_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.28 apply (zenon_L1165_); trivial. % 30.13/30.28 apply (zenon_L117_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.13/30.28 apply (zenon_L49_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.28 apply (zenon_L1158_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.28 apply (zenon_L1035_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.28 apply (zenon_L1151_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.28 apply (zenon_L1163_); trivial. % 30.13/30.28 apply (zenon_L27_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.28 apply (zenon_L1166_); trivial. % 30.13/30.28 apply (zenon_L117_); trivial. % 30.13/30.28 (* end of lemma zenon_L1167_ *) % 30.13/30.28 assert (zenon_L1168_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H8d zenon_H85 zenon_H185 zenon_H36 zenon_H15a zenon_H6b zenon_H1b9 zenon_He1 zenon_He2. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.28 apply (zenon_L1000_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.28 apply (zenon_L1149_); trivial. % 30.13/30.28 apply (zenon_L50_); trivial. % 30.13/30.28 (* end of lemma zenon_L1168_ *) % 30.13/30.28 assert (zenon_L1169_ : ((op (e0) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H88 zenon_H20 zenon_H92 zenon_Hd9 zenon_H2d zenon_H6f zenon_H1a8 zenon_H18c zenon_H188 zenon_H218 zenon_H159 zenon_H2b1 zenon_H1a5 zenon_H16f zenon_Ha4 zenon_H27 zenon_H16a zenon_H2bd zenon_H1dc zenon_H3f zenon_Had zenon_Hb8 zenon_H35 zenon_H20e zenon_H174 zenon_H65 zenon_Hde zenon_H1b3 zenon_H246 zenon_H267 zenon_H2e6 zenon_H198 zenon_Hee zenon_H23b zenon_H2d6 zenon_He4 zenon_H208 zenon_H135 zenon_Hcd zenon_Hbd zenon_H173 zenon_H19f zenon_H296 zenon_Hc0 zenon_Hc8 zenon_H8d zenon_H85 zenon_H185 zenon_H36 zenon_H15a zenon_H6b zenon_H1b9 zenon_He1. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.28 apply (zenon_L998_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.28 apply (zenon_L1148_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.28 apply (zenon_L1167_); trivial. % 30.13/30.28 apply (zenon_L1168_); trivial. % 30.13/30.28 (* end of lemma zenon_L1169_ *) % 30.13/30.28 assert (zenon_L1170_ : (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_He1 zenon_Hde zenon_Hcd zenon_H174 zenon_H188 zenon_H218 zenon_H135 zenon_H20 zenon_H1b3 zenon_H246 zenon_H2e6 zenon_H208 zenon_H27 zenon_H185 zenon_He4 zenon_H8d zenon_H85 zenon_H6f zenon_H68 zenon_H6b zenon_H1b9 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.13/30.28 exact (zenon_H1b3 zenon_H64). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.13/30.28 apply (zenon_L16_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.13/30.28 apply (zenon_L1154_); trivial. % 30.13/30.28 apply (zenon_L1150_); trivial. % 30.13/30.28 (* end of lemma zenon_L1170_ *) % 30.13/30.28 assert (zenon_L1171_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H92 zenon_H65 zenon_H6b zenon_He4 zenon_H208 zenon_H246 zenon_H1b3 zenon_H135 zenon_Hcd zenon_Hde zenon_He1 zenon_H2d zenon_H267 zenon_H1b9 zenon_H27 zenon_H16a zenon_H2e6 zenon_Ha4 zenon_H198 zenon_H1a8 zenon_H18c zenon_H218 zenon_H159 zenon_H20 zenon_H2b1 zenon_H188 zenon_Hee zenon_H1f zenon_H23b zenon_H16f zenon_H2bd zenon_H1dc zenon_H3f zenon_Had zenon_Hb8 zenon_H35 zenon_H20e zenon_H174 zenon_H8d zenon_H85 zenon_H15a zenon_H185 zenon_H36 zenon_Hc8 zenon_H6f. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.28 apply (zenon_L1035_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.28 apply (zenon_L1170_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.28 apply (zenon_L1163_); trivial. % 30.13/30.28 apply (zenon_L1046_); trivial. % 30.13/30.28 (* end of lemma zenon_L1171_ *) % 30.13/30.28 assert (zenon_L1172_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H135 zenon_He2 zenon_H1d8 zenon_H3c zenon_He9 zenon_H1b9 zenon_He1 zenon_H2e6. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.28 apply (zenon_L307_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.28 apply (zenon_L88_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.28 apply (zenon_L544_); trivial. % 30.13/30.28 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.28 (* end of lemma zenon_L1172_ *) % 30.13/30.28 assert (zenon_L1173_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e1)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H296 zenon_H19f zenon_H6f zenon_H1b9 zenon_H20e zenon_H2c zenon_H35 zenon_Hb8 zenon_Had zenon_H1dc zenon_H2bd zenon_H15a zenon_H16a zenon_H27 zenon_Ha4 zenon_H36 zenon_H16f zenon_H101 zenon_H138 zenon_Hda zenon_H198 zenon_Hc8 zenon_H208 zenon_H135 zenon_H185 zenon_H2b1 zenon_H20 zenon_Hcd zenon_H188 zenon_H218 zenon_H2d zenon_H8a zenon_Hbd zenon_H18c zenon_H173 zenon_H222 zenon_He1 zenon_H2e6 zenon_H159 zenon_Hdc zenon_H1a8 zenon_H3f zenon_H2d6 zenon_H88. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.28 apply (zenon_L4_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.28 exact (zenon_H19f zenon_Hc3). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.28 apply (zenon_L48_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.28 apply (zenon_L1133_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.28 apply (zenon_L1041_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.28 apply (zenon_L777_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.28 apply (zenon_L1139_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.28 apply (zenon_L1137_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.28 apply (zenon_L264_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.28 apply (zenon_L544_); trivial. % 30.13/30.28 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.28 apply (zenon_L1146_); trivial. % 30.13/30.28 apply (zenon_L1134_); trivial. % 30.13/30.28 (* end of lemma zenon_L1173_ *) % 30.13/30.28 assert (zenon_L1174_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H174 zenon_H88 zenon_H2d6 zenon_H3f zenon_H1a8 zenon_Hdc zenon_H159 zenon_He1 zenon_H222 zenon_H173 zenon_H18c zenon_Hbd zenon_H218 zenon_H188 zenon_Hcd zenon_H20 zenon_H2b1 zenon_H135 zenon_H208 zenon_Hc8 zenon_Hda zenon_H138 zenon_H101 zenon_H16f zenon_H15a zenon_H2bd zenon_H1dc zenon_Had zenon_Hb8 zenon_H35 zenon_H20e zenon_H6f zenon_H19f zenon_H296 zenon_H6b zenon_H85 zenon_H8d zenon_H198 zenon_Ha4 zenon_H2e6 zenon_H16a zenon_H27 zenon_H36 zenon_H1b9 zenon_H267 zenon_H185 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.28 apply (zenon_L1000_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.28 apply (zenon_L1149_); trivial. % 30.13/30.28 apply (zenon_L1173_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L1157_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 (* end of lemma zenon_L1174_ *) % 30.13/30.28 assert (zenon_L1175_ : ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((e3) = (op (op (e1) (e1)) (e1)))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H2c zenon_Hc3 zenon_H13d. % 30.13/30.28 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 30.13/30.28 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e3) = (op (op (e1) (e1)) (e1)))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H13d. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H13e. % 30.13/30.28 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 30.13/30.28 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 30.13/30.28 congruence. % 30.13/30.28 cut (((op (e0) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H140. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H2c. % 30.13/30.28 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.13/30.28 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 30.13/30.28 congruence. % 30.13/30.28 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 30.13/30.28 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H240. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H13e. % 30.13/30.28 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 30.13/30.28 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23f]. % 30.13/30.28 congruence. % 30.13/30.28 apply (zenon_L380_); trivial. % 30.13/30.28 apply zenon_H13f. apply refl_equal. % 30.13/30.28 apply zenon_H13f. apply refl_equal. % 30.13/30.28 apply zenon_H2f. apply refl_equal. % 30.13/30.28 apply zenon_H13f. apply refl_equal. % 30.13/30.28 apply zenon_H13f. apply refl_equal. % 30.13/30.28 (* end of lemma zenon_L1175_ *) % 30.13/30.28 assert (zenon_L1176_ : ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H73 zenon_H2c zenon_Hc3. % 30.13/30.28 apply (zenon_notand_s _ _ ax15); [ zenon_intro zenon_H250 | zenon_intro zenon_H2e7 ]. % 30.13/30.28 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 30.13/30.28 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e2) = (op (op (e1) (e1)) (op (e1) (e1))))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H250. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H145. % 30.13/30.28 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 30.13/30.28 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H251]. % 30.13/30.28 congruence. % 30.13/30.28 cut (((op (e0) (e0)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H251. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H73. % 30.13/30.28 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 30.13/30.28 cut (((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H244]. % 30.13/30.28 congruence. % 30.13/30.28 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 30.13/30.28 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H244. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H145. % 30.13/30.28 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 30.13/30.28 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 30.13/30.28 congruence. % 30.13/30.28 apply (zenon_L379_); trivial. % 30.13/30.28 apply zenon_H146. apply refl_equal. % 30.13/30.28 apply zenon_H146. apply refl_equal. % 30.13/30.28 apply zenon_H57. apply refl_equal. % 30.13/30.28 apply zenon_H146. apply refl_equal. % 30.13/30.28 apply zenon_H146. apply refl_equal. % 30.13/30.28 apply (zenon_notand_s _ _ zenon_H2e7); [ zenon_intro zenon_H13d | zenon_intro zenon_H245 ]. % 30.13/30.28 apply (zenon_L1175_); trivial. % 30.13/30.28 apply zenon_H245. apply sym_equal. exact zenon_Hc3. % 30.13/30.28 (* end of lemma zenon_L1176_ *) % 30.13/30.28 assert (zenon_L1177_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e2)) = (e2)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H1b1 zenon_H4c zenon_Hfe zenon_Hed. % 30.13/30.28 cut (((op (e1) (op (e1) (e2))) = (e2)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H1b1. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H4c. % 30.13/30.28 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 30.13/30.28 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H282]. % 30.13/30.28 congruence. % 30.13/30.28 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H280 | zenon_intro zenon_Hd4 ]. % 30.13/30.28 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e1) (op (e1) (e2))) = (op (e1) (e0)))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H282. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H280. % 30.13/30.28 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 30.13/30.28 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H281]. % 30.13/30.28 congruence. % 30.13/30.28 apply (zenon_L741_); trivial. % 30.13/30.28 apply zenon_Hd4. apply refl_equal. % 30.13/30.28 apply zenon_Hd4. apply refl_equal. % 30.13/30.28 apply zenon_Hf2. apply sym_equal. exact zenon_Hed. % 30.13/30.28 (* end of lemma zenon_L1177_ *) % 30.13/30.28 assert (zenon_L1178_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H174 zenon_H4e zenon_Had zenon_H173 zenon_Hcd zenon_H68 zenon_H2e6 zenon_He1 zenon_H19e zenon_Hc8 zenon_H73 zenon_H135 zenon_H4c zenon_H1b1 zenon_H20e zenon_H20 zenon_H172 zenon_H6b zenon_H6f zenon_H85 zenon_H8d zenon_H27 zenon_H1b9 zenon_H185 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.28 apply (zenon_L18_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.28 apply (zenon_L1149_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.28 apply (zenon_L16_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.28 apply (zenon_L1176_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.28 apply (zenon_L48_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.28 apply (zenon_L43_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.28 apply (zenon_L787_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.28 apply (zenon_L544_); trivial. % 30.13/30.28 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.28 apply (zenon_L1177_); trivial. % 30.13/30.28 apply (zenon_L829_); trivial. % 30.13/30.28 apply (zenon_L913_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L160_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 (* end of lemma zenon_L1178_ *) % 30.13/30.28 assert (zenon_L1179_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H135 zenon_Hfe zenon_H4c zenon_H18c zenon_H3c zenon_He9 zenon_H1b9 zenon_He1 zenon_H2e6. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.28 apply (zenon_L784_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.28 apply (zenon_L88_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.28 apply (zenon_L544_); trivial. % 30.13/30.28 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.28 (* end of lemma zenon_L1179_ *) % 30.13/30.28 assert (zenon_L1180_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_He4 zenon_H2d zenon_H185 zenon_H27 zenon_H172 zenon_H20 zenon_H2e6 zenon_He9 zenon_H3c zenon_H18c zenon_H4c zenon_H135 zenon_Had zenon_H4e zenon_H174 zenon_Hcd zenon_Hdf zenon_Hde zenon_H8d zenon_H85 zenon_H6f zenon_H68 zenon_H6b zenon_H1b9 zenon_He1. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.28 apply (zenon_L18_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.28 apply (zenon_L1149_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.28 apply (zenon_L16_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.28 apply (zenon_L1176_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.28 apply (zenon_L1179_); trivial. % 30.13/30.28 apply (zenon_L913_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L160_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.28 apply (zenon_L48_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.28 apply (zenon_L49_); trivial. % 30.13/30.28 apply (zenon_L1153_); trivial. % 30.13/30.28 (* end of lemma zenon_L1180_ *) % 30.13/30.28 assert (zenon_L1181_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_He4 zenon_Hda zenon_Hd9 zenon_Hcd zenon_Hdf zenon_Hde zenon_H8d zenon_H85 zenon_H6f zenon_H68 zenon_H6b zenon_H1b9 zenon_He1. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.28 apply (zenon_L47_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.28 apply (zenon_L48_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.28 apply (zenon_L49_); trivial. % 30.13/30.28 apply (zenon_L1153_); trivial. % 30.13/30.28 (* end of lemma zenon_L1181_ *) % 30.13/30.28 assert (zenon_L1182_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H225 zenon_H20e zenon_H1b1 zenon_Hc8 zenon_H19e zenon_H173 zenon_H174 zenon_H4e zenon_Had zenon_H135 zenon_H4c zenon_H18c zenon_H3c zenon_H2e6 zenon_H20 zenon_H172 zenon_H27 zenon_H2d zenon_He1 zenon_H1b9 zenon_H6b zenon_H68 zenon_H6f zenon_H85 zenon_H8d zenon_Hdf zenon_Hcd zenon_Hd9 zenon_He4 zenon_H185 zenon_Hde. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.28 apply (zenon_L1178_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.28 apply (zenon_L1180_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.28 apply (zenon_L1181_); trivial. % 30.13/30.28 apply (zenon_L817_); trivial. % 30.13/30.28 (* end of lemma zenon_L1182_ *) % 30.13/30.28 assert (zenon_L1183_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hc9 zenon_H1ba zenon_Hcd zenon_H19a zenon_H20e zenon_H4e zenon_H1b9. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.28 apply (zenon_L142_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.28 apply (zenon_L777_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.28 apply (zenon_L159_); trivial. % 30.13/30.28 apply (zenon_L829_); trivial. % 30.13/30.28 (* end of lemma zenon_L1183_ *) % 30.13/30.28 assert (zenon_L1184_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H100 zenon_H4c zenon_H19a zenon_H9d. % 30.13/30.28 cut (((op (e1) (op (e1) (e2))) = (e2)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H100. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_H4c. % 30.13/30.28 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 30.13/30.28 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ab]. % 30.13/30.28 congruence. % 30.13/30.28 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.13/30.28 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e2))) = (op (e1) (e1)))). % 30.13/30.28 intro zenon_D_pnotp. % 30.13/30.28 apply zenon_H2ab. % 30.13/30.28 rewrite <- zenon_D_pnotp. % 30.13/30.28 exact zenon_Hc4. % 30.13/30.28 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.13/30.28 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2aa]. % 30.13/30.28 congruence. % 30.13/30.28 apply (zenon_L823_); trivial. % 30.13/30.28 apply zenon_Hc5. apply refl_equal. % 30.13/30.28 apply zenon_Hc5. apply refl_equal. % 30.13/30.28 apply zenon_H9e. apply sym_equal. exact zenon_H9d. % 30.13/30.28 (* end of lemma zenon_L1184_ *) % 30.13/30.28 assert (zenon_L1185_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H267 zenon_Hde zenon_H20e zenon_H2e6 zenon_Hb8 zenon_Had zenon_H6e zenon_H95 zenon_H2d zenon_H1dc zenon_H1b9 zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.13/30.28 apply (zenon_L817_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.13/30.28 apply (zenon_L829_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.13/30.28 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.28 apply (zenon_L888_); trivial. % 30.13/30.28 (* end of lemma zenon_L1185_ *) % 30.13/30.28 assert (zenon_L1186_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H296 zenon_H6c zenon_H4a zenon_H101 zenon_He1 zenon_H3c zenon_H173 zenon_H18c zenon_Hcd zenon_H135 zenon_H19e zenon_H100 zenon_H4c zenon_H18f zenon_H6f zenon_H1a8 zenon_H267 zenon_Hde zenon_H20e zenon_H2e6 zenon_Hb8 zenon_Had zenon_H6e zenon_H2d zenon_H1dc zenon_H1b9 zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.28 apply (zenon_L4_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.28 apply (zenon_L763_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.28 apply (zenon_L18_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.28 exact (zenon_H18f zenon_Hd2). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.28 apply (zenon_L1183_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.28 apply (zenon_L88_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.28 apply (zenon_L544_); trivial. % 30.13/30.28 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.28 apply (zenon_L777_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.28 apply (zenon_L824_); trivial. % 30.13/30.28 apply (zenon_L1184_); trivial. % 30.13/30.28 apply (zenon_L730_); trivial. % 30.13/30.28 apply (zenon_L1185_); trivial. % 30.13/30.28 (* end of lemma zenon_L1186_ *) % 30.13/30.28 assert (zenon_L1187_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H23b zenon_H8a zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.28 apply (zenon_L39_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.28 apply (zenon_L336_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.28 apply (zenon_L337_); trivial. % 30.13/30.28 exact (zenon_H1ab zenon_H112). % 30.13/30.28 (* end of lemma zenon_L1187_ *) % 30.13/30.28 assert (zenon_L1188_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H1a8 zenon_H6c zenon_H18c zenon_H18f zenon_H1ab zenon_Hee zenon_H3f zenon_H1f zenon_H6f zenon_H8a zenon_H23b zenon_H4e zenon_H2c zenon_H35. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.28 apply (zenon_L120_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.28 exact (zenon_H18f zenon_Hd2). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.28 apply (zenon_L1187_); trivial. % 30.13/30.28 apply (zenon_L730_); trivial. % 30.13/30.28 (* end of lemma zenon_L1188_ *) % 30.13/30.28 assert (zenon_L1189_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H174 zenon_H85 zenon_H3f zenon_H40 zenon_H27 zenon_H1b9 zenon_H185 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_L746_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L160_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 (* end of lemma zenon_L1189_ *) % 30.13/30.28 assert (zenon_L1190_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_Hb8 zenon_H90 zenon_H6f zenon_H1b9 zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H9c zenon_H2d zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_Hf4 zenon_H14e zenon_H4e. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.13/30.28 apply (zenon_L39_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.13/30.28 apply (zenon_L1189_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.13/30.28 apply (zenon_L304_); trivial. % 30.13/30.28 apply (zenon_L887_); trivial. % 30.13/30.28 (* end of lemma zenon_L1190_ *) % 30.13/30.28 assert (zenon_L1191_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H267 zenon_Hde zenon_H20e zenon_H2e6 zenon_Hb8 zenon_H90 zenon_H6f zenon_H1b9 zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H9c zenon_H2d zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.13/30.28 apply (zenon_L817_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.13/30.28 apply (zenon_L829_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.13/30.28 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.28 apply (zenon_L1190_); trivial. % 30.13/30.28 (* end of lemma zenon_L1191_ *) % 30.13/30.28 assert (zenon_L1192_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_Hbd zenon_H69 zenon_H1dc zenon_Had zenon_H4e zenon_H2c zenon_H35 zenon_H16a zenon_H185 zenon_H256 zenon_H2d zenon_H174 zenon_H85 zenon_H3f zenon_H27 zenon_H1b9 zenon_H6f zenon_H90 zenon_Hb8 zenon_H2e6 zenon_H20e zenon_Hde zenon_H267 zenon_H14e zenon_H48 zenon_H6e. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.13/30.28 apply (zenon_L749_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.13/30.28 apply (zenon_L1185_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.13/30.28 apply (zenon_L1191_); trivial. % 30.13/30.28 apply (zenon_L770_); trivial. % 30.13/30.28 (* end of lemma zenon_L1192_ *) % 30.13/30.28 assert (zenon_L1193_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H174 zenon_H85 zenon_H1e zenon_H27 zenon_H1b9 zenon_H185 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_L4_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L160_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 (* end of lemma zenon_L1193_ *) % 30.13/30.28 assert (zenon_L1194_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H8d zenon_H185 zenon_H16a zenon_H18c zenon_H4c zenon_Had zenon_H4a zenon_Hbd zenon_H1dc zenon_H4e zenon_H2c zenon_H35 zenon_H256 zenon_H2d zenon_H174 zenon_H85 zenon_H3f zenon_H27 zenon_H1b9 zenon_Hb8 zenon_H2e6 zenon_H20e zenon_Hde zenon_H267 zenon_H14e zenon_H48 zenon_H172 zenon_He1 zenon_Hc9 zenon_H6f zenon_H90. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.28 apply (zenon_L1192_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.28 apply (zenon_L769_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.28 apply (zenon_L784_); trivial. % 30.13/30.28 apply (zenon_L886_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.28 apply (zenon_L273_); trivial. % 30.13/30.28 apply (zenon_L39_); trivial. % 30.13/30.28 (* end of lemma zenon_L1194_ *) % 30.13/30.28 assert (zenon_L1195_ : (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.28 do 0 intro. intros zenon_H2e6 zenon_He1 zenon_He9 zenon_H3c zenon_H8d zenon_H16a zenon_H18c zenon_H4c zenon_Had zenon_H4a zenon_Hbd zenon_H1dc zenon_H4e zenon_H35 zenon_H256 zenon_H174 zenon_H85 zenon_H3f zenon_Hb8 zenon_H20e zenon_Hde zenon_H267 zenon_H14e zenon_H48 zenon_H172 zenon_H6f zenon_H90 zenon_H135 zenon_H27 zenon_H1b9 zenon_H185 zenon_H2d. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.28 exact (zenon_H85 zenon_H89). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.28 apply (zenon_L1194_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.28 apply (zenon_L88_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.28 apply (zenon_L544_); trivial. % 30.13/30.28 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.28 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.28 apply (zenon_L160_); trivial. % 30.13/30.28 apply (zenon_L848_); trivial. % 30.13/30.28 (* end of lemma zenon_L1195_ *) % 30.13/30.28 assert (zenon_L1196_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H101 zenon_H2d zenon_H185 zenon_H27 zenon_H135 zenon_H90 zenon_H6f zenon_H172 zenon_H48 zenon_H14e zenon_H267 zenon_Hde zenon_H20e zenon_Hb8 zenon_H3f zenon_H85 zenon_H174 zenon_H256 zenon_H35 zenon_H4e zenon_H1dc zenon_Hbd zenon_H4a zenon_Had zenon_H18c zenon_H16a zenon_H8d zenon_H3c zenon_He1 zenon_H2e6 zenon_H1ba zenon_H1b9 zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.28 apply (zenon_L1195_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.28 apply (zenon_L777_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.28 apply (zenon_L824_); trivial. % 30.13/30.28 apply (zenon_L1184_); trivial. % 30.13/30.28 (* end of lemma zenon_L1196_ *) % 30.13/30.28 assert (zenon_L1197_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.28 do 0 intro. intros zenon_H296 zenon_Hfe zenon_Hfc zenon_Hd1 zenon_H101 zenon_H27 zenon_H135 zenon_H90 zenon_H6f zenon_H172 zenon_H48 zenon_H3f zenon_H85 zenon_H174 zenon_Hbd zenon_H4a zenon_H18c zenon_H8d zenon_H3c zenon_He1 zenon_H19e zenon_H100 zenon_H4c zenon_H18f zenon_H1a8 zenon_H267 zenon_Hde zenon_H20e zenon_H2e6 zenon_Hb8 zenon_Had zenon_H6e zenon_H2d zenon_H1dc zenon_H1b9 zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.28 apply (zenon_L1193_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.28 apply (zenon_L59_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.28 apply (zenon_L18_); trivial. % 30.13/30.28 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.29 exact (zenon_H18f zenon_Hd2). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.29 apply (zenon_L1196_); trivial. % 30.13/30.29 apply (zenon_L729_); trivial. % 30.13/30.29 apply (zenon_L1185_); trivial. % 30.13/30.29 (* end of lemma zenon_L1197_ *) % 30.13/30.29 assert (zenon_L1198_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H1a8 zenon_H69 zenon_H20 zenon_H18f zenon_H1ab zenon_Hee zenon_H3f zenon_H1f zenon_H6f zenon_H8a zenon_H23b zenon_H4e zenon_H2c zenon_H35. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.29 apply (zenon_L16_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.29 exact (zenon_H18f zenon_Hd2). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.29 apply (zenon_L1187_); trivial. % 30.13/30.29 apply (zenon_L730_); trivial. % 30.13/30.29 (* end of lemma zenon_L1198_ *) % 30.13/30.29 assert (zenon_L1199_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H8d zenon_H48 zenon_H14e zenon_H267 zenon_Hde zenon_H20e zenon_H2e6 zenon_Hb8 zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H2d zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H4e zenon_Had zenon_H1dc zenon_H69 zenon_Hbd zenon_H6b zenon_H1b9 zenon_H6f zenon_H90. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.29 apply (zenon_L1192_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.29 apply (zenon_L1149_); trivial. % 30.13/30.29 apply (zenon_L39_); trivial. % 30.13/30.29 (* end of lemma zenon_L1199_ *) % 30.13/30.29 assert (zenon_L1200_ : ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H90 zenon_H6f zenon_H6b zenon_Hbd zenon_H69 zenon_H1dc zenon_Had zenon_H4e zenon_H35 zenon_H16a zenon_H256 zenon_H174 zenon_H85 zenon_H3f zenon_Hb8 zenon_H2e6 zenon_H20e zenon_Hde zenon_H267 zenon_H14e zenon_H48 zenon_H8d zenon_H27 zenon_H1b9 zenon_H185 zenon_H2d. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.29 apply (zenon_L1199_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.29 apply (zenon_L160_); trivial. % 30.13/30.29 apply (zenon_L848_); trivial. % 30.13/30.29 (* end of lemma zenon_L1200_ *) % 30.13/30.29 assert (zenon_L1201_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H1a8 zenon_H6c zenon_H18c zenon_H18f zenon_H1a5 zenon_H26 zenon_H4e zenon_H2c zenon_H35. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.29 apply (zenon_L120_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.29 exact (zenon_H18f zenon_Hd2). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.29 apply (zenon_L136_); trivial. % 30.13/30.29 apply (zenon_L730_); trivial. % 30.13/30.29 (* end of lemma zenon_L1201_ *) % 30.13/30.29 assert (zenon_L1202_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H174 zenon_H85 zenon_H35 zenon_H4e zenon_H26 zenon_H1a5 zenon_H18f zenon_H18c zenon_H6c zenon_H1a8 zenon_H27 zenon_H1b9 zenon_H185 zenon_H2d. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.29 apply (zenon_L1201_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.29 apply (zenon_L160_); trivial. % 30.13/30.29 apply (zenon_L848_); trivial. % 30.13/30.29 (* end of lemma zenon_L1202_ *) % 30.13/30.29 assert (zenon_L1203_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H8d zenon_H85 zenon_Hd1 zenon_H4e zenon_H26 zenon_H1a5 zenon_H18f zenon_H1a8 zenon_H6b zenon_H1b9 zenon_H6f zenon_H90. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.29 apply (zenon_L834_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.29 apply (zenon_L1149_); trivial. % 30.13/30.29 apply (zenon_L39_); trivial. % 30.13/30.29 (* end of lemma zenon_L1203_ *) % 30.13/30.29 assert (zenon_L1204_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H92 zenon_H84 zenon_H69 zenon_H20 zenon_H2d zenon_H185 zenon_H27 zenon_H18c zenon_H35 zenon_H174 zenon_H8d zenon_H85 zenon_Hd1 zenon_H4e zenon_H26 zenon_H1a5 zenon_H18f zenon_H1a8 zenon_H6b zenon_H1b9 zenon_H6f. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.29 exact (zenon_H84 zenon_H88). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.29 apply (zenon_L16_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.29 apply (zenon_L1202_); trivial. % 30.13/30.29 apply (zenon_L1203_); trivial. % 30.13/30.29 (* end of lemma zenon_L1204_ *) % 30.13/30.29 assert (zenon_L1205_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hc0 zenon_H48 zenon_H14e zenon_H267 zenon_Hde zenon_H20e zenon_H2e6 zenon_Hb8 zenon_H3f zenon_H256 zenon_H16a zenon_Had zenon_H1dc zenon_Hbd zenon_H23b zenon_Hee zenon_H1ab zenon_H296 zenon_H4a zenon_H101 zenon_He1 zenon_H3c zenon_H173 zenon_Hcd zenon_H135 zenon_H19e zenon_H100 zenon_H4c zenon_H6f zenon_H1b9 zenon_H6b zenon_H1a8 zenon_H18f zenon_H1a5 zenon_H4e zenon_Hd1 zenon_H85 zenon_H8d zenon_H174 zenon_H35 zenon_H18c zenon_H27 zenon_H2d zenon_H69 zenon_H84 zenon_H92 zenon_H185 zenon_H20. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.29 exact (zenon_H84 zenon_H88). % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.29 exact (zenon_H84 zenon_H88). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.29 apply (zenon_L16_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.29 apply (zenon_L1186_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.29 apply (zenon_L1149_); trivial. % 30.13/30.29 apply (zenon_L1198_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.29 apply (zenon_L160_); trivial. % 30.13/30.29 apply (zenon_L848_); trivial. % 30.13/30.29 apply (zenon_L1200_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.29 apply (zenon_L1204_); trivial. % 30.13/30.29 apply (zenon_L117_); trivial. % 30.13/30.29 (* end of lemma zenon_L1205_ *) % 30.13/30.29 assert (zenon_L1206_ : (~((op (e1) (e2)) = (op (e1) (op (e1) (e2))))) -> ((op (e1) (e2)) = (e2)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H2e8 zenon_Hed. % 30.13/30.29 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 30.13/30.29 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.13/30.29 congruence. % 30.13/30.29 apply zenon_H22. apply refl_equal. % 30.13/30.29 apply zenon_Hf2. apply sym_equal. exact zenon_Hed. % 30.13/30.29 (* end of lemma zenon_L1206_ *) % 30.13/30.29 assert (zenon_L1207_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hee zenon_H4c zenon_Hed zenon_Heb. % 30.13/30.29 cut (((op (e1) (op (e1) (e2))) = (e2)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 30.13/30.29 intro zenon_D_pnotp. % 30.13/30.29 apply zenon_Hee. % 30.13/30.29 rewrite <- zenon_D_pnotp. % 30.13/30.29 exact zenon_H4c. % 30.13/30.29 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 30.13/30.29 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e9]. % 30.13/30.29 congruence. % 30.13/30.29 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 30.13/30.29 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (op (e1) (e2))) = (op (e1) (e2)))). % 30.13/30.29 intro zenon_D_pnotp. % 30.13/30.29 apply zenon_H2e9. % 30.13/30.29 rewrite <- zenon_D_pnotp. % 30.13/30.29 exact zenon_H19b. % 30.13/30.29 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 30.13/30.29 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2e8]. % 30.13/30.29 congruence. % 30.13/30.29 apply (zenon_L1206_); trivial. % 30.13/30.29 apply zenon_H19c. apply refl_equal. % 30.13/30.29 apply zenon_H19c. apply refl_equal. % 30.13/30.29 apply zenon_Hec. apply sym_equal. exact zenon_Heb. % 30.13/30.29 (* end of lemma zenon_L1207_ *) % 30.13/30.29 assert (zenon_L1208_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H2b7 zenon_H142 zenon_H1dc zenon_H26 zenon_H10d zenon_Hed zenon_H4c zenon_Hee zenon_H8a zenon_Hb5. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.13/30.29 apply (zenon_L177_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.13/30.29 apply (zenon_L699_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.13/30.29 apply (zenon_L1207_); trivial. % 30.13/30.29 apply (zenon_L461_); trivial. % 30.13/30.29 (* end of lemma zenon_L1208_ *) % 30.13/30.29 assert (zenon_L1209_ : (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hde zenon_H73 zenon_H64. % 30.13/30.29 cut (((op (e0) (e0)) = (e2)) = ((e0) = (e2))). % 30.13/30.29 intro zenon_D_pnotp. % 30.13/30.29 apply zenon_Hde. % 30.13/30.29 rewrite <- zenon_D_pnotp. % 30.13/30.29 exact zenon_H73. % 30.13/30.29 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 30.13/30.29 cut (((op (e0) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1b3]. % 30.13/30.29 congruence. % 30.13/30.29 exact (zenon_H1b3 zenon_H64). % 30.13/30.29 apply zenon_H57. apply refl_equal. % 30.13/30.29 (* end of lemma zenon_L1209_ *) % 30.13/30.29 assert (zenon_L1210_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H173 zenon_Hcd zenon_H68 zenon_H1a5 zenon_H26 zenon_H4a zenon_Hfe zenon_H4c zenon_H1b1 zenon_H20e zenon_H4e zenon_H1b9. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.29 apply (zenon_L48_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.29 apply (zenon_L748_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.29 apply (zenon_L1177_); trivial. % 30.13/30.29 apply (zenon_L829_); trivial. % 30.13/30.29 (* end of lemma zenon_L1210_ *) % 30.13/30.29 assert (zenon_L1211_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H6c zenon_H4a zenon_H2e6 zenon_He1 zenon_H1b9 zenon_He9 zenon_H3c zenon_H18c zenon_H4c zenon_H135 zenon_H16a zenon_H185. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.29 apply (zenon_L740_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.29 apply (zenon_L763_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.29 apply (zenon_L1179_); trivial. % 30.13/30.29 apply (zenon_L886_); trivial. % 30.13/30.29 (* end of lemma zenon_L1211_ *) % 30.13/30.29 assert (zenon_L1212_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H1a8 zenon_H6c zenon_H18c zenon_H18f zenon_H55 zenon_H4c zenon_H19e zenon_H4e zenon_H2c zenon_H35. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.29 apply (zenon_L120_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.29 exact (zenon_H18f zenon_Hd2). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.29 apply (zenon_L824_); trivial. % 30.13/30.29 apply (zenon_L730_); trivial. % 30.13/30.29 (* end of lemma zenon_L1212_ *) % 30.13/30.29 assert (zenon_L1213_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H6c zenon_H4a zenon_H18c zenon_He2 zenon_H4c zenon_Had zenon_H16a zenon_H185. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.29 apply (zenon_L740_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.29 apply (zenon_L763_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.29 apply (zenon_L742_); trivial. % 30.13/30.29 apply (zenon_L886_); trivial. % 30.13/30.29 (* end of lemma zenon_L1213_ *) % 30.13/30.29 assert (zenon_L1214_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H23b zenon_H20 zenon_H8b zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.29 apply (zenon_L27_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.29 apply (zenon_L336_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.29 apply (zenon_L337_); trivial. % 30.13/30.29 exact (zenon_H1ab zenon_H112). % 30.13/30.29 (* end of lemma zenon_L1214_ *) % 30.13/30.29 assert (zenon_L1215_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hc0 zenon_H84 zenon_H1ab zenon_Hee zenon_H3f zenon_H8b zenon_H23b zenon_H1a5 zenon_H19a zenon_H185 zenon_H20. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.29 exact (zenon_H84 zenon_H88). % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.29 apply (zenon_L1214_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.29 apply (zenon_L136_); trivial. % 30.13/30.29 apply (zenon_L117_); trivial. % 30.13/30.29 (* end of lemma zenon_L1215_ *) % 30.13/30.29 assert (zenon_L1216_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H92 zenon_H1b9 zenon_H6b zenon_H2d zenon_H6f zenon_H1a8 zenon_H18f zenon_H185 zenon_H1a5 zenon_H23b zenon_H3f zenon_Hee zenon_H1ab zenon_H84 zenon_Hc0 zenon_H4e zenon_Hd1 zenon_H85 zenon_H8d zenon_H8b zenon_H20. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.29 exact (zenon_H84 zenon_H88). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.29 apply (zenon_L1150_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.13/30.29 apply (zenon_L18_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.13/30.29 exact (zenon_H18f zenon_Hd2). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.13/30.29 apply (zenon_L1215_); trivial. % 30.13/30.29 apply (zenon_L729_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.29 apply (zenon_L157_); trivial. % 30.13/30.29 apply (zenon_L25_); trivial. % 30.13/30.29 apply (zenon_L27_); trivial. % 30.13/30.29 (* end of lemma zenon_L1216_ *) % 30.13/30.29 assert (zenon_L1217_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hc0 zenon_H84 zenon_H35 zenon_H1ab zenon_H10d zenon_H100 zenon_H4a zenon_Hd2 zenon_H6f zenon_H8a zenon_H23b zenon_H185 zenon_H20. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.29 exact (zenon_H84 zenon_H88). % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.29 apply (zenon_L868_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.29 apply (zenon_L892_); trivial. % 30.13/30.29 apply (zenon_L117_); trivial. % 30.13/30.29 (* end of lemma zenon_L1217_ *) % 30.13/30.29 assert (zenon_L1218_ : (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H20 zenon_H23b zenon_H6f zenon_Hd2 zenon_H4a zenon_H100 zenon_H10d zenon_H1ab zenon_H35 zenon_H84 zenon_Hc0 zenon_Hc9 zenon_He1 zenon_Hbd zenon_H69 zenon_H1dc zenon_Had zenon_H4e zenon_H16a zenon_H256 zenon_H174 zenon_H85 zenon_H3f zenon_H90 zenon_Hb8 zenon_H2e6 zenon_H20e zenon_Hde zenon_H267 zenon_H14e zenon_H48 zenon_H8d zenon_H27 zenon_H1b9 zenon_H185 zenon_H2d. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.29 apply (zenon_L1192_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.29 apply (zenon_L273_); trivial. % 30.13/30.29 apply (zenon_L1217_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.29 apply (zenon_L160_); trivial. % 30.13/30.29 apply (zenon_L848_); trivial. % 30.13/30.29 (* end of lemma zenon_L1218_ *) % 30.13/30.29 assert (zenon_L1219_ : (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H2d zenon_H185 zenon_H1b9 zenon_H27 zenon_H8d zenon_H48 zenon_H14e zenon_H267 zenon_Hde zenon_H20e zenon_H2e6 zenon_Hb8 zenon_H3f zenon_H85 zenon_H174 zenon_H256 zenon_H16a zenon_H4e zenon_Had zenon_H1dc zenon_H69 zenon_Hbd zenon_He1 zenon_Hc9 zenon_Hc0 zenon_H84 zenon_H35 zenon_H6f zenon_H23b zenon_H20 zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.29 apply (zenon_L1218_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.29 apply (zenon_L880_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.29 apply (zenon_L699_); trivial. % 30.13/30.29 exact (zenon_H1ab zenon_H112). % 30.13/30.29 (* end of lemma zenon_L1219_ *) % 30.13/30.29 assert (zenon_L1220_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hc0 zenon_H84 zenon_H35 zenon_H1ab zenon_H10d zenon_H100 zenon_H4a zenon_Hd2 zenon_H8b zenon_H23b zenon_H185 zenon_H20. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.29 exact (zenon_H84 zenon_H88). % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.29 apply (zenon_L868_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.29 apply (zenon_L881_); trivial. % 30.13/30.29 apply (zenon_L117_); trivial. % 30.13/30.29 (* end of lemma zenon_L1220_ *) % 30.13/30.29 assert (zenon_L1221_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hf9 zenon_Hfe zenon_H4c zenon_H55 zenon_H222 zenon_Hda zenon_H10d zenon_Hb8 zenon_Had zenon_H6e zenon_H95 zenon_H2d zenon_H1dc zenon_H1b9 zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.13/30.29 apply (zenon_L742_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.13/30.29 apply (zenon_L264_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.13/30.29 apply (zenon_L64_); trivial. % 30.13/30.29 apply (zenon_L888_); trivial. % 30.13/30.29 (* end of lemma zenon_L1221_ *) % 30.13/30.29 assert (zenon_L1222_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_H55 zenon_H222 zenon_Hda zenon_H10d zenon_Hb8 zenon_H90 zenon_H6f zenon_H1b9 zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H9c zenon_H2d zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.13/30.29 apply (zenon_L386_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.13/30.29 apply (zenon_L264_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.13/30.29 apply (zenon_L64_); trivial. % 30.13/30.29 apply (zenon_L1190_); trivial. % 30.13/30.29 (* end of lemma zenon_L1222_ *) % 30.13/30.29 assert (zenon_L1223_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H23b zenon_H4e zenon_H14e zenon_H2c zenon_H35 zenon_H16a zenon_H185 zenon_H256 zenon_H2d zenon_H9c zenon_H174 zenon_H85 zenon_H3f zenon_H27 zenon_H1b9 zenon_H6f zenon_Hb8 zenon_Hda zenon_H222 zenon_H55 zenon_Hcd zenon_Hf9 zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.29 apply (zenon_L1222_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.29 apply (zenon_L880_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.29 apply (zenon_L699_); trivial. % 30.13/30.29 exact (zenon_H1ab zenon_H112). % 30.13/30.29 (* end of lemma zenon_L1223_ *) % 30.13/30.29 assert (zenon_L1224_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (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) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H84 zenon_Hc0 zenon_H1dc zenon_H6e zenon_Had zenon_H4c zenon_Hfe zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H4a zenon_Hd2 zenon_Hf9 zenon_Hcd zenon_H55 zenon_H222 zenon_Hda zenon_Hb8 zenon_H6f zenon_H1b9 zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H2d zenon_H256 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e zenon_H23b zenon_Ha4 zenon_H185. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.13/30.29 apply (zenon_L1220_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.13/30.29 apply (zenon_L1221_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.13/30.29 apply (zenon_L1223_); trivial. % 30.13/30.29 apply (zenon_L869_); trivial. % 30.13/30.29 (* end of lemma zenon_L1224_ *) % 30.13/30.29 assert (zenon_L1225_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H14b zenon_Hde zenon_Ha4 zenon_H4c zenon_Had zenon_H6e zenon_H1dc zenon_Hc0 zenon_H84 zenon_H20 zenon_Hbd zenon_H23b zenon_H4e zenon_H14e zenon_H2c zenon_H35 zenon_H16a zenon_H185 zenon_H256 zenon_H2d zenon_H174 zenon_H85 zenon_H3f zenon_H27 zenon_H1b9 zenon_H6f zenon_Hb8 zenon_Hda zenon_H222 zenon_H55 zenon_Hcd zenon_Hf9 zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.13/30.29 apply (zenon_L192_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.13/30.29 apply (zenon_L1224_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.13/30.29 apply (zenon_L175_); trivial. % 30.13/30.29 apply (zenon_L1223_); trivial. % 30.13/30.29 (* end of lemma zenon_L1225_ *) % 30.13/30.29 assert (zenon_L1226_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H225 zenon_H6c zenon_H3c zenon_H2d zenon_H1b9 zenon_H27 zenon_H8d zenon_Hf9 zenon_Hcd zenon_H55 zenon_H222 zenon_Hb8 zenon_H3f zenon_H85 zenon_H174 zenon_H256 zenon_H16a zenon_H35 zenon_H14e zenon_H4e zenon_Hbd zenon_H20 zenon_H84 zenon_Hc0 zenon_H1dc zenon_Had zenon_H4c zenon_Ha4 zenon_H14b zenon_H6b zenon_H23b zenon_H6f zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab zenon_H185 zenon_Hde. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.29 apply (zenon_L244_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.29 apply (zenon_L88_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.29 apply (zenon_L1225_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.29 apply (zenon_L1149_); trivial. % 30.13/30.29 apply (zenon_L892_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.29 apply (zenon_L160_); trivial. % 30.13/30.29 apply (zenon_L848_); trivial. % 30.13/30.29 apply (zenon_L817_); trivial. % 30.13/30.29 (* end of lemma zenon_L1226_ *) % 30.13/30.29 assert (zenon_L1227_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H135 zenon_H69 zenon_H20e zenon_H267 zenon_H48 zenon_Hde zenon_H185 zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H4a zenon_Hd2 zenon_H6f zenon_H23b zenon_H6b zenon_H14b zenon_Ha4 zenon_H4c zenon_Had zenon_H1dc zenon_Hc0 zenon_H84 zenon_H20 zenon_Hbd zenon_H4e zenon_H14e zenon_H35 zenon_H16a zenon_H256 zenon_H174 zenon_H85 zenon_H3f zenon_Hb8 zenon_H222 zenon_Hcd zenon_Hf9 zenon_H8d zenon_H27 zenon_H2d zenon_H3c zenon_H6c zenon_H225 zenon_H1b9 zenon_He1 zenon_H2e6. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.29 apply (zenon_L1219_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.29 apply (zenon_L1226_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.29 apply (zenon_L544_); trivial. % 30.13/30.29 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.29 (* end of lemma zenon_L1227_ *) % 30.13/30.29 assert (zenon_L1228_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H135 zenon_H69 zenon_H20e zenon_H267 zenon_H48 zenon_H8d zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H4a zenon_Hd2 zenon_Hf9 zenon_Hcd zenon_H222 zenon_Hda zenon_Hb8 zenon_H6f zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H2d zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e zenon_H23b zenon_Hbd zenon_H20 zenon_H84 zenon_Hc0 zenon_H1dc zenon_H6e zenon_Had zenon_H4c zenon_Ha4 zenon_Hde zenon_H14b zenon_H1b9 zenon_He1 zenon_H2e6. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.29 apply (zenon_L1219_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.29 apply (zenon_L1225_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.29 apply (zenon_L544_); trivial. % 30.13/30.29 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.29 (* end of lemma zenon_L1228_ *) % 30.13/30.29 assert (zenon_L1229_ : ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H185 zenon_H16a zenon_H18c zenon_H4c zenon_Hc9 zenon_H135 zenon_H20e zenon_H267 zenon_H48 zenon_H8d zenon_Hf9 zenon_Hcd zenon_H222 zenon_Hda zenon_Hb8 zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H2d zenon_H256 zenon_H35 zenon_H2c zenon_H14e zenon_H4e zenon_Hbd zenon_H20 zenon_H84 zenon_Hc0 zenon_H1dc zenon_Had zenon_Ha4 zenon_Hde zenon_H14b zenon_H1b9 zenon_He1 zenon_H2e6 zenon_H172 zenon_H6c zenon_H23b zenon_H6f zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.29 apply (zenon_L1228_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.29 apply (zenon_L763_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.29 apply (zenon_L784_); trivial. % 30.13/30.29 apply (zenon_L886_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.29 apply (zenon_L157_); trivial. % 30.13/30.29 apply (zenon_L892_); trivial. % 30.13/30.29 (* end of lemma zenon_L1229_ *) % 30.13/30.29 assert (zenon_L1230_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H14b zenon_Hda zenon_Hc9 zenon_H4c zenon_H18c zenon_Hd6 zenon_H1ba zenon_H267 zenon_Hde zenon_H20e zenon_H2e6 zenon_Hb8 zenon_H90 zenon_H6f zenon_H1b9 zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H2d zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.13/30.29 apply (zenon_L192_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.13/30.29 apply (zenon_L784_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.13/30.29 apply (zenon_L161_); trivial. % 30.13/30.29 apply (zenon_L1191_); trivial. % 30.13/30.29 (* end of lemma zenon_L1230_ *) % 30.13/30.29 assert (zenon_L1231_ : ((op (e3) (e0)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H90 zenon_H1b9 zenon_H6b zenon_H296 zenon_H174 zenon_H85 zenon_H3f zenon_H27 zenon_Hd6 zenon_H135 zenon_H18c zenon_H14b zenon_Ha4 zenon_H23b zenon_Hda zenon_H222 zenon_Hcd zenon_Hf9 zenon_Hd2 zenon_H4a zenon_H100 zenon_H10d zenon_H1ab zenon_H4c zenon_Hc0 zenon_H84 zenon_H20 zenon_Hbd zenon_He1 zenon_H267 zenon_Hde zenon_H20e zenon_H2e6 zenon_Hb8 zenon_Had zenon_H1dc zenon_H256 zenon_H16a zenon_H35 zenon_H14e zenon_H4e zenon_H8d zenon_H6f zenon_H26 zenon_H185 zenon_H2d. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.29 apply (zenon_L4_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.29 apply (zenon_L906_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.13/30.29 apply (zenon_L192_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.29 apply (zenon_L1230_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.29 apply (zenon_L1224_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.29 apply (zenon_L544_); trivial. % 30.13/30.29 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.13/30.29 apply (zenon_L161_); trivial. % 30.13/30.29 apply (zenon_L1191_); trivial. % 30.13/30.29 apply (zenon_L1185_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.29 apply (zenon_L1149_); trivial. % 30.13/30.29 apply (zenon_L39_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.29 apply (zenon_L598_); trivial. % 30.13/30.29 apply (zenon_L848_); trivial. % 30.13/30.29 (* end of lemma zenon_L1231_ *) % 30.13/30.29 assert (zenon_L1232_ : ((op (e3) (e0)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H90 zenon_H1b9 zenon_H6b zenon_Hbd zenon_H69 zenon_H1dc zenon_Had zenon_H4e zenon_H35 zenon_H16a zenon_H256 zenon_H174 zenon_H85 zenon_H3f zenon_H27 zenon_Hb8 zenon_H2e6 zenon_H20e zenon_Hde zenon_H267 zenon_H14e zenon_H48 zenon_H8d zenon_H6f zenon_H26 zenon_H185 zenon_H2d. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.29 apply (zenon_L1199_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.29 apply (zenon_L598_); trivial. % 30.13/30.29 apply (zenon_L848_); trivial. % 30.13/30.29 (* end of lemma zenon_L1232_ *) % 30.13/30.29 assert (zenon_L1233_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_H90 zenon_H55 zenon_H222 zenon_Hed zenon_H4c zenon_Hee zenon_Hb8 zenon_Had zenon_H6e zenon_H95 zenon_H2d zenon_H1dc zenon_H1b9 zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.13/30.29 apply (zenon_L386_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.13/30.29 apply (zenon_L264_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.13/30.29 apply (zenon_L1207_); trivial. % 30.13/30.29 apply (zenon_L888_); trivial. % 30.13/30.29 (* end of lemma zenon_L1233_ *) % 30.13/30.29 assert (zenon_L1234_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H173 zenon_H73 zenon_H15a zenon_H55 zenon_H19e zenon_Hfe zenon_H4c zenon_H1b1 zenon_H20e zenon_H4e zenon_H1b9. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.29 apply (zenon_L94_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.29 apply (zenon_L787_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.29 apply (zenon_L1177_); trivial. % 30.13/30.29 apply (zenon_L829_); trivial. % 30.13/30.29 (* end of lemma zenon_L1234_ *) % 30.13/30.29 assert (zenon_L1235_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hf9 zenon_H73 zenon_He7 zenon_H55 zenon_H222 zenon_Hed zenon_H4c zenon_Hee zenon_Hb8 zenon_H90 zenon_H6f zenon_H1b9 zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H9c zenon_H2d zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.13/30.29 apply (zenon_L52_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.13/30.29 apply (zenon_L264_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.13/30.29 apply (zenon_L1207_); trivial. % 30.13/30.29 apply (zenon_L1190_); trivial. % 30.13/30.29 (* end of lemma zenon_L1235_ *) % 30.13/30.29 assert (zenon_L1236_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.13/30.29 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H1dc zenon_Had zenon_H4c zenon_Hfe zenon_H4e zenon_H2c zenon_H35 zenon_H16a zenon_H185 zenon_H256 zenon_H2d zenon_H174 zenon_H85 zenon_H3f zenon_H27 zenon_H1b9 zenon_H6f zenon_H90 zenon_Hb8 zenon_H10d zenon_Hda zenon_H222 zenon_H55 zenon_Hcd zenon_Hf9 zenon_H14e zenon_H48 zenon_H6e. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.13/30.29 apply (zenon_L27_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.13/30.29 apply (zenon_L1221_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.13/30.29 apply (zenon_L1222_); trivial. % 30.13/30.29 apply (zenon_L770_); trivial. % 30.13/30.29 (* end of lemma zenon_L1236_ *) % 30.13/30.29 assert (zenon_L1237_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H14b zenon_Hde zenon_H6e zenon_H48 zenon_H4c zenon_Had zenon_H1dc zenon_H20 zenon_Hbd zenon_Hd6 zenon_H1ba zenon_Hf9 zenon_Hcd zenon_H55 zenon_H222 zenon_Hda zenon_H10d zenon_Hb8 zenon_H90 zenon_H6f zenon_H1b9 zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H2d zenon_H256 zenon_H185 zenon_H16a zenon_H35 zenon_H2c zenon_H14e zenon_H4e. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.13/30.29 apply (zenon_L192_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.13/30.29 apply (zenon_L1236_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.13/30.29 apply (zenon_L161_); trivial. % 30.13/30.29 apply (zenon_L1222_); trivial. % 30.13/30.29 (* end of lemma zenon_L1237_ *) % 30.13/30.29 assert (zenon_L1238_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H14b zenon_Hde zenon_H1dc zenon_H95 zenon_H6e zenon_Had zenon_H4c zenon_H23b zenon_H4e zenon_H14e zenon_H2c zenon_H35 zenon_H16a zenon_H185 zenon_H256 zenon_H2d zenon_H174 zenon_H85 zenon_H3f zenon_H27 zenon_H1b9 zenon_H6f zenon_Hb8 zenon_Hda zenon_H222 zenon_H55 zenon_Hcd zenon_Hf9 zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.13/30.29 apply (zenon_L192_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.13/30.29 apply (zenon_L1221_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.13/30.29 apply (zenon_L175_); trivial. % 30.13/30.29 apply (zenon_L1223_); trivial. % 30.13/30.29 (* end of lemma zenon_L1238_ *) % 30.13/30.29 assert (zenon_L1239_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H92 zenon_Hd1 zenon_Ha4 zenon_Hc0 zenon_H84 zenon_H225 zenon_H20e zenon_Hee zenon_H1a5 zenon_H15a zenon_H173 zenon_He7 zenon_H19e zenon_H1b1 zenon_H3c zenon_H2d zenon_H26 zenon_H6f zenon_H8d zenon_H1ab zenon_H10d zenon_H100 zenon_H4a zenon_Hd2 zenon_Hf9 zenon_Hcd zenon_H55 zenon_H222 zenon_Hb8 zenon_H27 zenon_H3f zenon_H85 zenon_H174 zenon_H256 zenon_H16a zenon_H35 zenon_H14e zenon_H4e zenon_H23b zenon_H4c zenon_Had zenon_H1dc zenon_H14b zenon_H48 zenon_H20 zenon_Hbd zenon_Hd6 zenon_H296 zenon_H6b zenon_H1b9 zenon_H185 zenon_Hde. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.13/30.29 exact (zenon_H84 zenon_H88). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.13/30.29 apply (zenon_L45_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.13/30.29 apply (zenon_L1226_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.29 apply (zenon_L4_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.29 apply (zenon_L906_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.29 apply (zenon_L94_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.29 apply (zenon_L122_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.13/30.29 apply (zenon_L27_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.13/30.29 apply (zenon_L1233_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.13/30.29 apply (zenon_L63_); trivial. % 30.13/30.29 apply (zenon_L770_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.13/30.29 apply (zenon_L1234_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.13/30.29 apply (zenon_L161_); trivial. % 30.13/30.29 apply (zenon_L1235_); trivial. % 30.13/30.29 apply (zenon_L829_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.29 apply (zenon_L94_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.29 apply (zenon_L748_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.29 apply (zenon_L1233_); trivial. % 30.13/30.29 apply (zenon_L829_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.29 apply (zenon_L1149_); trivial. % 30.13/30.29 apply (zenon_L892_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.29 apply (zenon_L160_); trivial. % 30.13/30.29 apply (zenon_L848_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.29 apply (zenon_L88_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.29 exact (zenon_H85 zenon_H89). % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.29 apply (zenon_L1119_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.29 apply (zenon_L769_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.29 apply (zenon_L1237_); trivial. % 30.13/30.29 apply (zenon_L1238_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.29 apply (zenon_L1149_); trivial. % 30.13/30.29 apply (zenon_L39_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.29 apply (zenon_L598_); trivial. % 30.13/30.29 apply (zenon_L848_); trivial. % 30.13/30.29 apply (zenon_L817_); trivial. % 30.13/30.29 (* end of lemma zenon_L1239_ *) % 30.13/30.29 assert (zenon_L1240_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (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) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H53 zenon_H84 zenon_H35 zenon_H4a zenon_Hd2 zenon_H92 zenon_H296 zenon_H1a5 zenon_H15a zenon_He7 zenon_Hd6 zenon_H19e zenon_H1b1 zenon_H20e zenon_H173 zenon_Hee zenon_H48 zenon_H1b9 zenon_H3c zenon_H55 zenon_H14b zenon_Hc0 zenon_H185 zenon_H20 zenon_H100 zenon_H10d zenon_H23b zenon_Hf9 zenon_H2d zenon_H1dc zenon_H256 zenon_H14e zenon_H4e zenon_H16a zenon_Hb8 zenon_H222 zenon_H4c zenon_Had zenon_Hcd zenon_H3f zenon_H27 zenon_H174 zenon_H6f zenon_Ha4 zenon_Hbd zenon_Hde zenon_H6b zenon_H8d zenon_H85 zenon_H225 zenon_Hd1. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.29 exact (zenon_H84 zenon_H88). % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.29 apply (zenon_L868_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.29 apply (zenon_L1239_); trivial. % 30.13/30.29 apply (zenon_L117_); trivial. % 30.13/30.29 apply (zenon_L1189_); trivial. % 30.13/30.29 (* end of lemma zenon_L1240_ *) % 30.13/30.29 assert (zenon_L1241_ : (((op (e2) (op (e2) (e0))) = (e0))/\(((op (e2) (op (e2) (e1))) = (e1))/\(((op (e2) (op (e2) (e2))) = (e2))/\(((op (e2) (op (e2) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0)))/\(((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3)))))))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 30.13/30.29 do 0 intro. intros zenon_H5a zenon_H1dc zenon_H218 zenon_H1b9 zenon_H156 zenon_H2e6 zenon_H267. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.13/30.29 apply (zenon_L259_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.13/30.29 apply (zenon_L179_); trivial. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.13/30.29 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.29 exact (zenon_H231 zenon_Hf4). % 30.13/30.29 apply (zenon_L200_); trivial. % 30.13/30.29 (* end of lemma zenon_L1241_ *) % 30.13/30.29 assert (zenon_L1242_ : (((op (e3) (op (e3) (e0))) = (e0))/\(((op (e3) (op (e3) (e1))) = (e1))/\(((op (e3) (op (e3) (e2))) = (e2))/\(((op (e3) (op (e3) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0)))/\(((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1)))/\(((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3)))))))))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e2)) = (e3)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H270 zenon_H2e6 zenon_H1b9. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H2eb); [ zenon_intro zenon_H1db | zenon_intro zenon_Hf5 ]. % 30.13/30.29 exact (zenon_H1db zenon_H1b9). % 30.13/30.29 exact (zenon_H2e6 zenon_Hf5). % 30.13/30.29 (* end of lemma zenon_L1242_ *) % 30.13/30.29 assert (zenon_L1243_ : (((op (e0) (op (e0) (e0))) = (e0))/\(((op (e0) (op (e0) (e1))) = (e1))/\(((op (e0) (op (e0) (e2))) = (e2))/\(((op (e0) (op (e0) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1)))/\(((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2)))/\((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3)))))))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e0)) -> False). % 30.13/30.29 do 0 intro. intros zenon_H2ec zenon_H2ed zenon_H142. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.13/30.29 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.13/30.29 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H260 | zenon_intro zenon_Hc9 ]. % 30.13/30.29 exact (zenon_H260 zenon_H142). % 30.13/30.29 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 (* end of lemma zenon_L1243_ *) % 30.13/30.30 assert (zenon_L1244_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H172 zenon_H68 zenon_H20 zenon_H19f zenon_He2 zenon_H4c zenon_Had zenon_H18c zenon_H4e zenon_H76. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.30 apply (zenon_L16_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.30 exact (zenon_H19f zenon_Hc3). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.30 apply (zenon_L742_); trivial. % 30.13/30.30 apply (zenon_L864_); trivial. % 30.13/30.30 (* end of lemma zenon_L1244_ *) % 30.13/30.30 assert (zenon_L1245_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H8d zenon_H64 zenon_H2d zenon_H6f zenon_H4e zenon_H18c zenon_Had zenon_H4c zenon_H19f zenon_H20 zenon_H68 zenon_H172 zenon_He1 zenon_He2. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.30 apply (zenon_L148_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.30 apply (zenon_L18_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.30 apply (zenon_L1244_); trivial. % 30.13/30.30 apply (zenon_L50_); trivial. % 30.13/30.30 (* end of lemma zenon_L1245_ *) % 30.13/30.30 assert (zenon_L1246_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H172 zenon_H68 zenon_H20 zenon_H19f zenon_H20e zenon_H142 zenon_H18c zenon_H4e zenon_H76. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.30 apply (zenon_L16_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.30 exact (zenon_H19f zenon_Hc3). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.30 apply (zenon_L350_); trivial. % 30.13/30.30 apply (zenon_L864_); trivial. % 30.13/30.30 (* end of lemma zenon_L1246_ *) % 30.13/30.30 assert (zenon_L1247_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H135 zenon_H2ed zenon_H1bd zenon_Hd0 zenon_H20d zenon_H60 zenon_H142. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.30 apply (zenon_L165_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.30 exact (zenon_Hd0 zenon_Hcc). % 30.13/30.30 apply (zenon_L223_); trivial. % 30.13/30.30 (* end of lemma zenon_L1247_ *) % 30.13/30.30 assert (zenon_L1248_ : (((op (e2) (op (e2) (e0))) = (e0))/\(((op (e2) (op (e2) (e1))) = (e1))/\(((op (e2) (op (e2) (e2))) = (e2))/\(((op (e2) (op (e2) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0)))/\(((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3)))))))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H5a zenon_Hde zenon_H2ed zenon_H1bd zenon_H142 zenon_H20d zenon_H135. % 30.13/30.30 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.13/30.30 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.13/30.30 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.13/30.30 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.13/30.30 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.13/30.30 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.13/30.30 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.13/30.30 apply (zenon_L1247_); trivial. % 30.13/30.30 apply (zenon_L89_); trivial. % 30.13/30.30 (* end of lemma zenon_L1248_ *) % 30.13/30.30 assert (zenon_L1249_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_Hed zenon_Hfc zenon_H103. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.13/30.30 exact (zenon_H19f zenon_Hc3). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.13/30.30 apply (zenon_L45_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.13/30.30 apply (zenon_L58_); trivial. % 30.13/30.30 exact (zenon_H103 zenon_H37). % 30.13/30.30 (* end of lemma zenon_L1249_ *) % 30.13/30.30 assert (zenon_L1250_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H23b zenon_H20 zenon_H8b zenon_H40 zenon_H6f zenon_H26 zenon_H10d zenon_Hfd zenon_H14f. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.30 apply (zenon_L27_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.30 apply (zenon_L80_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.30 apply (zenon_L699_); trivial. % 30.13/30.30 apply (zenon_L416_); trivial. % 30.13/30.30 (* end of lemma zenon_L1250_ *) % 30.13/30.30 assert (zenon_L1251_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 30.13/30.30 do 0 intro. intros zenon_Hbd zenon_H14f zenon_Hfd zenon_H10d zenon_H26 zenon_H6f zenon_H20 zenon_H23b zenon_H2d zenon_H142 zenon_H1dc zenon_H97 zenon_Hb3 zenon_H40. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.13/30.30 apply (zenon_L1250_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.13/30.30 apply (zenon_L766_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.13/30.30 apply (zenon_L177_); trivial. % 30.13/30.30 apply (zenon_L36_); trivial. % 30.13/30.30 (* end of lemma zenon_L1251_ *) % 30.13/30.30 assert (zenon_L1252_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.13/30.30 do 0 intro. intros zenon_Hb8 zenon_H1d8 zenon_H76 zenon_Hb3 zenon_H97 zenon_H1dc zenon_H142 zenon_H2d zenon_H23b zenon_H20 zenon_H6f zenon_H26 zenon_H10d zenon_Hfd zenon_H14f zenon_Hbd zenon_Hee zenon_H15e zenon_Hb9. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.13/30.30 apply (zenon_L174_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.13/30.30 apply (zenon_L1251_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.13/30.30 apply (zenon_L490_); trivial. % 30.13/30.30 exact (zenon_Hb9 zenon_Hbc). % 30.13/30.30 (* end of lemma zenon_L1252_ *) % 30.13/30.30 assert (zenon_L1253_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H1c7 zenon_H55 zenon_Hf5. % 30.13/30.30 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e3)))). % 30.13/30.30 intro zenon_D_pnotp. % 30.13/30.30 apply zenon_H1c7. % 30.13/30.30 rewrite <- zenon_D_pnotp. % 30.13/30.30 exact zenon_H55. % 30.13/30.30 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 30.13/30.30 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 30.13/30.30 congruence. % 30.13/30.30 apply zenon_H63. apply refl_equal. % 30.13/30.30 apply zenon_Hf8. apply sym_equal. exact zenon_Hf5. % 30.13/30.30 (* end of lemma zenon_L1253_ *) % 30.13/30.30 assert (zenon_L1254_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H1ca zenon_Hd6 zenon_H25 zenon_Hf5 zenon_H1c7 zenon_H142 zenon_Hfd. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1cb ]. % 30.13/30.30 apply (zenon_L161_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H1cc ]. % 30.13/30.30 apply (zenon_L46_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H55 | zenon_intro zenon_H3d ]. % 30.13/30.30 apply (zenon_L1253_); trivial. % 30.13/30.30 apply (zenon_L79_); trivial. % 30.13/30.30 (* end of lemma zenon_L1254_ *) % 30.13/30.30 assert (zenon_L1255_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H1a2 zenon_Hb9 zenon_Hee zenon_Hbd zenon_H14f zenon_H10d zenon_H20 zenon_H23b zenon_H2d zenon_H1dc zenon_H97 zenon_Hb3 zenon_H76 zenon_H1d8 zenon_Hb8 zenon_H6f zenon_H15e zenon_H142 zenon_H1c7 zenon_Hf5 zenon_Hd6 zenon_H1ca zenon_H9b zenon_Hfd zenon_H100. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.30 apply (zenon_L1252_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.30 apply (zenon_L235_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.30 apply (zenon_L1254_); trivial. % 30.13/30.30 apply (zenon_L804_); trivial. % 30.13/30.30 (* end of lemma zenon_L1255_ *) % 30.13/30.30 assert (zenon_L1256_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H26 zenon_H103 zenon_Hfc zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H1a2 zenon_Hb9 zenon_Hee zenon_Hbd zenon_H14f zenon_H10d zenon_H20 zenon_H23b zenon_H2d zenon_H1dc zenon_H97 zenon_Hb3 zenon_H76 zenon_H1d8 zenon_Hb8 zenon_H6f zenon_H142 zenon_H1c7 zenon_Hf5 zenon_Hd6 zenon_H1ca zenon_H9b zenon_Hfd zenon_H100. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.13/30.30 apply (zenon_L350_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.13/30.30 apply (zenon_L136_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.13/30.30 apply (zenon_L1249_); trivial. % 30.13/30.30 apply (zenon_L1255_); trivial. % 30.13/30.30 (* end of lemma zenon_L1256_ *) % 30.13/30.30 assert (zenon_L1257_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H135 zenon_H2ed zenon_Hd5 zenon_Hcd zenon_Hde zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H26 zenon_H103 zenon_Hfc zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H1a2 zenon_Hb9 zenon_Hee zenon_Hbd zenon_H14f zenon_H10d zenon_H20 zenon_H23b zenon_H2d zenon_H1dc zenon_H97 zenon_Hb3 zenon_H76 zenon_H1d8 zenon_Hb8 zenon_H6f zenon_H142 zenon_H1c7 zenon_Hd6 zenon_H1ca zenon_H9b zenon_Hfd zenon_H100. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.30 apply (zenon_L212_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.30 apply (zenon_L89_); trivial. % 30.13/30.30 apply (zenon_L1256_); trivial. % 30.13/30.30 (* end of lemma zenon_L1257_ *) % 30.13/30.30 assert (zenon_L1258_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H55 zenon_H19e zenon_H103. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.13/30.30 exact (zenon_H19f zenon_Hc3). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.13/30.30 apply (zenon_L45_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.13/30.30 apply (zenon_L787_); trivial. % 30.13/30.30 exact (zenon_H103 zenon_H37). % 30.13/30.30 (* end of lemma zenon_L1258_ *) % 30.13/30.30 assert (zenon_L1259_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H135 zenon_H2ed zenon_H103 zenon_H19e zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_Hcd zenon_H1ca zenon_Hd6 zenon_H25 zenon_H1c7 zenon_H142 zenon_Hfd. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.30 apply (zenon_L1258_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.30 apply (zenon_L44_); trivial. % 30.13/30.30 apply (zenon_L1254_); trivial. % 30.13/30.30 (* end of lemma zenon_L1259_ *) % 30.13/30.30 assert (zenon_L1260_ : (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H6f zenon_Hb8 zenon_H1d8 zenon_H76 zenon_Hb3 zenon_H97 zenon_H1dc zenon_H2d zenon_H23b zenon_H20 zenon_H10d zenon_H14f zenon_Hbd zenon_Hee zenon_Hb9 zenon_H1a2 zenon_Hfc zenon_H1a5 zenon_H20e zenon_H2f8 zenon_Hde zenon_Hd5 zenon_H1b1 zenon_H142 zenon_H1c7 zenon_Hd6 zenon_H1ca zenon_Hcd zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H19e zenon_H103 zenon_H2ed zenon_H135 zenon_H9b zenon_Hfd zenon_H100. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.30 apply (zenon_L1257_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.30 apply (zenon_L147_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.30 apply (zenon_L1259_); trivial. % 30.13/30.30 apply (zenon_L804_); trivial. % 30.13/30.30 (* end of lemma zenon_L1260_ *) % 30.13/30.30 assert (zenon_L1261_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H135 zenon_H2ed zenon_Hfd zenon_H19e zenon_Hde zenon_H142 zenon_Hcd zenon_H1e5. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.30 apply (zenon_L787_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.30 apply (zenon_L89_); trivial. % 30.13/30.30 apply (zenon_L1017_); trivial. % 30.13/30.30 (* end of lemma zenon_L1261_ *) % 30.13/30.30 assert (zenon_L1262_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H135 zenon_H2ed zenon_Hd5 zenon_Hcd zenon_Hde zenon_H142 zenon_H155 zenon_H156. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.30 apply (zenon_L212_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.30 apply (zenon_L89_); trivial. % 30.13/30.30 apply (zenon_L90_); trivial. % 30.13/30.30 (* end of lemma zenon_L1262_ *) % 30.13/30.30 assert (zenon_L1263_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H173 zenon_Hcd zenon_H35 zenon_He9 zenon_H103 zenon_Hfc zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_Hf5 zenon_H156. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.30 apply (zenon_L48_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.30 apply (zenon_L95_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.30 apply (zenon_L1249_); trivial. % 30.13/30.30 apply (zenon_L90_); trivial. % 30.13/30.30 (* end of lemma zenon_L1263_ *) % 30.13/30.30 assert (zenon_L1264_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H135 zenon_H2ed zenon_H19e zenon_H25 zenon_H173 zenon_Hcd zenon_H35 zenon_He9 zenon_H103 zenon_Hfc zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H156. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.30 apply (zenon_L1258_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.30 apply (zenon_L44_); trivial. % 30.13/30.30 apply (zenon_L1263_); trivial. % 30.13/30.30 (* end of lemma zenon_L1264_ *) % 30.13/30.30 assert (zenon_L1265_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H135 zenon_H2ed zenon_H3c zenon_He9 zenon_Hde zenon_H142 zenon_Hcd zenon_H1e5. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.30 apply (zenon_L88_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.30 apply (zenon_L89_); trivial. % 30.13/30.30 apply (zenon_L1017_); trivial. % 30.13/30.30 (* end of lemma zenon_L1265_ *) % 30.13/30.30 assert (zenon_L1266_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H208 zenon_H18c zenon_H155 zenon_H156 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_Hfc zenon_H103 zenon_H35 zenon_H173 zenon_H19e zenon_H135 zenon_H2ed zenon_H3c zenon_He9 zenon_Hde zenon_H142 zenon_Hcd. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.30 apply (zenon_L120_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.30 apply (zenon_L1262_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.30 apply (zenon_L1264_); trivial. % 30.13/30.30 apply (zenon_L1265_); trivial. % 30.13/30.30 (* end of lemma zenon_L1266_ *) % 30.13/30.30 assert (zenon_L1267_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H101 zenon_Hcd zenon_H3c zenon_H2ed zenon_H173 zenon_H35 zenon_Hfc zenon_H18c zenon_H208 zenon_H159 zenon_H103 zenon_H19e zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H135 zenon_He1 zenon_H76 zenon_H222 zenon_Hde zenon_H142 zenon_H155 zenon_H156. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.30 apply (zenon_L1266_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.30 apply (zenon_L93_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.30 apply (zenon_L1258_); trivial. % 30.13/30.30 apply (zenon_L330_); trivial. % 30.13/30.30 (* end of lemma zenon_L1267_ *) % 30.13/30.30 assert (zenon_L1268_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (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) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H8d zenon_H85 zenon_H156 zenon_H142 zenon_Hde zenon_H222 zenon_H135 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H19e zenon_H103 zenon_H159 zenon_H208 zenon_H18c zenon_Hfc zenon_H35 zenon_H173 zenon_H2ed zenon_H3c zenon_Hcd zenon_H101 zenon_H100 zenon_H9b zenon_H1b1 zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1a2 zenon_Hb9 zenon_Hee zenon_Hbd zenon_H10d zenon_H20 zenon_H23b zenon_H2d zenon_H1dc zenon_H97 zenon_Hb3 zenon_H1d8 zenon_Hb8 zenon_H6f zenon_H1c7 zenon_Hd6 zenon_H1ca zenon_H172 zenon_He1 zenon_He2. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.30 exact (zenon_H85 zenon_H89). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.30 apply (zenon_L18_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.30 apply (zenon_L16_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.30 exact (zenon_H19f zenon_Hc3). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.30 apply (zenon_L350_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.30 apply (zenon_L48_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.30 apply (zenon_L157_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.30 apply (zenon_L1260_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.30 apply (zenon_L1259_); trivial. % 30.13/30.30 apply (zenon_L1261_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.30 apply (zenon_L1249_); trivial. % 30.13/30.30 apply (zenon_L1267_); trivial. % 30.13/30.30 apply (zenon_L50_); trivial. % 30.13/30.30 (* end of lemma zenon_L1268_ *) % 30.13/30.30 assert (zenon_L1269_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.13/30.30 do 0 intro. intros zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H95 zenon_H2d zenon_H10d zenon_H117 zenon_Hb9. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.13/30.30 apply (zenon_L174_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.13/30.30 apply (zenon_L766_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.13/30.30 apply (zenon_L151_); trivial. % 30.13/30.30 exact (zenon_Hb9 zenon_Hbc). % 30.13/30.30 (* end of lemma zenon_L1269_ *) % 30.13/30.30 assert (zenon_L1270_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H8d zenon_Hd9 zenon_H6f zenon_H14e zenon_H1dc zenon_H142 zenon_Hb8 zenon_H1d8 zenon_H2d zenon_H10d zenon_H117 zenon_Hb9 zenon_Hde zenon_Hbd zenon_H20e zenon_H19f zenon_H20 zenon_H68 zenon_H172 zenon_He1 zenon_He2. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.30 apply (zenon_L149_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.30 apply (zenon_L18_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.30 apply (zenon_L16_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.30 exact (zenon_H19f zenon_Hc3). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.30 apply (zenon_L350_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.13/30.30 apply (zenon_L288_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.13/30.30 apply (zenon_L1269_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.13/30.30 apply (zenon_L177_); trivial. % 30.13/30.30 apply (zenon_L84_); trivial. % 30.13/30.30 apply (zenon_L50_); trivial. % 30.13/30.30 (* end of lemma zenon_L1270_ *) % 30.13/30.30 assert (zenon_L1271_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H1a2 zenon_H40 zenon_Hb3 zenon_H97 zenon_H1dc zenon_H142 zenon_H2d zenon_H23b zenon_H20 zenon_H10d zenon_H14f zenon_Hbd zenon_H6f zenon_H15e zenon_Hd6 zenon_Hd5 zenon_H9b zenon_Hfd zenon_H100. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.30 apply (zenon_L1251_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.30 apply (zenon_L235_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.30 apply (zenon_L46_); trivial. % 30.13/30.30 apply (zenon_L804_); trivial. % 30.13/30.30 (* end of lemma zenon_L1271_ *) % 30.13/30.30 assert (zenon_L1272_ : (((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 (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H23b zenon_H68 zenon_Had zenon_H40 zenon_H6f zenon_H26 zenon_H10d zenon_Hf6 zenon_H1e5. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.30 apply (zenon_L639_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.30 apply (zenon_L80_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.30 apply (zenon_L699_); trivial. % 30.13/30.30 apply (zenon_L187_); trivial. % 30.13/30.30 (* end of lemma zenon_L1272_ *) % 30.13/30.30 assert (zenon_L1273_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hf6 zenon_H1e5. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.30 apply (zenon_L386_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.30 apply (zenon_L336_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.30 apply (zenon_L337_); trivial. % 30.13/30.30 apply (zenon_L187_); trivial. % 30.13/30.30 (* end of lemma zenon_L1273_ *) % 30.13/30.30 assert (zenon_L1274_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H108 zenon_H25 zenon_H1e5. % 30.13/30.30 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 30.13/30.30 intro zenon_D_pnotp. % 30.13/30.30 apply zenon_H108. % 30.13/30.30 rewrite <- zenon_D_pnotp. % 30.13/30.30 exact zenon_H25. % 30.13/30.30 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 30.13/30.30 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 30.13/30.30 congruence. % 30.13/30.30 apply zenon_H29. apply refl_equal. % 30.13/30.30 apply zenon_H205. apply sym_equal. exact zenon_H1e5. % 30.13/30.30 (* end of lemma zenon_L1274_ *) % 30.13/30.30 assert (zenon_L1275_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H208 zenon_H76 zenon_H15e zenon_Hbd zenon_H14f zenon_H20 zenon_H2d zenon_H1dc zenon_H97 zenon_Hb3 zenon_H142 zenon_H1c7 zenon_Hd6 zenon_H1ca zenon_H102 zenon_H19f zenon_Hd1 zenon_H19e zenon_H103 zenon_H2ed zenon_H135 zenon_H1a2 zenon_H10d zenon_H6f zenon_H40 zenon_Had zenon_H68 zenon_Hf6 zenon_Hee zenon_H3f zenon_H1f zenon_He2 zenon_Hcd zenon_H23b zenon_H108 zenon_H9b zenon_Hfd zenon_H100. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.30 apply (zenon_L157_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.30 apply (zenon_L1271_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.30 apply (zenon_L1259_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.30 apply (zenon_L1272_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.30 apply (zenon_L1273_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.30 apply (zenon_L1274_); trivial. % 30.13/30.30 apply (zenon_L804_); trivial. % 30.13/30.30 (* end of lemma zenon_L1275_ *) % 30.13/30.30 assert (zenon_L1276_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.13/30.30 do 0 intro. intros zenon_H174 zenon_Hb9 zenon_H1d8 zenon_Hb8 zenon_H14e zenon_Hd9 zenon_H8d zenon_H85 zenon_H156 zenon_H142 zenon_Hde zenon_H222 zenon_H135 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H19e zenon_H103 zenon_H159 zenon_H208 zenon_H18c zenon_Hfc zenon_H35 zenon_H173 zenon_H2ed zenon_H3c zenon_Hcd zenon_H101 zenon_H16f zenon_H100 zenon_H9b zenon_H108 zenon_H23b zenon_H1f zenon_H3f zenon_Hee zenon_Hf6 zenon_Had zenon_H6f zenon_H10d zenon_H1a2 zenon_H1ca zenon_Hd6 zenon_H1c7 zenon_Hb3 zenon_H97 zenon_H1dc zenon_H2d zenon_H20 zenon_Hbd zenon_H1e zenon_H42 zenon_H16a zenon_H20e zenon_H172 zenon_He1 zenon_He2. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.30 exact (zenon_H85 zenon_H89). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.30 apply (zenon_L4_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.30 apply (zenon_L1270_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.30 exact (zenon_H85 zenon_H89). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.30 apply (zenon_L18_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.30 apply (zenon_L16_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.30 exact (zenon_H19f zenon_Hc3). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.30 apply (zenon_L350_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.30 apply (zenon_L48_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.13/30.30 apply (zenon_L18_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.13/30.30 exact (zenon_H103 zenon_H37). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.30 apply (zenon_L4_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.30 exact (zenon_H103 zenon_H37). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.30 apply (zenon_L79_); trivial. % 30.13/30.30 apply (zenon_L1275_); trivial. % 30.13/30.30 apply (zenon_L101_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.30 apply (zenon_L1249_); trivial. % 30.13/30.30 apply (zenon_L1267_); trivial. % 30.13/30.30 apply (zenon_L50_); trivial. % 30.13/30.30 (* end of lemma zenon_L1276_ *) % 30.13/30.30 assert (zenon_L1277_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H156 zenon_H155 zenon_H27 zenon_H26 zenon_H135 zenon_H2ed zenon_H3c zenon_He9 zenon_Hde zenon_H142 zenon_Hcd. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.30 apply (zenon_L157_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.30 apply (zenon_L1262_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.30 apply (zenon_L3_); trivial. % 30.13/30.30 apply (zenon_L1265_); trivial. % 30.13/30.30 (* end of lemma zenon_L1277_ *) % 30.13/30.30 assert (zenon_L1278_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 30.13/30.30 do 0 intro. intros zenon_He4 zenon_H64 zenon_H8d zenon_H85 zenon_Hcd zenon_H142 zenon_Hde zenon_He9 zenon_H3c zenon_H2ed zenon_H135 zenon_H26 zenon_H27 zenon_H156 zenon_H6f zenon_H208 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_Hfc zenon_H103 zenon_H35 zenon_H173 zenon_He1. % 30.13/30.30 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.30 apply (zenon_L1209_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.30 apply (zenon_L48_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.30 exact (zenon_H85 zenon_H89). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.30 apply (zenon_L18_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.30 apply (zenon_L48_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.30 apply (zenon_L95_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.30 apply (zenon_L1249_); trivial. % 30.13/30.30 apply (zenon_L1277_); trivial. % 30.13/30.30 apply (zenon_L50_); trivial. % 30.13/30.30 (* end of lemma zenon_L1278_ *) % 30.13/30.30 assert (zenon_L1279_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H101 zenon_Hcd zenon_H3c zenon_H2ed zenon_H26 zenon_H27 zenon_H6f zenon_H208 zenon_H159 zenon_H103 zenon_H19e zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H135 zenon_He1 zenon_H76 zenon_H222 zenon_Hde zenon_H142 zenon_H155 zenon_H156. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.30 apply (zenon_L1277_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.30 apply (zenon_L93_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.30 apply (zenon_L1258_); trivial. % 30.13/30.30 apply (zenon_L330_); trivial. % 30.13/30.30 (* end of lemma zenon_L1279_ *) % 30.13/30.30 assert (zenon_L1280_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.13/30.30 do 0 intro. intros zenon_He4 zenon_Hda zenon_Hd9 zenon_H8d zenon_H85 zenon_H156 zenon_H142 zenon_Hde zenon_H222 zenon_H135 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H19e zenon_H103 zenon_H159 zenon_H208 zenon_H6f zenon_H27 zenon_H26 zenon_H2ed zenon_H3c zenon_Hcd zenon_H101 zenon_Hfc zenon_H42 zenon_H1e zenon_Hbd zenon_H10d zenon_H20 zenon_H23b zenon_H2d zenon_H1dc zenon_H97 zenon_Hb3 zenon_H173 zenon_H20e zenon_H172 zenon_He1. % 30.13/30.30 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.30 apply (zenon_L47_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.30 apply (zenon_L48_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.30 exact (zenon_H85 zenon_H89). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.30 apply (zenon_L18_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.30 apply (zenon_L16_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.30 exact (zenon_H19f zenon_Hc3). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.30 apply (zenon_L350_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.30 apply (zenon_L48_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.30 apply (zenon_L4_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.30 exact (zenon_H103 zenon_H37). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.30 apply (zenon_L79_); trivial. % 30.13/30.30 apply (zenon_L1251_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.30 apply (zenon_L1249_); trivial. % 30.13/30.30 apply (zenon_L1279_); trivial. % 30.13/30.30 apply (zenon_L50_); trivial. % 30.13/30.30 (* end of lemma zenon_L1280_ *) % 30.13/30.30 assert (zenon_L1281_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.30 do 0 intro. intros zenon_H135 zenon_H2ed zenon_Hfd zenon_H19e zenon_Hde zenon_H142 zenon_H17b zenon_H218. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.30 apply (zenon_L787_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.30 apply (zenon_L89_); trivial. % 30.13/30.30 apply (zenon_L405_); trivial. % 30.13/30.30 (* end of lemma zenon_L1281_ *) % 30.13/30.30 assert (zenon_L1282_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> False). % 30.13/30.30 do 0 intro. intros zenon_He4 zenon_H64 zenon_H8d zenon_H85 zenon_H6f zenon_H156 zenon_H142 zenon_Hde zenon_H222 zenon_H135 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H19e zenon_H103 zenon_H159 zenon_H208 zenon_H18c zenon_Hfc zenon_H35 zenon_H173 zenon_H2ed zenon_H3c zenon_Hcd zenon_H101 zenon_H17b zenon_H218 zenon_He1. % 30.13/30.30 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.30 apply (zenon_L1209_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.30 apply (zenon_L48_); trivial. % 30.13/30.30 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.30 exact (zenon_H2ed zenon_Hc9). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.30 exact (zenon_H85 zenon_H89). % 30.13/30.30 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.30 apply (zenon_L18_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.31 apply (zenon_L1281_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.31 apply (zenon_L1249_); trivial. % 30.13/30.31 apply (zenon_L1267_); trivial. % 30.13/30.31 apply (zenon_L50_); trivial. % 30.13/30.31 (* end of lemma zenon_L1282_ *) % 30.13/30.31 assert (zenon_L1283_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.13/30.31 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H155 zenon_H142 zenon_Hde zenon_H156 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_Hfc zenon_H103 zenon_He9 zenon_H35 zenon_Hcd zenon_H173 zenon_H19e zenon_H2ed zenon_H135 zenon_H218 zenon_H33. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.31 apply (zenon_L157_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.31 apply (zenon_L1262_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.31 apply (zenon_L1264_); trivial. % 30.13/30.31 apply (zenon_L870_); trivial. % 30.13/30.31 (* end of lemma zenon_L1283_ *) % 30.13/30.31 assert (zenon_L1284_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 30.13/30.31 do 0 intro. intros zenon_He4 zenon_H64 zenon_H8d zenon_H85 zenon_H33 zenon_H218 zenon_H135 zenon_H2ed zenon_H19e zenon_H173 zenon_Hcd zenon_H35 zenon_He9 zenon_H103 zenon_Hfc zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H156 zenon_Hde zenon_H142 zenon_H6f zenon_H208 zenon_He1. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.31 apply (zenon_L1209_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.31 exact (zenon_H2ed zenon_Hc9). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.31 exact (zenon_H85 zenon_H89). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.31 apply (zenon_L18_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.31 apply (zenon_L95_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.31 apply (zenon_L1249_); trivial. % 30.13/30.31 apply (zenon_L1283_); trivial. % 30.13/30.31 apply (zenon_L50_); trivial. % 30.13/30.31 (* end of lemma zenon_L1284_ *) % 30.13/30.31 assert (zenon_L1285_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (op (e3) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_Hfd zenon_H142 zenon_Ha3 zenon_H33 zenon_Ha4. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.31 apply (zenon_L4_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.31 exact (zenon_H103 zenon_H37). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.31 apply (zenon_L79_); trivial. % 30.13/30.31 apply (zenon_L32_); trivial. % 30.13/30.31 (* end of lemma zenon_L1285_ *) % 30.13/30.31 assert (zenon_L1286_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H101 zenon_H33 zenon_H218 zenon_H2ed zenon_H173 zenon_Hcd zenon_H35 zenon_Hfc zenon_H6f zenon_H208 zenon_H159 zenon_H103 zenon_H19e zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H135 zenon_He1 zenon_H76 zenon_H222 zenon_Hde zenon_H142 zenon_H155 zenon_H156. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.31 apply (zenon_L1283_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.31 apply (zenon_L93_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.31 apply (zenon_L1258_); trivial. % 30.13/30.31 apply (zenon_L330_); trivial. % 30.13/30.31 (* end of lemma zenon_L1286_ *) % 30.13/30.31 assert (zenon_L1287_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 30.13/30.31 do 0 intro. intros zenon_H97 zenon_H8b zenon_H95. % 30.13/30.31 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 30.13/30.31 intro zenon_D_pnotp. % 30.13/30.31 apply zenon_H97. % 30.13/30.31 rewrite <- zenon_D_pnotp. % 30.13/30.31 exact zenon_H8b. % 30.13/30.31 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 30.13/30.31 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 30.13/30.31 congruence. % 30.13/30.31 apply zenon_H9a. apply refl_equal. % 30.13/30.31 apply zenon_H96. apply sym_equal. exact zenon_H95. % 30.13/30.31 (* end of lemma zenon_L1287_ *) % 30.13/30.31 assert (zenon_L1288_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.13/30.31 do 0 intro. intros zenon_H296 zenon_H2d zenon_H2c zenon_H19f zenon_Hd6 zenon_H142 zenon_H97 zenon_H8b. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.31 apply (zenon_L4_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.31 exact (zenon_H19f zenon_Hc3). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.31 apply (zenon_L161_); trivial. % 30.13/30.31 apply (zenon_L1287_); trivial. % 30.13/30.31 (* end of lemma zenon_L1288_ *) % 30.13/30.31 assert (zenon_L1289_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H101 zenon_H3c zenon_Hc8 zenon_H73 zenon_H159 zenon_H103 zenon_H19e zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H135 zenon_He1 zenon_H76 zenon_H222 zenon_Hde zenon_H142 zenon_H155 zenon_H156. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.31 apply (zenon_L91_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.31 apply (zenon_L93_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.31 apply (zenon_L1258_); trivial. % 30.13/30.31 apply (zenon_L330_); trivial. % 30.13/30.31 (* end of lemma zenon_L1289_ *) % 30.13/30.31 assert (zenon_L1290_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.13/30.31 do 0 intro. intros zenon_H8d zenon_H85 zenon_H156 zenon_H142 zenon_Hde zenon_H222 zenon_He1 zenon_H135 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H19e zenon_H103 zenon_H159 zenon_H73 zenon_Hc8 zenon_H3c zenon_H101 zenon_Hfc zenon_H42 zenon_H97 zenon_Hd6 zenon_H296 zenon_H1a2 zenon_H10d zenon_H6f zenon_H20 zenon_H23b zenon_H1b1 zenon_H9b zenon_H100 zenon_Hcd zenon_H173 zenon_H20e zenon_H172 zenon_H2d zenon_H8b. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.31 exact (zenon_H85 zenon_H89). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.31 apply (zenon_L18_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.31 apply (zenon_L16_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.31 exact (zenon_H19f zenon_Hc3). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.31 apply (zenon_L350_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.31 apply (zenon_L1288_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.31 exact (zenon_H103 zenon_H37). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.31 apply (zenon_L79_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.31 apply (zenon_L1250_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.31 apply (zenon_L147_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.31 apply (zenon_L23_); trivial. % 30.13/30.31 apply (zenon_L804_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.31 apply (zenon_L1249_); trivial. % 30.13/30.31 apply (zenon_L1289_); trivial. % 30.13/30.31 apply (zenon_L25_); trivial. % 30.13/30.31 (* end of lemma zenon_L1290_ *) % 30.13/30.31 assert (zenon_L1291_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.31 do 0 intro. intros zenon_He4 zenon_H2d zenon_H172 zenon_H20e zenon_H173 zenon_H100 zenon_H9b zenon_H1b1 zenon_H23b zenon_H20 zenon_H6f zenon_H10d zenon_H1a2 zenon_H296 zenon_Hd6 zenon_H97 zenon_H42 zenon_Hfc zenon_H101 zenon_H3c zenon_Hc8 zenon_H159 zenon_H103 zenon_H19e zenon_Hd1 zenon_H19f zenon_H102 zenon_H135 zenon_He1 zenon_H222 zenon_H142 zenon_H156 zenon_H85 zenon_H8d zenon_Hcd zenon_H68 zenon_H2ed zenon_H8b zenon_Hde. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.31 apply (zenon_L1290_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.31 exact (zenon_H2ed zenon_Hc9). % 30.13/30.31 apply (zenon_L288_); trivial. % 30.13/30.31 (* end of lemma zenon_L1291_ *) % 30.13/30.31 assert (zenon_L1292_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.13/30.31 do 0 intro. intros zenon_H172 zenon_H68 zenon_H19f zenon_H20e zenon_H142 zenon_H20 zenon_H182. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.31 apply (zenon_L16_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.31 exact (zenon_H19f zenon_Hc3). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.31 apply (zenon_L350_); trivial. % 30.13/30.31 apply (zenon_L658_); trivial. % 30.13/30.31 (* end of lemma zenon_L1292_ *) % 30.13/30.31 assert (zenon_L1293_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H2b1 zenon_H185 zenon_H20 zenon_H142 zenon_H20e zenon_H19f zenon_H68 zenon_H172 zenon_Hf5 zenon_Hcd zenon_Hb3 zenon_H2c zenon_H3f. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.13/30.31 apply (zenon_L117_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.13/30.31 apply (zenon_L1292_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.13/30.31 apply (zenon_L1017_); trivial. % 30.13/30.31 apply (zenon_L720_); trivial. % 30.13/30.31 (* end of lemma zenon_L1293_ *) % 30.13/30.31 assert (zenon_L1294_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H135 zenon_H2ed zenon_H103 zenon_H19e zenon_Hd1 zenon_H102 zenon_Hde zenon_H2b1 zenon_H185 zenon_H20 zenon_H142 zenon_H20e zenon_H19f zenon_H68 zenon_H172 zenon_Hcd zenon_Hb3 zenon_H2c zenon_H3f. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.31 exact (zenon_H2ed zenon_Hc9). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.31 apply (zenon_L1258_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.31 apply (zenon_L89_); trivial. % 30.13/30.31 apply (zenon_L1293_); trivial. % 30.13/30.31 (* end of lemma zenon_L1294_ *) % 30.13/30.31 assert (zenon_L1295_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H174 zenon_H64 zenon_H3f zenon_Hb3 zenon_Hcd zenon_H2b1 zenon_H102 zenon_Hd1 zenon_H19e zenon_H103 zenon_H2ed zenon_H135 zenon_He2 zenon_He1 zenon_H172 zenon_H68 zenon_H20 zenon_H19f zenon_H20e zenon_Hbd zenon_Hde zenon_Hb9 zenon_H10d zenon_H1d8 zenon_Hb8 zenon_H142 zenon_H1dc zenon_H14e zenon_H6f zenon_Hd9 zenon_H8d zenon_H185 zenon_H2d. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.31 apply (zenon_L148_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.31 apply (zenon_L1294_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.31 apply (zenon_L1270_); trivial. % 30.13/30.31 apply (zenon_L848_); trivial. % 30.13/30.31 (* end of lemma zenon_L1295_ *) % 30.13/30.31 assert (zenon_L1296_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H174 zenon_He1 zenon_H73 zenon_H8b zenon_H97 zenon_H142 zenon_Hd6 zenon_H19f zenon_H296 zenon_H6f zenon_H26 zenon_H185 zenon_H2d. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.31 apply (zenon_L232_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.31 apply (zenon_L1288_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.31 apply (zenon_L598_); trivial. % 30.13/30.31 apply (zenon_L848_); trivial. % 30.13/30.31 (* end of lemma zenon_L1296_ *) % 30.13/30.31 assert (zenon_L1297_ : ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H9b zenon_H1a0 zenon_H55 zenon_H222. % 30.13/30.31 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.13/30.31 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 30.13/30.31 intro zenon_D_pnotp. % 30.13/30.31 apply zenon_H222. % 30.13/30.31 rewrite <- zenon_D_pnotp. % 30.13/30.31 exact zenon_H1b4. % 30.13/30.31 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.13/30.31 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 30.13/30.31 congruence. % 30.13/30.31 cut (((op (e3) (op (e3) (e2))) = (e2)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 30.13/30.31 intro zenon_D_pnotp. % 30.13/30.31 apply zenon_H26f. % 30.13/30.31 rewrite <- zenon_D_pnotp. % 30.13/30.31 exact zenon_H9b. % 30.13/30.31 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 30.13/30.31 cut (((op (e3) (op (e3) (e2))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a8]. % 30.13/30.31 congruence. % 30.13/30.31 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.13/30.31 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (op (e3) (e2))) = (op (e3) (e1)))). % 30.13/30.31 intro zenon_D_pnotp. % 30.13/30.31 apply zenon_H2a8. % 30.13/30.31 rewrite <- zenon_D_pnotp. % 30.13/30.31 exact zenon_H1b4. % 30.13/30.31 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.13/30.31 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2a7]. % 30.13/30.31 congruence. % 30.13/30.31 apply (zenon_L803_); trivial. % 30.13/30.31 apply zenon_H1b5. apply refl_equal. % 30.13/30.31 apply zenon_H1b5. apply refl_equal. % 30.13/30.31 apply zenon_H1c2. apply sym_equal. exact zenon_H55. % 30.13/30.31 apply zenon_H1b5. apply refl_equal. % 30.13/30.31 apply zenon_H1b5. apply refl_equal. % 30.13/30.31 (* end of lemma zenon_L1297_ *) % 30.13/30.31 assert (zenon_L1298_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H2b1 zenon_H185 zenon_H14f zenon_H20 zenon_Hf5 zenon_Hcd zenon_H1a0 zenon_H110. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.13/30.31 apply (zenon_L117_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.13/30.31 apply (zenon_L658_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.13/30.31 apply (zenon_L1017_); trivial. % 30.13/30.31 apply (zenon_L133_); trivial. % 30.13/30.31 (* end of lemma zenon_L1298_ *) % 30.13/30.31 assert (zenon_L1299_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H135 zenon_H2ed zenon_H222 zenon_H9b zenon_Hde zenon_H142 zenon_H2b1 zenon_H185 zenon_H14f zenon_H20 zenon_Hcd zenon_H1a0 zenon_H110. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.31 exact (zenon_H2ed zenon_Hc9). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.31 apply (zenon_L1297_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.31 apply (zenon_L89_); trivial. % 30.13/30.31 apply (zenon_L1298_); trivial. % 30.13/30.31 (* end of lemma zenon_L1299_ *) % 30.13/30.31 assert (zenon_L1300_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H1a2 zenon_H6f zenon_H117 zenon_Hed zenon_H73 zenon_H76 zenon_H135 zenon_H2ed zenon_H222 zenon_H9b zenon_Hde zenon_H142 zenon_H2b1 zenon_H185 zenon_H14f zenon_H20 zenon_Hcd zenon_H110. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.31 apply (zenon_L598_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.31 apply (zenon_L159_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.31 apply (zenon_L23_); trivial. % 30.13/30.31 apply (zenon_L1299_); trivial. % 30.13/30.31 (* end of lemma zenon_L1300_ *) % 30.13/30.31 assert (zenon_L1301_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.31 do 0 intro. intros zenon_He4 zenon_Hda zenon_Hd9 zenon_Hcd zenon_H68 zenon_H2ed zenon_H8b zenon_Hde. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.31 apply (zenon_L47_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.31 exact (zenon_H2ed zenon_Hc9). % 30.13/30.31 apply (zenon_L288_); trivial. % 30.13/30.31 (* end of lemma zenon_L1301_ *) % 30.13/30.31 assert (zenon_L1302_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H246 zenon_H14e zenon_H1dc zenon_Hb8 zenon_H1d8 zenon_H10d zenon_Hb9 zenon_Hbd zenon_H6b zenon_H225 zenon_H1b1 zenon_H97 zenon_Hd6 zenon_H296 zenon_H174 zenon_H3f zenon_Hb3 zenon_H102 zenon_Hd1 zenon_H19e zenon_H103 zenon_H172 zenon_H19f zenon_H20e zenon_H173 zenon_H15a zenon_H35 zenon_H110 zenon_H20 zenon_H2b1 zenon_H9b zenon_H222 zenon_H6f zenon_H1a2 zenon_H135 zenon_Hc8 zenon_H3c zenon_H142 zenon_H156 zenon_He1 zenon_H8d zenon_H2d zenon_H2ed zenon_H68 zenon_Hcd zenon_Hd9 zenon_He4 zenon_H185 zenon_Hde. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.31 apply (zenon_L1209_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.31 exact (zenon_H2ed zenon_Hc9). % 30.13/30.31 apply (zenon_L1295_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.13/30.31 apply (zenon_L16_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.13/30.31 apply (zenon_L303_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.31 apply (zenon_L232_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.31 apply (zenon_L1288_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.31 apply (zenon_L149_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.31 apply (zenon_L18_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.31 apply (zenon_L16_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.31 exact (zenon_H19f zenon_Hc3). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.31 apply (zenon_L350_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.31 apply (zenon_L1296_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.31 apply (zenon_L147_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.31 apply (zenon_L23_); trivial. % 30.13/30.31 apply (zenon_L1299_); trivial. % 30.13/30.31 apply (zenon_L25_); trivial. % 30.13/30.31 apply (zenon_L848_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.31 apply (zenon_L232_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.31 apply (zenon_L1294_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.31 apply (zenon_L232_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.31 apply (zenon_L18_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.31 apply (zenon_L16_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.31 exact (zenon_H19f zenon_Hc3). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.31 apply (zenon_L350_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.31 apply (zenon_L94_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.31 apply (zenon_L95_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.31 apply (zenon_L1300_); trivial. % 30.13/30.31 apply (zenon_L91_); trivial. % 30.13/30.31 apply (zenon_L25_); trivial. % 30.13/30.31 apply (zenon_L848_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.31 exact (zenon_H2ed zenon_Hc9). % 30.13/30.31 apply (zenon_L288_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.31 apply (zenon_L1301_); trivial. % 30.13/30.31 apply (zenon_L817_); trivial. % 30.13/30.31 (* end of lemma zenon_L1302_ *) % 30.13/30.31 assert (zenon_L1303_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 30.13/30.31 do 0 intro. intros zenon_H110 zenon_Hb6 zenon_Hbc. % 30.13/30.31 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e3)))). % 30.13/30.31 intro zenon_D_pnotp. % 30.13/30.31 apply zenon_H110. % 30.13/30.31 rewrite <- zenon_D_pnotp. % 30.13/30.31 exact zenon_Hb6. % 30.13/30.31 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 30.13/30.31 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 30.13/30.31 congruence. % 30.13/30.31 apply zenon_Hf0. apply refl_equal. % 30.13/30.31 apply zenon_H17e. apply sym_equal. exact zenon_Hbc. % 30.13/30.31 (* end of lemma zenon_L1303_ *) % 30.13/30.31 assert (zenon_L1304_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 30.13/30.31 do 0 intro. intros zenon_H2b7 zenon_H142 zenon_H1dc zenon_H26 zenon_Hda zenon_H10d zenon_H110 zenon_Hbc. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.13/30.31 apply (zenon_L177_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.13/30.31 apply (zenon_L699_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.13/30.31 apply (zenon_L64_); trivial. % 30.13/30.31 apply (zenon_L1303_); trivial. % 30.13/30.31 (* end of lemma zenon_L1304_ *) % 30.13/30.31 assert (zenon_L1305_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H16f zenon_H100 zenon_Hfd zenon_H9b zenon_H135 zenon_H2ed zenon_H103 zenon_H19e zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_Hcd zenon_H1ca zenon_Hd6 zenon_H1c7 zenon_H142 zenon_H6f zenon_H2b7 zenon_H1dc zenon_Hda zenon_H10d zenon_H110 zenon_H1a2 zenon_Hb3 zenon_Hbc zenon_H14e. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.13/30.31 apply (zenon_L18_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.13/30.31 exact (zenon_H103 zenon_H37). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.31 apply (zenon_L1304_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.31 apply (zenon_L235_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.31 apply (zenon_L1259_); trivial. % 30.13/30.31 apply (zenon_L804_); trivial. % 30.13/30.31 apply (zenon_L113_); trivial. % 30.13/30.31 (* end of lemma zenon_L1305_ *) % 30.13/30.31 assert (zenon_L1306_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 30.13/30.31 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_Hfd zenon_H142 zenon_H113 zenon_Hbc. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.31 apply (zenon_L4_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.31 exact (zenon_H103 zenon_H37). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.31 apply (zenon_L79_); trivial. % 30.13/30.31 apply (zenon_L753_); trivial. % 30.13/30.31 (* end of lemma zenon_L1306_ *) % 30.13/30.31 assert (zenon_L1307_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H156 zenon_H155 zenon_H3d zenon_He1 zenon_H135 zenon_H2ed zenon_H3c zenon_He9 zenon_Hde zenon_H142 zenon_Hcd. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.31 apply (zenon_L157_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.31 apply (zenon_L1262_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.31 exact (zenon_H2ed zenon_Hc9). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.31 apply (zenon_L126_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.31 apply (zenon_L44_); trivial. % 30.13/30.31 apply (zenon_L90_); trivial. % 30.13/30.31 apply (zenon_L1265_); trivial. % 30.13/30.31 (* end of lemma zenon_L1307_ *) % 30.13/30.31 assert (zenon_L1308_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 30.13/30.31 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_He1 zenon_H55 zenon_H113 zenon_Hbc. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.31 apply (zenon_L4_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.31 exact (zenon_H103 zenon_H37). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.31 apply (zenon_L126_); trivial. % 30.13/30.31 apply (zenon_L753_); trivial. % 30.13/30.31 (* end of lemma zenon_L1308_ *) % 30.13/30.31 assert (zenon_L1309_ : ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_Hb3 zenon_Hbc zenon_H16b zenon_Ha4. % 30.13/30.31 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.13/30.31 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 30.13/30.31 intro zenon_D_pnotp. % 30.13/30.31 apply zenon_Ha4. % 30.13/30.31 rewrite <- zenon_D_pnotp. % 30.13/30.31 exact zenon_Ha5. % 30.13/30.31 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.13/30.31 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 30.13/30.31 congruence. % 30.13/30.31 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 30.13/30.31 intro zenon_D_pnotp. % 30.13/30.31 apply zenon_Ha7. % 30.13/30.31 rewrite <- zenon_D_pnotp. % 30.13/30.31 exact zenon_Hb3. % 30.13/30.31 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 30.13/30.31 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 30.13/30.31 congruence. % 30.13/30.31 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.13/30.31 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e3)))). % 30.13/30.31 intro zenon_D_pnotp. % 30.13/30.31 apply zenon_H181. % 30.13/30.31 rewrite <- zenon_D_pnotp. % 30.13/30.31 exact zenon_Ha5. % 30.13/30.31 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.13/30.31 cut (((op (e3) (e3)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 30.13/30.31 congruence. % 30.13/30.31 apply (zenon_L112_); trivial. % 30.13/30.31 apply zenon_Ha6. apply refl_equal. % 30.13/30.31 apply zenon_Ha6. apply refl_equal. % 30.13/30.31 apply zenon_H21a. apply sym_equal. exact zenon_H16b. % 30.13/30.31 apply zenon_Ha6. apply refl_equal. % 30.13/30.31 apply zenon_Ha6. apply refl_equal. % 30.13/30.31 (* end of lemma zenon_L1309_ *) % 30.13/30.31 assert (zenon_L1310_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H174 zenon_H64 zenon_H2d zenon_H3f zenon_Hcd zenon_H172 zenon_H68 zenon_H19f zenon_H20e zenon_H142 zenon_H20 zenon_H185 zenon_H2b1 zenon_Hde zenon_H102 zenon_Hd1 zenon_H19e zenon_H103 zenon_H2ed zenon_H135 zenon_H6f zenon_H26 zenon_Hb3 zenon_Hbc zenon_Ha4. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.31 apply (zenon_L148_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.31 apply (zenon_L1294_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.31 apply (zenon_L598_); trivial. % 30.13/30.31 apply (zenon_L1309_); trivial. % 30.13/30.31 (* end of lemma zenon_L1310_ *) % 30.13/30.31 assert (zenon_L1311_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H174 zenon_H64 zenon_H3f zenon_Hb3 zenon_Hcd zenon_Hf5 zenon_H2b1 zenon_He2 zenon_He1 zenon_H172 zenon_H68 zenon_H20 zenon_H19f zenon_H20e zenon_Hbd zenon_Hde zenon_Hb9 zenon_H10d zenon_H1d8 zenon_Hb8 zenon_H142 zenon_H1dc zenon_H14e zenon_H6f zenon_Hd9 zenon_H8d zenon_H185 zenon_H2d. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.31 apply (zenon_L148_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.31 apply (zenon_L1293_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.31 apply (zenon_L1270_); trivial. % 30.13/30.31 apply (zenon_L848_); trivial. % 30.13/30.31 (* end of lemma zenon_L1311_ *) % 30.13/30.31 assert (zenon_L1312_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.31 do 0 intro. intros zenon_He4 zenon_He1 zenon_H89 zenon_Hcd zenon_H68 zenon_Hf5 zenon_H20d zenon_H8b zenon_Hde. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.31 apply (zenon_L232_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.31 apply (zenon_L627_); trivial. % 30.13/30.31 apply (zenon_L288_); trivial. % 30.13/30.31 (* end of lemma zenon_L1312_ *) % 30.13/30.31 assert (zenon_L1313_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 30.13/30.31 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H110 zenon_H20 zenon_H14f zenon_H185 zenon_H2b1 zenon_Hd6 zenon_Hed zenon_H117 zenon_H6f zenon_H1a2 zenon_H73 zenon_H76 zenon_Hcd zenon_Hf5. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.31 apply (zenon_L120_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.31 apply (zenon_L598_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.31 apply (zenon_L159_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.31 apply (zenon_L46_); trivial. % 30.13/30.31 apply (zenon_L1298_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.31 apply (zenon_L23_); trivial. % 30.13/30.31 apply (zenon_L1017_); trivial. % 30.13/30.31 (* end of lemma zenon_L1313_ *) % 30.13/30.31 assert (zenon_L1314_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.13/30.31 do 0 intro. intros zenon_He4 zenon_Hda zenon_Hd9 zenon_Hcd zenon_H68 zenon_Hf5 zenon_H20d zenon_H8b zenon_Hde. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.31 apply (zenon_L47_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.31 apply (zenon_L627_); trivial. % 30.13/30.31 apply (zenon_L288_); trivial. % 30.13/30.31 (* end of lemma zenon_L1314_ *) % 30.13/30.31 assert (zenon_L1315_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 30.13/30.31 do 0 intro. intros zenon_H2ea zenon_He4 zenon_H2d zenon_H2b1 zenon_Hb3 zenon_H3f zenon_Hf5 zenon_H19f zenon_H20e zenon_H142 zenon_H172 zenon_H185 zenon_H20 zenon_H8d zenon_He1 zenon_Hbd zenon_H14e zenon_H1dc zenon_H1d8 zenon_H10d zenon_Hb8 zenon_H6f zenon_Hd9 zenon_H174 zenon_H2ed zenon_H68 zenon_Hcd zenon_Hde zenon_H6b zenon_H225 zenon_H218 zenon_H35 zenon_H208 zenon_H18c zenon_H135 zenon_H156 zenon_H3c zenon_Hc8 zenon_H173 zenon_H20d zenon_H296 zenon_H97 zenon_Hd6 zenon_H1a2 zenon_H110 zenon_H1b1 zenon_H246. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.31 apply (zenon_L1209_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.31 exact (zenon_H2ed zenon_Hc9). % 30.13/30.31 apply (zenon_L1311_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.13/30.31 apply (zenon_L16_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.13/30.31 apply (zenon_L303_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.31 apply (zenon_L1312_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.31 apply (zenon_L1288_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.31 apply (zenon_L149_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.31 apply (zenon_L18_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.31 apply (zenon_L16_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.31 exact (zenon_H19f zenon_Hc3). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.31 apply (zenon_L350_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.31 apply (zenon_L598_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.31 apply (zenon_L147_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.31 apply (zenon_L23_); trivial. % 30.13/30.31 apply (zenon_L1298_); trivial. % 30.13/30.31 apply (zenon_L25_); trivial. % 30.13/30.31 apply (zenon_L848_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.31 apply (zenon_L232_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.31 apply (zenon_L1288_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.31 apply (zenon_L232_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.31 apply (zenon_L18_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.31 apply (zenon_L16_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.31 exact (zenon_H19f zenon_Hc3). % 30.13/30.31 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.31 apply (zenon_L350_); trivial. % 30.13/30.31 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.31 apply (zenon_L48_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.32 apply (zenon_L95_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.32 apply (zenon_L1313_); trivial. % 30.13/30.32 apply (zenon_L91_); trivial. % 30.13/30.32 apply (zenon_L25_); trivial. % 30.13/30.32 apply (zenon_L848_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.32 apply (zenon_L48_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.32 exact (zenon_H2ed zenon_Hc9). % 30.13/30.32 apply (zenon_L288_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.13/30.32 apply (zenon_L1314_); trivial. % 30.13/30.32 apply (zenon_L405_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.13/30.32 apply (zenon_L117_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.13/30.32 apply (zenon_L1292_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.13/30.32 apply (zenon_L1017_); trivial. % 30.13/30.32 apply (zenon_L152_); trivial. % 30.13/30.32 (* end of lemma zenon_L1315_ *) % 30.13/30.32 assert (zenon_L1316_ : ((op (e2) (e1)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H3d zenon_H25 zenon_H2ea zenon_He4 zenon_H2d zenon_H2b1 zenon_Hb3 zenon_H3f zenon_H19f zenon_H20e zenon_H142 zenon_H172 zenon_H185 zenon_H20 zenon_H8d zenon_He1 zenon_Hbd zenon_H14e zenon_H1dc zenon_H1d8 zenon_H10d zenon_Hb8 zenon_H6f zenon_Hd9 zenon_H174 zenon_H2ed zenon_H68 zenon_Hcd zenon_Hde zenon_H6b zenon_H225 zenon_H218 zenon_H35 zenon_H208 zenon_H18c zenon_H135 zenon_H156 zenon_H3c zenon_Hc8 zenon_H173 zenon_H20d zenon_H296 zenon_H97 zenon_Hd6 zenon_H1a2 zenon_H110 zenon_H1b1 zenon_H246. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.32 exact (zenon_H2ed zenon_Hc9). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.32 apply (zenon_L126_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.32 apply (zenon_L44_); trivial. % 30.13/30.32 apply (zenon_L1315_); trivial. % 30.13/30.32 (* end of lemma zenon_L1316_ *) % 30.13/30.32 assert (zenon_L1317_ : ((op (e1) (e3)) = (e0)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H14f zenon_H9b zenon_H222 zenon_H64 zenon_H102 zenon_Hd1 zenon_H19e zenon_H103 zenon_Hbc zenon_Ha4 zenon_H246 zenon_H1b1 zenon_H110 zenon_H1a2 zenon_Hd6 zenon_H97 zenon_H296 zenon_H20d zenon_H173 zenon_Hc8 zenon_H156 zenon_H18c zenon_H208 zenon_H35 zenon_H218 zenon_H225 zenon_H6b zenon_H68 zenon_H174 zenon_Hd9 zenon_H6f zenon_Hb8 zenon_H10d zenon_H1d8 zenon_H1dc zenon_H14e zenon_Hbd zenon_He1 zenon_H8d zenon_H20 zenon_H185 zenon_H172 zenon_H20e zenon_H19f zenon_H3f zenon_Hb3 zenon_H2b1 zenon_H2d zenon_He4 zenon_H2ea zenon_H3d zenon_H135 zenon_H2ed zenon_H3c zenon_He9 zenon_Hde zenon_H142 zenon_Hcd. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.32 apply (zenon_L120_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.32 apply (zenon_L1310_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.32 apply (zenon_L147_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.32 apply (zenon_L46_); trivial. % 30.13/30.32 apply (zenon_L1299_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.32 apply (zenon_L1316_); trivial. % 30.13/30.32 apply (zenon_L1265_); trivial. % 30.13/30.32 (* end of lemma zenon_L1317_ *) % 30.13/30.32 assert (zenon_L1318_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H1a2 zenon_H6f zenon_H117 zenon_H3d zenon_H19e zenon_H100 zenon_H9d zenon_Hfc zenon_H19f zenon_H102 zenon_Hd6 zenon_Hd5 zenon_H135 zenon_H2ed zenon_H222 zenon_H9b zenon_Hde zenon_H142 zenon_H2b1 zenon_H185 zenon_H14f zenon_H20 zenon_Hcd zenon_H110. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.32 apply (zenon_L598_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.32 apply (zenon_L132_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.32 apply (zenon_L46_); trivial. % 30.13/30.32 apply (zenon_L1299_); trivial. % 30.13/30.32 (* end of lemma zenon_L1318_ *) % 30.13/30.32 assert (zenon_L1319_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> False). % 30.13/30.32 do 0 intro. intros zenon_H135 zenon_H2ed zenon_H9d zenon_H222 zenon_Hde zenon_H142 zenon_Hcd zenon_H1e5. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.32 exact (zenon_H2ed zenon_Hc9). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.32 apply (zenon_L264_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.32 apply (zenon_L89_); trivial. % 30.13/30.32 apply (zenon_L1017_); trivial. % 30.13/30.32 (* end of lemma zenon_L1319_ *) % 30.13/30.32 assert (zenon_L1320_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H23b zenon_H20 zenon_H8b zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hbc zenon_H6f. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.32 apply (zenon_L27_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.32 apply (zenon_L336_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.32 apply (zenon_L337_); trivial. % 30.13/30.32 apply (zenon_L152_); trivial. % 30.13/30.32 (* end of lemma zenon_L1320_ *) % 30.13/30.32 assert (zenon_L1321_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.13/30.32 do 0 intro. intros zenon_Hc0 zenon_Hcd zenon_H73 zenon_H6f zenon_Hbc zenon_Hee zenon_H3f zenon_H8b zenon_H23b zenon_H1a5 zenon_H19a zenon_H185 zenon_H20. % 30.13/30.32 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.13/30.32 apply (zenon_L998_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.13/30.32 apply (zenon_L1320_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.13/30.32 apply (zenon_L136_); trivial. % 30.13/30.32 apply (zenon_L117_); trivial. % 30.13/30.32 (* end of lemma zenon_L1321_ *) % 30.13/30.32 assert (zenon_L1322_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> (~((e0) = (e2))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H156 zenon_H102 zenon_Hd1 zenon_H19e zenon_H103 zenon_H159 zenon_H42 zenon_H3c zenon_H2ea zenon_Hb3 zenon_Hbd zenon_H14e zenon_H1dc zenon_H1d8 zenon_H10d zenon_Hb8 zenon_Hd9 zenon_H225 zenon_H218 zenon_H35 zenon_H208 zenon_H18c zenon_Hc8 zenon_H173 zenon_H20d zenon_H1b1 zenon_H246 zenon_H113 zenon_H101 zenon_Ha4 zenon_H100 zenon_Hfc zenon_H6b zenon_He4 zenon_H2d zenon_H185 zenon_H8d zenon_He1 zenon_H110 zenon_H20 zenon_H2b1 zenon_H142 zenon_H9b zenon_H222 zenon_H135 zenon_Hc0 zenon_H6f zenon_Hee zenon_H3f zenon_H23b zenon_H1a5 zenon_H1a2 zenon_H20e zenon_H19f zenon_H172 zenon_H17d zenon_Hbc zenon_H296 zenon_Hd6 zenon_H97 zenon_H174 zenon_Hcd zenon_H68 zenon_H2ed zenon_Hde. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.32 apply (zenon_L148_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.32 apply (zenon_L1294_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.32 apply (zenon_L149_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.32 apply (zenon_L18_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.32 apply (zenon_L16_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.32 exact (zenon_H19f zenon_Hc3). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.32 apply (zenon_L350_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.32 apply (zenon_L48_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.32 apply (zenon_L1294_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.32 exact (zenon_H103 zenon_H37). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.32 apply (zenon_L79_); trivial. % 30.13/30.32 apply (zenon_L753_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.32 apply (zenon_L1294_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.32 exact (zenon_H103 zenon_H37). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.32 apply (zenon_L1317_); trivial. % 30.13/30.32 apply (zenon_L753_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.32 apply (zenon_L58_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.32 apply (zenon_L1258_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.32 apply (zenon_L1294_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.32 exact (zenon_H103 zenon_H37). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.32 apply (zenon_L157_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.32 apply (zenon_L1318_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.32 apply (zenon_L1316_); trivial. % 30.13/30.32 apply (zenon_L1319_); trivial. % 30.13/30.32 apply (zenon_L753_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.32 apply (zenon_L1294_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.32 exact (zenon_H103 zenon_H37). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.32 apply (zenon_L157_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.32 apply (zenon_L1262_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.32 apply (zenon_L1316_); trivial. % 30.13/30.32 apply (zenon_L1265_); trivial. % 30.13/30.32 apply (zenon_L753_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.32 apply (zenon_L93_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.32 apply (zenon_L1258_); trivial. % 30.13/30.32 apply (zenon_L330_); trivial. % 30.13/30.32 apply (zenon_L110_); trivial. % 30.13/30.32 apply (zenon_L848_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.13/30.32 apply (zenon_L16_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.13/30.32 apply (zenon_L303_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.13/30.32 apply (zenon_L232_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.13/30.32 apply (zenon_L1288_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.32 apply (zenon_L232_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.32 apply (zenon_L18_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.32 apply (zenon_L16_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.32 exact (zenon_H19f zenon_Hc3). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.32 apply (zenon_L350_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.13/30.32 apply (zenon_L598_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.13/30.32 apply (zenon_L1321_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.13/30.32 apply (zenon_L23_); trivial. % 30.13/30.32 apply (zenon_L1299_); trivial. % 30.13/30.32 apply (zenon_L110_); trivial. % 30.13/30.32 apply (zenon_L848_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.32 apply (zenon_L48_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.32 exact (zenon_H2ed zenon_Hc9). % 30.13/30.32 apply (zenon_L288_); trivial. % 30.13/30.32 (* end of lemma zenon_L1322_ *) % 30.13/30.32 assert (zenon_L1323_ : (((op (e0) (op (e0) (e0))) = (e0))/\(((op (e0) (op (e0) (e1))) = (e1))/\(((op (e0) (op (e0) (e2))) = (e2))/\(((op (e0) (op (e0) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1)))/\(((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2)))/\((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3)))))))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.13/30.32 do 0 intro. intros zenon_H2ec zenon_H2fb zenon_Hb1. % 30.13/30.32 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.13/30.32 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.13/30.32 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.13/30.32 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.13/30.32 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.13/30.32 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.13/30.32 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.13/30.32 exact (zenon_H122 zenon_Hb1). % 30.13/30.32 exact (zenon_H2fb zenon_H8a). % 30.13/30.32 (* end of lemma zenon_L1323_ *) % 30.13/30.32 assert (zenon_L1324_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H8d zenon_H64 zenon_H2d zenon_H6f zenon_H68 zenon_He1 zenon_Hc9 zenon_H2fb. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.32 apply (zenon_L148_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.32 apply (zenon_L18_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.32 apply (zenon_L273_); trivial. % 30.13/30.32 exact (zenon_H2fb zenon_H8a). % 30.13/30.32 (* end of lemma zenon_L1324_ *) % 30.13/30.32 assert (zenon_L1325_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H8d zenon_H64 zenon_H2d zenon_Hb1 zenon_H48 zenon_H14e zenon_H4e zenon_H18c zenon_Had zenon_H4c zenon_He2 zenon_H19f zenon_H20 zenon_H68 zenon_H172 zenon_H2fb. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.32 apply (zenon_L148_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.32 apply (zenon_L770_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.32 apply (zenon_L1244_); trivial. % 30.13/30.32 exact (zenon_H2fb zenon_H8a). % 30.13/30.32 (* end of lemma zenon_L1325_ *) % 30.13/30.32 assert (zenon_L1326_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.13/30.32 do 0 intro. intros zenon_He4 zenon_Hde zenon_Hcd zenon_He1 zenon_H6f zenon_H8d zenon_H64 zenon_H2d zenon_Hb1 zenon_H48 zenon_H14e zenon_H4e zenon_H18c zenon_Had zenon_H4c zenon_H19f zenon_H20 zenon_H68 zenon_H172 zenon_H2fb. % 30.13/30.32 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.32 apply (zenon_L1209_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.32 apply (zenon_L48_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.32 apply (zenon_L1324_); trivial. % 30.13/30.32 apply (zenon_L1325_); trivial. % 30.13/30.32 (* end of lemma zenon_L1326_ *) % 30.13/30.32 assert (zenon_L1327_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.13/30.32 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H35 zenon_H1e zenon_He2 zenon_H4c zenon_Had zenon_H18c zenon_H4e zenon_H76. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.32 apply (zenon_L740_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.32 apply (zenon_L42_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.32 apply (zenon_L742_); trivial. % 30.13/30.32 apply (zenon_L864_); trivial. % 30.13/30.32 (* end of lemma zenon_L1327_ *) % 30.13/30.32 assert (zenon_L1328_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H8d zenon_H15a zenon_Hb1 zenon_H14e zenon_H4e zenon_H18c zenon_Had zenon_H4c zenon_He2 zenon_H1e zenon_H35 zenon_H48 zenon_Hdf zenon_H172 zenon_H2fb. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.32 apply (zenon_L745_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.32 apply (zenon_L770_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.32 apply (zenon_L1327_); trivial. % 30.13/30.32 exact (zenon_H2fb zenon_H8a). % 30.13/30.32 (* end of lemma zenon_L1328_ *) % 30.13/30.32 assert (zenon_L1329_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H246 zenon_H2d zenon_H2fb zenon_H172 zenon_H48 zenon_H35 zenon_H1e zenon_H4c zenon_Had zenon_H18c zenon_H4e zenon_H14e zenon_H15a zenon_H8d zenon_Hde zenon_H68 zenon_Hcd zenon_He1 zenon_H6f zenon_H2fc zenon_H19f zenon_H20 zenon_He4 zenon_Hb1 zenon_H17d. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.13/30.32 apply (zenon_L1326_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.13/30.32 apply (zenon_L16_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.32 apply (zenon_L232_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.32 apply (zenon_L18_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.32 apply (zenon_L16_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.32 exact (zenon_H19f zenon_Hc3). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H8b | zenon_intro zenon_H2fd ]. % 30.13/30.32 apply (zenon_L772_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H90 | zenon_intro zenon_H2fe ]. % 30.13/30.32 apply (zenon_L639_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_He2 | zenon_intro zenon_H8a ]. % 30.13/30.32 apply (zenon_L742_); trivial. % 30.13/30.32 exact (zenon_H2fb zenon_H8a). % 30.13/30.32 apply (zenon_L864_); trivial. % 30.13/30.32 exact (zenon_H2fb zenon_H8a). % 30.13/30.32 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.13/30.32 apply (zenon_L48_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.13/30.32 apply (zenon_L49_); trivial. % 30.13/30.32 apply (zenon_L1328_); trivial. % 30.13/30.32 apply (zenon_L772_); trivial. % 30.13/30.32 (* end of lemma zenon_L1329_ *) % 30.13/30.32 assert (zenon_L1330_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.13/30.32 do 0 intro. intros zenon_H172 zenon_H68 zenon_H20 zenon_H19f zenon_H10e zenon_H1a5 zenon_H14e zenon_Hb1. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.32 apply (zenon_L16_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.32 exact (zenon_H19f zenon_Hc3). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.32 apply (zenon_L764_); trivial. % 30.13/30.32 apply (zenon_L84_); trivial. % 30.13/30.32 (* end of lemma zenon_L1330_ *) % 30.13/30.32 assert (zenon_L1331_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H2c zenon_H35. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.13/30.32 exact (zenon_H19f zenon_Hc3). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.13/30.32 apply (zenon_L45_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.13/30.32 exact (zenon_H13b zenon_Hfd). % 30.13/30.32 apply (zenon_L1002_); trivial. % 30.13/30.32 (* end of lemma zenon_L1331_ *) % 30.13/30.32 assert (zenon_L1332_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.13/30.32 do 0 intro. intros zenon_Hb8 zenon_H2fb zenon_H100 zenon_H37 zenon_H10d zenon_H117 zenon_Hb1 zenon_H2d. % 30.13/30.32 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.13/30.32 exact (zenon_H2fb zenon_H8a). % 30.13/30.32 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.13/30.32 apply (zenon_L150_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.13/30.32 apply (zenon_L151_); trivial. % 30.13/30.32 apply (zenon_L107_); trivial. % 30.13/30.32 (* end of lemma zenon_L1332_ *) % 30.13/30.32 assert (zenon_L1333_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 30.13/30.32 do 0 intro. intros zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H19e zenon_H3d. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.13/30.32 exact (zenon_H19f zenon_Hc3). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.13/30.32 apply (zenon_L45_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.13/30.32 exact (zenon_H13b zenon_Hfd). % 30.13/30.32 apply (zenon_L131_); trivial. % 30.13/30.32 (* end of lemma zenon_L1333_ *) % 30.13/30.32 assert (zenon_L1334_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H40 zenon_H100. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.13/30.32 exact (zenon_H19f zenon_Hc3). % 30.13/30.32 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.13/30.32 apply (zenon_L45_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.13/30.32 exact (zenon_H13b zenon_Hfd). % 30.13/30.32 apply (zenon_L150_); trivial. % 30.13/30.32 (* end of lemma zenon_L1334_ *) % 30.13/30.32 assert (zenon_L1335_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H42 zenon_H35 zenon_H2d zenon_Hb1 zenon_H117 zenon_H10d zenon_H2fb zenon_Hb8 zenon_H19e zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H100. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.32 apply (zenon_L1331_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.32 apply (zenon_L1332_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.32 apply (zenon_L1333_); trivial. % 30.13/30.32 apply (zenon_L1334_); trivial. % 30.13/30.32 (* end of lemma zenon_L1335_ *) % 30.13/30.32 assert (zenon_L1336_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H42 zenon_H35 zenon_H1af zenon_H60 zenon_He9 zenon_H3c zenon_H5e zenon_H1f zenon_H18c zenon_H208 zenon_H19e zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H100. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.32 apply (zenon_L1331_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.32 apply (zenon_L454_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.32 apply (zenon_L1333_); trivial. % 30.13/30.32 apply (zenon_L1334_); trivial. % 30.13/30.32 (* end of lemma zenon_L1336_ *) % 30.13/30.32 assert (zenon_L1337_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> False). % 30.13/30.32 do 0 intro. intros zenon_H222 zenon_H1af zenon_H1e5 zenon_H40. % 30.13/30.32 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 30.13/30.32 intro zenon_D_pnotp. % 30.13/30.32 apply zenon_H222. % 30.13/30.32 rewrite <- zenon_D_pnotp. % 30.13/30.32 exact zenon_H1af. % 30.13/30.32 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 30.13/30.32 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 30.13/30.32 congruence. % 30.13/30.32 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ]. % 30.13/30.32 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e1)))). % 30.13/30.32 intro zenon_D_pnotp. % 30.13/30.32 apply zenon_H207. % 30.13/30.32 rewrite <- zenon_D_pnotp. % 30.13/30.32 exact zenon_H62. % 30.13/30.32 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 30.13/30.32 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H204]. % 30.13/30.32 congruence. % 30.13/30.32 apply (zenon_L213_); trivial. % 30.13/30.32 apply zenon_H63. apply refl_equal. % 30.13/30.32 apply zenon_H63. apply refl_equal. % 30.13/30.32 apply zenon_H41. apply sym_equal. exact zenon_H40. % 30.13/30.32 (* end of lemma zenon_L1337_ *) % 30.13/30.32 assert (zenon_L1338_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H40 zenon_H222 zenon_H20e zenon_H15e zenon_H1af zenon_H16b zenon_H218. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.13/30.32 apply (zenon_L690_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.13/30.32 apply (zenon_L1337_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.13/30.32 apply (zenon_L358_); trivial. % 30.13/30.32 apply (zenon_L245_); trivial. % 30.13/30.32 (* end of lemma zenon_L1338_ *) % 30.13/30.32 assert (zenon_L1339_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H42 zenon_H35 zenon_Hfc zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H222 zenon_H20e zenon_H15e zenon_H1af zenon_H16b zenon_H218. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.32 apply (zenon_L1331_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.32 apply (zenon_L203_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.32 apply (zenon_L1333_); trivial. % 30.13/30.32 apply (zenon_L1338_); trivial. % 30.13/30.32 (* end of lemma zenon_L1339_ *) % 30.13/30.32 assert (zenon_L1340_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H19e zenon_H37 zenon_H6b zenon_H76 zenon_H1af zenon_H16c zenon_H156. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.13/30.32 apply (zenon_L690_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.13/30.32 apply (zenon_L214_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.13/30.32 apply (zenon_L193_); trivial. % 30.13/30.32 apply (zenon_L290_); trivial. % 30.13/30.32 (* end of lemma zenon_L1340_ *) % 30.13/30.32 assert (zenon_L1341_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H42 zenon_H35 zenon_H156 zenon_H16c zenon_H1af zenon_H76 zenon_H6b zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H19e zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H100. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.32 apply (zenon_L1331_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.32 apply (zenon_L1340_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.32 apply (zenon_L1333_); trivial. % 30.13/30.32 apply (zenon_L1334_); trivial. % 30.13/30.32 (* end of lemma zenon_L1341_ *) % 30.13/30.32 assert (zenon_L1342_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H16f zenon_H6f zenon_Hfe zenon_Hcd zenon_H55 zenon_H18c zenon_H208 zenon_H218 zenon_H16b zenon_H20e zenon_H222 zenon_Hfc zenon_H42 zenon_H35 zenon_H156 zenon_H1af zenon_H76 zenon_H6b zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H19e zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H100. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.13/30.32 apply (zenon_L18_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.13/30.32 apply (zenon_L603_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.13/30.32 apply (zenon_L1339_); trivial. % 30.13/30.32 apply (zenon_L1341_); trivial. % 30.13/30.32 (* end of lemma zenon_L1342_ *) % 30.13/30.32 assert (zenon_L1343_ : ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H1af zenon_H1c5 zenon_H76 zenon_H20d. % 30.13/30.32 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 30.13/30.32 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 30.13/30.32 intro zenon_D_pnotp. % 30.13/30.32 apply zenon_H20d. % 30.13/30.32 rewrite <- zenon_D_pnotp. % 30.13/30.32 exact zenon_H109. % 30.13/30.32 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 30.13/30.32 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2ff]. % 30.13/30.32 congruence. % 30.13/30.32 cut (((op (e2) (op (e2) (e3))) = (e3)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 30.13/30.32 intro zenon_D_pnotp. % 30.13/30.32 apply zenon_H2ff. % 30.13/30.32 rewrite <- zenon_D_pnotp. % 30.13/30.32 exact zenon_H1af. % 30.13/30.32 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 30.13/30.32 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 30.13/30.32 congruence. % 30.13/30.32 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H109 | zenon_intro zenon_H10a ]. % 30.13/30.32 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (op (e2) (e3))) = (op (e2) (e3)))). % 30.13/30.32 intro zenon_D_pnotp. % 30.13/30.32 apply zenon_H1c9. % 30.13/30.32 rewrite <- zenon_D_pnotp. % 30.13/30.32 exact zenon_H109. % 30.13/30.32 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 30.13/30.32 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 30.13/30.32 congruence. % 30.13/30.32 apply (zenon_L166_); trivial. % 30.13/30.32 apply zenon_H10a. apply refl_equal. % 30.13/30.32 apply zenon_H10a. apply refl_equal. % 30.13/30.32 apply zenon_H1da. apply sym_equal. exact zenon_H76. % 30.13/30.32 apply zenon_H10a. apply refl_equal. % 30.13/30.32 apply zenon_H10a. apply refl_equal. % 30.13/30.32 (* end of lemma zenon_L1343_ *) % 30.13/30.32 assert (zenon_L1344_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H1e6 zenon_Hdf zenon_H19e zenon_H37 zenon_H218 zenon_H17b zenon_H1af zenon_H76 zenon_H20d. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.13/30.32 apply (zenon_L548_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.13/30.32 apply (zenon_L214_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.13/30.32 apply (zenon_L405_); trivial. % 30.13/30.32 apply (zenon_L1343_); trivial. % 30.13/30.32 (* end of lemma zenon_L1344_ *) % 30.13/30.32 assert (zenon_L1345_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H25 zenon_H108 zenon_H218 zenon_H17b zenon_H1af zenon_H3d zenon_H1c7. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.13/30.32 apply (zenon_L690_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.13/30.32 apply (zenon_L1274_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.13/30.32 apply (zenon_L405_); trivial. % 30.13/30.32 apply (zenon_L167_); trivial. % 30.13/30.32 (* end of lemma zenon_L1345_ *) % 30.13/30.32 assert (zenon_L1346_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H1d5 zenon_H20d zenon_H37 zenon_H19e zenon_Hdf zenon_H1c7 zenon_H17b zenon_H108 zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H6f zenon_H25 zenon_H1af zenon_H16b zenon_H218. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.13/30.32 apply (zenon_L1344_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.13/30.32 apply (zenon_L1345_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.13/30.32 apply (zenon_L1138_); trivial. % 30.13/30.32 apply (zenon_L245_); trivial. % 30.13/30.32 (* end of lemma zenon_L1346_ *) % 30.13/30.32 assert (zenon_L1347_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H25 zenon_H108 zenon_H156 zenon_H155 zenon_H1af zenon_H76 zenon_H20d. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.13/30.32 apply (zenon_L690_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.13/30.32 apply (zenon_L1274_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.13/30.32 apply (zenon_L90_); trivial. % 30.13/30.32 apply (zenon_L1343_); trivial. % 30.13/30.32 (* end of lemma zenon_L1347_ *) % 30.13/30.32 assert (zenon_L1348_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H267 zenon_H218 zenon_H16b zenon_H6f zenon_Hdf zenon_H19e zenon_H37 zenon_H1d5 zenon_H20d zenon_H76 zenon_H1af zenon_H156 zenon_H108 zenon_H25 zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H55 zenon_H1c7 zenon_He2 zenon_H17d. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.13/30.32 apply (zenon_L1346_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.13/30.32 apply (zenon_L1347_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.13/30.32 apply (zenon_L1253_); trivial. % 30.13/30.32 apply (zenon_L847_); trivial. % 30.13/30.32 (* end of lemma zenon_L1348_ *) % 30.13/30.32 assert (zenon_L1349_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_Hcd zenon_H17d zenon_He2 zenon_H1c7 zenon_H55 zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H108 zenon_H156 zenon_H76 zenon_H20d zenon_H1d5 zenon_Hdf zenon_H6f zenon_H16b zenon_H218 zenon_H267 zenon_H1af zenon_H37 zenon_H19e. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.32 apply (zenon_L120_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.32 apply (zenon_L212_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.32 apply (zenon_L1348_); trivial. % 30.13/30.32 apply (zenon_L214_); trivial. % 30.13/30.32 (* end of lemma zenon_L1349_ *) % 30.13/30.32 assert (zenon_L1350_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H135 zenon_H1d8 zenon_H19e zenon_H37 zenon_H267 zenon_H218 zenon_H16b zenon_H6f zenon_Hdf zenon_H1d5 zenon_H20d zenon_H156 zenon_H108 zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H1c7 zenon_He2 zenon_H17d zenon_Hcd zenon_H18c zenon_H68 zenon_H208 zenon_Hd0 zenon_H1af zenon_H76 zenon_H6b. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.32 apply (zenon_L307_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.32 apply (zenon_L1349_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.32 exact (zenon_Hd0 zenon_Hcc). % 30.13/30.32 apply (zenon_L193_); trivial. % 30.13/30.32 (* end of lemma zenon_L1350_ *) % 30.13/30.32 assert (zenon_L1351_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.32 do 0 intro. intros zenon_H16f zenon_Hfe zenon_H1bd zenon_H5e zenon_Hd5 zenon_H135 zenon_H1d8 zenon_H267 zenon_H6f zenon_H1d5 zenon_H20d zenon_H108 zenon_H1c7 zenon_He2 zenon_H17d zenon_Hcd zenon_H18c zenon_H208 zenon_Hd0 zenon_H200 zenon_H218 zenon_H16b zenon_H20e zenon_H222 zenon_Hfc zenon_H42 zenon_H35 zenon_H156 zenon_H1af zenon_H76 zenon_H6b zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H19e zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H100. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.13/30.32 apply (zenon_L18_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.13/30.32 apply (zenon_L1350_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.13/30.32 apply (zenon_L608_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.13/30.32 apply (zenon_L350_); trivial. % 30.13/30.32 apply (zenon_L690_); trivial. % 30.13/30.32 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.13/30.32 apply (zenon_L1339_); trivial. % 30.13/30.32 apply (zenon_L1341_); trivial. % 30.13/30.32 (* end of lemma zenon_L1351_ *) % 30.13/30.32 assert (zenon_L1352_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H42 zenon_H35 zenon_H1af zenon_Hfe zenon_H222 zenon_H5e zenon_H18c zenon_H208 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H6f zenon_H98. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.33 apply (zenon_L1331_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.33 apply (zenon_L612_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.33 apply (zenon_L1333_); trivial. % 30.13/30.33 apply (zenon_L80_); trivial. % 30.13/30.33 (* end of lemma zenon_L1352_ *) % 30.13/30.33 assert (zenon_L1353_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H8d zenon_H64 zenon_H2d zenon_Hb1 zenon_H14e zenon_H124 zenon_H60 zenon_H3c zenon_H101 zenon_H100 zenon_H1e6 zenon_Hf6 zenon_H6b zenon_H156 zenon_Hfc zenon_H20e zenon_H16b zenon_H218 zenon_H200 zenon_Hd0 zenon_Hcd zenon_H17d zenon_He2 zenon_H1c7 zenon_H108 zenon_H20d zenon_H1d5 zenon_H267 zenon_H1d8 zenon_H135 zenon_H1bd zenon_H16f zenon_H42 zenon_H35 zenon_H1af zenon_H222 zenon_H5e zenon_H18c zenon_H208 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H6f zenon_H20 zenon_H172 zenon_H2fb. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.33 apply (zenon_L148_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.33 apply (zenon_L18_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.33 apply (zenon_L16_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.33 exact (zenon_H19f zenon_Hc3). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.33 apply (zenon_L1336_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.33 exact (zenon_H13b zenon_Hfd). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.33 apply (zenon_L1342_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.13/30.33 apply (zenon_L18_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.13/30.33 apply (zenon_L320_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.13/30.33 apply (zenon_L1339_); trivial. % 30.13/30.33 apply (zenon_L1341_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.33 apply (zenon_L45_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.33 apply (zenon_L1351_); trivial. % 30.13/30.33 apply (zenon_L1352_); trivial. % 30.13/30.33 apply (zenon_L84_); trivial. % 30.13/30.33 exact (zenon_H2fb zenon_H8a). % 30.13/30.33 (* end of lemma zenon_L1353_ *) % 30.13/30.33 assert (zenon_L1354_ : (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> False). % 30.13/30.33 do 0 intro. intros zenon_He1 zenon_H40 zenon_H9d. % 30.13/30.33 cut (((op (e3) (e1)) = (e3)) = ((e2) = (e3))). % 30.13/30.33 intro zenon_D_pnotp. % 30.13/30.33 apply zenon_He1. % 30.13/30.33 rewrite <- zenon_D_pnotp. % 30.13/30.33 exact zenon_H40. % 30.13/30.33 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.13/30.33 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H300]. % 30.13/30.33 congruence. % 30.13/30.33 exact (zenon_H300 zenon_H9d). % 30.13/30.33 apply zenon_H2f. apply refl_equal. % 30.13/30.33 (* end of lemma zenon_L1354_ *) % 30.13/30.33 assert (zenon_L1355_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_Hb1 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_He1 zenon_H9d. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.33 apply (zenon_L4_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.33 apply (zenon_L320_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.33 apply (zenon_L1333_); trivial. % 30.13/30.33 apply (zenon_L1354_); trivial. % 30.13/30.33 (* end of lemma zenon_L1355_ *) % 30.13/30.33 assert (zenon_L1356_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H101 zenon_H1f zenon_H5e zenon_H3c zenon_H60 zenon_H35 zenon_H100 zenon_H208 zenon_H18c zenon_Hcd zenon_Hfe zenon_H1af zenon_H42 zenon_H2d zenon_H1e zenon_Hb1 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_He1. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.33 apply (zenon_L1336_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.33 exact (zenon_H13b zenon_Hfd). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.33 apply (zenon_L4_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.33 apply (zenon_L603_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.33 apply (zenon_L126_); trivial. % 30.13/30.33 apply (zenon_L1334_); trivial. % 30.13/30.33 apply (zenon_L1355_); trivial. % 30.13/30.33 (* end of lemma zenon_L1356_ *) % 30.13/30.33 assert (zenon_L1357_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H124 zenon_He1 zenon_H1e zenon_H2d zenon_H60 zenon_H3c zenon_H101 zenon_H100 zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H6b zenon_H76 zenon_H156 zenon_Hfc zenon_H20e zenon_H16b zenon_H218 zenon_H200 zenon_Hd0 zenon_Hcd zenon_H17d zenon_He2 zenon_H1c7 zenon_H108 zenon_H20d zenon_H1d5 zenon_H267 zenon_H1d8 zenon_H135 zenon_H1bd zenon_H16f zenon_H42 zenon_H35 zenon_H1af zenon_Hfe zenon_H222 zenon_H5e zenon_H18c zenon_H208 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H6f. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.33 apply (zenon_L1356_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.33 apply (zenon_L45_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.33 apply (zenon_L1351_); trivial. % 30.13/30.33 apply (zenon_L1352_); trivial. % 30.13/30.33 (* end of lemma zenon_L1357_ *) % 30.13/30.33 assert (zenon_L1358_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H172 zenon_H20 zenon_H6f zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H19e zenon_H208 zenon_H18c zenon_H5e zenon_H222 zenon_H1af zenon_H35 zenon_H42 zenon_H16f zenon_H1bd zenon_H135 zenon_H1d8 zenon_H267 zenon_H1d5 zenon_H20d zenon_H108 zenon_H1c7 zenon_He2 zenon_H17d zenon_Hcd zenon_Hd0 zenon_H200 zenon_H218 zenon_H16b zenon_H20e zenon_Hfc zenon_H156 zenon_H76 zenon_H6b zenon_Hf6 zenon_H1e6 zenon_H100 zenon_H101 zenon_H3c zenon_H60 zenon_H2d zenon_H1e zenon_He1 zenon_H124 zenon_H14e zenon_Hb1. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.33 apply (zenon_L16_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.33 exact (zenon_H19f zenon_Hc3). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.33 apply (zenon_L1357_); trivial. % 30.13/30.33 apply (zenon_L84_); trivial. % 30.13/30.33 (* end of lemma zenon_L1358_ *) % 30.13/30.33 assert (zenon_L1359_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H8d zenon_H64 zenon_Hb1 zenon_H14e zenon_H124 zenon_He1 zenon_H1e zenon_H2d zenon_H60 zenon_H3c zenon_H101 zenon_H100 zenon_H1e6 zenon_Hf6 zenon_H6b zenon_H156 zenon_Hfc zenon_H20e zenon_H16b zenon_H218 zenon_H200 zenon_Hd0 zenon_Hcd zenon_H17d zenon_He2 zenon_H1c7 zenon_H108 zenon_H20d zenon_H1d5 zenon_H267 zenon_H1d8 zenon_H135 zenon_H1bd zenon_H16f zenon_H42 zenon_H35 zenon_H1af zenon_H222 zenon_H5e zenon_H18c zenon_H208 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H6f zenon_H20 zenon_H172 zenon_H2fb. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.13/30.33 apply (zenon_L148_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.13/30.33 apply (zenon_L18_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.13/30.33 apply (zenon_L1358_); trivial. % 30.13/30.33 exact (zenon_H2fb zenon_H8a). % 30.13/30.33 (* end of lemma zenon_L1359_ *) % 30.13/30.33 assert (zenon_L1360_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H23b zenon_Had zenon_H19e zenon_H37 zenon_H1af zenon_Hfe zenon_H222 zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_H1b9 zenon_Hb1 zenon_He2 zenon_H89. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.33 apply (zenon_L639_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.33 apply (zenon_L612_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.33 apply (zenon_L751_); trivial. % 30.13/30.33 apply (zenon_L252_); trivial. % 30.13/30.33 (* end of lemma zenon_L1360_ *) % 30.13/30.33 assert (zenon_L1361_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H42 zenon_H35 zenon_H15e zenon_Hfc zenon_H19e zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H100. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.33 apply (zenon_L1331_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.33 apply (zenon_L203_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.33 apply (zenon_L1333_); trivial. % 30.13/30.33 apply (zenon_L1334_); trivial. % 30.13/30.33 (* end of lemma zenon_L1361_ *) % 30.13/30.33 assert (zenon_L1362_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H172 zenon_H20 zenon_H6f zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H19e zenon_H208 zenon_H18c zenon_H5e zenon_H222 zenon_H1af zenon_H35 zenon_H42 zenon_H16f zenon_H15a zenon_Hde zenon_Hdf zenon_Hfc zenon_H2d zenon_H1e zenon_He1 zenon_H23b zenon_Had zenon_He2 zenon_H89 zenon_Hd6 zenon_H1e6 zenon_Hf6 zenon_H6b zenon_H156 zenon_H1d5 zenon_Hd0 zenon_Hcd zenon_H1d8 zenon_H135 zenon_H100 zenon_H101 zenon_H3c zenon_H60 zenon_H124 zenon_H14e zenon_Hb1. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.33 apply (zenon_L16_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.33 exact (zenon_H19f zenon_Hc3). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.33 apply (zenon_L1356_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.33 apply (zenon_L45_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.13/30.33 apply (zenon_L241_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.33 apply (zenon_L49_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.33 apply (zenon_L212_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.33 exact (zenon_Hd0 zenon_Hcc). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.13/30.33 apply (zenon_L193_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.13/30.33 apply (zenon_L144_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.13/30.33 apply (zenon_L1360_); trivial. % 30.13/30.33 apply (zenon_L221_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.13/30.33 apply (zenon_L1361_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.33 apply (zenon_L4_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.13/30.33 apply (zenon_L307_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.13/30.33 apply (zenon_L603_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.13/30.33 exact (zenon_Hd0 zenon_Hcc). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.13/30.33 apply (zenon_L1340_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.13/30.33 apply (zenon_L144_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.13/30.33 apply (zenon_L1360_); trivial. % 30.13/30.33 apply (zenon_L221_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.33 apply (zenon_L1333_); trivial. % 30.13/30.33 apply (zenon_L1334_); trivial. % 30.13/30.33 apply (zenon_L1352_); trivial. % 30.13/30.33 apply (zenon_L84_); trivial. % 30.13/30.33 (* end of lemma zenon_L1362_ *) % 30.13/30.33 assert (zenon_L1363_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H42 zenon_H35 zenon_H1af zenon_H60 zenon_He9 zenon_H3c zenon_H5e zenon_H1f zenon_H76 zenon_H6f zenon_H208 zenon_H19e zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H100. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.33 apply (zenon_L1331_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.33 apply (zenon_L220_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.33 apply (zenon_L1333_); trivial. % 30.13/30.33 apply (zenon_L1334_); trivial. % 30.13/30.33 (* end of lemma zenon_L1363_ *) % 30.13/30.33 assert (zenon_L1364_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H101 zenon_H100 zenon_H208 zenon_H6f zenon_H76 zenon_H1f zenon_H5e zenon_H3c zenon_H60 zenon_H1af zenon_H35 zenon_Hcc zenon_Hd6 zenon_H42 zenon_H2d zenon_H1e zenon_Hb1 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_He1. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.33 apply (zenon_L1363_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.33 exact (zenon_H13b zenon_Hfd). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.33 apply (zenon_L555_); trivial. % 30.13/30.33 apply (zenon_L1355_); trivial. % 30.13/30.33 (* end of lemma zenon_L1364_ *) % 30.13/30.33 assert (zenon_L1365_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H40 zenon_H222 zenon_H6b zenon_H76 zenon_H1af zenon_H16b zenon_H218. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.13/30.33 apply (zenon_L690_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.13/30.33 apply (zenon_L1337_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.13/30.33 apply (zenon_L193_); trivial. % 30.13/30.33 apply (zenon_L245_); trivial. % 30.13/30.33 (* end of lemma zenon_L1365_ *) % 30.13/30.33 assert (zenon_L1366_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H42 zenon_H35 zenon_Hcc zenon_Hcd zenon_H1bd zenon_H5e zenon_H1ba zenon_H18c zenon_H208 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H222 zenon_H6b zenon_H76 zenon_H1af zenon_H16b zenon_H218. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.33 apply (zenon_L1331_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.33 apply (zenon_L1126_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.33 apply (zenon_L1333_); trivial. % 30.13/30.33 apply (zenon_L1365_); trivial. % 30.13/30.33 (* end of lemma zenon_L1366_ *) % 30.13/30.33 assert (zenon_L1367_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H218 zenon_H16b zenon_H108 zenon_Hcc zenon_Hf6 zenon_H20d zenon_Hdf zenon_H1e6 zenon_H10d zenon_H26 zenon_H222 zenon_H5e zenon_He2 zenon_Hcd zenon_H23b zenon_H3c zenon_He9 zenon_H60 zenon_H1af zenon_H37 zenon_H19e. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.33 apply (zenon_L120_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.33 apply (zenon_L700_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.33 apply (zenon_L219_); trivial. % 30.13/30.33 apply (zenon_L214_); trivial. % 30.13/30.33 (* end of lemma zenon_L1367_ *) % 30.13/30.33 assert (zenon_L1368_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H200 zenon_H60 zenon_He9 zenon_H3c zenon_H23b zenon_He2 zenon_H222 zenon_H26 zenon_H10d zenon_H1e6 zenon_H20d zenon_H108 zenon_H16b zenon_H218 zenon_H19e zenon_H37 zenon_H1af zenon_Hcc zenon_Hcd zenon_H1bd zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_H20e zenon_Hfe zenon_Hf6 zenon_Hb1. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.13/30.33 apply (zenon_L1367_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.13/30.33 apply (zenon_L1126_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.13/30.33 apply (zenon_L350_); trivial. % 30.13/30.33 apply (zenon_L690_); trivial. % 30.13/30.33 (* end of lemma zenon_L1368_ *) % 30.13/30.33 assert (zenon_L1369_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H172 zenon_H20 zenon_He1 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H19e zenon_H1e zenon_H2d zenon_H42 zenon_H60 zenon_Hcc zenon_Hd6 zenon_H35 zenon_Hf6 zenon_H20e zenon_H208 zenon_H18c zenon_H5e zenon_H1bd zenon_Hcd zenon_H1af zenon_H218 zenon_H16b zenon_H108 zenon_H20d zenon_H1e6 zenon_H10d zenon_H26 zenon_H222 zenon_He2 zenon_H23b zenon_H3c zenon_H200 zenon_H100 zenon_H101 zenon_H14e zenon_Hb1. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.13/30.33 apply (zenon_L16_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.13/30.33 exact (zenon_H19f zenon_Hc3). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.33 apply (zenon_L1331_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.33 apply (zenon_L1368_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.33 apply (zenon_L1333_); trivial. % 30.13/30.33 apply (zenon_L1334_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.33 exact (zenon_H13b zenon_Hfd). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.33 apply (zenon_L575_); trivial. % 30.13/30.33 apply (zenon_L1355_); trivial. % 30.13/30.33 apply (zenon_L84_); trivial. % 30.13/30.33 (* end of lemma zenon_L1369_ *) % 30.13/30.33 assert (zenon_L1370_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H1ba zenon_H5e zenon_H1bd zenon_Hcd zenon_Hcc zenon_H218 zenon_H33. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.33 apply (zenon_L120_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.33 apply (zenon_L608_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.33 apply (zenon_L44_); trivial. % 30.13/30.33 apply (zenon_L870_); trivial. % 30.13/30.33 (* end of lemma zenon_L1370_ *) % 30.13/30.33 assert (zenon_L1371_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H296 zenon_H2d zenon_H2c zenon_H19f zenon_H33 zenon_H218 zenon_Hcc zenon_Hcd zenon_H1bd zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_Hb1 zenon_H113. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.33 apply (zenon_L4_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.33 exact (zenon_H19f zenon_Hc3). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.33 apply (zenon_L1370_); trivial. % 30.13/30.33 apply (zenon_L798_); trivial. % 30.13/30.33 (* end of lemma zenon_L1371_ *) % 30.13/30.33 assert (zenon_L1372_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H98 zenon_H5e zenon_H222 zenon_H3c zenon_He9 zenon_H60 zenon_H218 zenon_H33. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.33 apply (zenon_L120_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.33 apply (zenon_L514_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.33 apply (zenon_L219_); trivial. % 30.13/30.33 apply (zenon_L870_); trivial. % 30.13/30.33 (* end of lemma zenon_L1372_ *) % 30.13/30.33 assert (zenon_L1373_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_Hb1 zenon_H19e zenon_H100 zenon_H19a zenon_Hfc zenon_H19f zenon_H102 zenon_He1 zenon_H9d. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.13/30.33 apply (zenon_L4_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.13/30.33 apply (zenon_L320_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.13/30.33 apply (zenon_L132_); trivial. % 30.13/30.33 apply (zenon_L1354_); trivial. % 30.13/30.33 (* end of lemma zenon_L1373_ *) % 30.13/30.33 assert (zenon_L1374_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H101 zenon_H33 zenon_H218 zenon_H60 zenon_H3c zenon_H222 zenon_H5e zenon_H98 zenon_H18c zenon_H68 zenon_H208 zenon_H155 zenon_H159 zenon_Hcc zenon_Hd6 zenon_H42 zenon_H2d zenon_H1e zenon_Hb1 zenon_H19e zenon_H100 zenon_H19a zenon_Hfc zenon_H19f zenon_H102 zenon_He1. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.33 apply (zenon_L1372_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.33 apply (zenon_L93_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.33 apply (zenon_L555_); trivial. % 30.13/30.33 apply (zenon_L1373_); trivial. % 30.13/30.33 (* end of lemma zenon_L1374_ *) % 30.13/30.33 assert (zenon_L1375_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_He1 zenon_H102 zenon_H19f zenon_Hfc zenon_H100 zenon_H19e zenon_Hb1 zenon_H1e zenon_H2d zenon_H42 zenon_Hd6 zenon_H159 zenon_H155 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_H3c zenon_H33 zenon_H101 zenon_H19a zenon_Hee zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.33 apply (zenon_L386_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.33 apply (zenon_L1374_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.33 apply (zenon_L337_); trivial. % 30.13/30.33 apply (zenon_L551_); trivial. % 30.13/30.33 (* end of lemma zenon_L1375_ *) % 30.13/30.33 assert (zenon_L1376_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H173 zenon_H35 zenon_He9 zenon_H23b zenon_Hcd zenon_He2 zenon_He1 zenon_H102 zenon_H19f zenon_Hfc zenon_H100 zenon_H19e zenon_Hb1 zenon_H1e zenon_H2d zenon_H42 zenon_Hd6 zenon_H159 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_H3c zenon_H33 zenon_H101 zenon_H19a zenon_Hee zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.13/30.33 apply (zenon_L48_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.13/30.33 apply (zenon_L95_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.13/30.33 apply (zenon_L159_); trivial. % 30.13/30.33 apply (zenon_L1375_); trivial. % 30.13/30.33 (* end of lemma zenon_L1376_ *) % 30.13/30.33 assert (zenon_L1377_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.13/30.33 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H1ba zenon_H5e zenon_H1bd zenon_H20e zenon_H19a zenon_H218 zenon_H33. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.13/30.33 apply (zenon_L120_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.13/30.33 apply (zenon_L608_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.13/30.33 apply (zenon_L225_); trivial. % 30.13/30.33 apply (zenon_L870_); trivial. % 30.13/30.33 (* end of lemma zenon_L1377_ *) % 30.13/30.33 assert (zenon_L1378_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H296 zenon_H16b zenon_H1af zenon_H108 zenon_H60 zenon_Hcc zenon_Hf6 zenon_H20d zenon_Hdf zenon_H1e6 zenon_Hee zenon_H101 zenon_H3c zenon_H222 zenon_H159 zenon_Hd6 zenon_H42 zenon_H2d zenon_H19e zenon_H100 zenon_Hfc zenon_H102 zenon_He1 zenon_He2 zenon_Hcd zenon_H23b zenon_He9 zenon_H35 zenon_H173 zenon_H19f zenon_H33 zenon_H218 zenon_H19a zenon_H20e zenon_H1bd zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_Hb1 zenon_H113. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.13/30.33 apply (zenon_L1376_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.13/30.33 exact (zenon_H19f zenon_Hc3). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.13/30.33 apply (zenon_L1377_); trivial. % 30.13/30.33 apply (zenon_L798_); trivial. % 30.13/30.33 (* end of lemma zenon_L1378_ *) % 30.13/30.33 assert (zenon_L1379_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H1d5 zenon_H6b zenon_Hf6 zenon_H1e6 zenon_H222 zenon_H40 zenon_H1a0 zenon_Hb1 zenon_H1af zenon_H16b zenon_H218. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.13/30.33 apply (zenon_L1365_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.13/30.33 apply (zenon_L775_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.13/30.33 apply (zenon_L751_); trivial. % 30.13/30.33 apply (zenon_L245_); trivial. % 30.13/30.33 (* end of lemma zenon_L1379_ *) % 30.13/30.33 assert (zenon_L1380_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H101 zenon_Hf6 zenon_H6f zenon_Hb6 zenon_H3f zenon_H1f zenon_Had zenon_H23b zenon_H3c zenon_H5e zenon_H18c zenon_H208 zenon_Hd6 zenon_Hcc zenon_H60 zenon_H42 zenon_H2d zenon_H1e zenon_Hb1 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_He1. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.13/30.33 apply (zenon_L641_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.13/30.33 exact (zenon_H13b zenon_Hfd). % 30.13/30.33 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.13/30.33 apply (zenon_L575_); trivial. % 30.13/30.33 apply (zenon_L1355_); trivial. % 30.13/30.33 (* end of lemma zenon_L1380_ *) % 30.13/30.33 assert (zenon_L1381_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H1ca zenon_H1e zenon_H3c zenon_H98 zenon_H5e zenon_H222 zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H19e. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1cb ]. % 30.13/30.33 apply (zenon_L207_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H1cc ]. % 30.13/30.33 apply (zenon_L514_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H55 | zenon_intro zenon_H3d ]. % 30.13/30.33 apply (zenon_L575_); trivial. % 30.13/30.33 apply (zenon_L1333_); trivial. % 30.13/30.33 (* end of lemma zenon_L1381_ *) % 30.13/30.33 assert (zenon_L1382_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H124 zenon_He1 zenon_Hb1 zenon_H2d zenon_H42 zenon_H208 zenon_H18c zenon_Had zenon_H3f zenon_Hb6 zenon_H6f zenon_H101 zenon_H218 zenon_H16b zenon_H1af zenon_H108 zenon_Hf6 zenon_H20d zenon_Hdf zenon_H1e6 zenon_H10d zenon_H26 zenon_He2 zenon_Hcd zenon_H23b zenon_H1ca zenon_H1e zenon_H3c zenon_H5e zenon_H222 zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H19e. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.13/30.33 apply (zenon_L1380_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.13/30.33 apply (zenon_L45_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.13/30.33 apply (zenon_L700_); trivial. % 30.13/30.33 apply (zenon_L1381_); trivial. % 30.13/30.33 (* end of lemma zenon_L1382_ *) % 30.13/30.33 assert (zenon_L1383_ : (((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 (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.13/30.33 do 0 intro. intros zenon_H23b zenon_H68 zenon_Had zenon_Hd5 zenon_H5e zenon_H222 zenon_H19a zenon_Hee zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.13/30.33 apply (zenon_L639_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.13/30.33 apply (zenon_L514_); trivial. % 30.13/30.33 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.13/30.33 apply (zenon_L337_); trivial. % 30.13/30.33 apply (zenon_L551_); trivial. % 30.13/30.33 (* end of lemma zenon_L1383_ *) % 30.13/30.33 assert (zenon_L1384_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (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) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H1a2 zenon_H19e zenon_H13b zenon_Hd1 zenon_H19f zenon_H102 zenon_Hd6 zenon_H1e zenon_H1ca zenon_Hcd zenon_He2 zenon_H10d zenon_H101 zenon_H3f zenon_H18c zenon_H208 zenon_H42 zenon_H2d zenon_Hb1 zenon_He1 zenon_H124 zenon_H218 zenon_H16b zenon_H1af zenon_H108 zenon_Hcc zenon_Hf6 zenon_H20d zenon_Hdf zenon_H1e6 zenon_Hee zenon_H222 zenon_H5e zenon_Hd5 zenon_Had zenon_H68 zenon_H23b zenon_H3c zenon_He9 zenon_H60 zenon_H6f zenon_Hb6. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.22/30.34 apply (zenon_L1382_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.22/30.34 apply (zenon_L1383_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.22/30.34 apply (zenon_L219_); trivial. % 30.22/30.34 apply (zenon_L540_); trivial. % 30.22/30.34 (* end of lemma zenon_L1384_ *) % 30.22/30.34 assert (zenon_L1385_ : (~((e2) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.22/30.34 do 0 intro. intros zenon_He1 zenon_Hb1 zenon_H2d zenon_H42 zenon_H200 zenon_Hb6 zenon_H6f zenon_H23b zenon_Had zenon_Hee zenon_H1e6 zenon_H20d zenon_H108 zenon_H1af zenon_H16b zenon_H218 zenon_H124 zenon_H208 zenon_H18c zenon_H3f zenon_H101 zenon_H10d zenon_He2 zenon_Hcd zenon_H1a2 zenon_H1bd zenon_H20e zenon_Hfe zenon_Hf6 zenon_H1ca zenon_H1e zenon_H3c zenon_H5e zenon_H222 zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H19e. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.22/30.34 apply (zenon_L1380_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.22/30.34 apply (zenon_L45_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.34 apply (zenon_L1384_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.34 apply (zenon_L608_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.34 apply (zenon_L350_); trivial. % 30.22/30.34 apply (zenon_L690_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.34 exact (zenon_H13b zenon_Hfd). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.34 apply (zenon_L575_); trivial. % 30.22/30.34 apply (zenon_L1355_); trivial. % 30.22/30.34 apply (zenon_L1381_); trivial. % 30.22/30.34 (* end of lemma zenon_L1385_ *) % 30.22/30.34 assert (zenon_L1386_ : ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 30.22/30.34 do 0 intro. intros zenon_Hb6 zenon_H6f zenon_H60 zenon_H3c zenon_H23b zenon_Had zenon_H5e zenon_H222 zenon_Hee zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H108 zenon_H1af zenon_H16b zenon_H218 zenon_H124 zenon_H208 zenon_H18c zenon_H3f zenon_H101 zenon_H10d zenon_He2 zenon_H1ca zenon_Hd6 zenon_H1a2 zenon_Hd5 zenon_Hcd zenon_H42 zenon_H2d zenon_H1e zenon_Hb1 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_He1. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.34 apply (zenon_L1384_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.34 exact (zenon_H13b zenon_Hfd). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.34 apply (zenon_L212_); trivial. % 30.22/30.34 apply (zenon_L1355_); trivial. % 30.22/30.34 (* end of lemma zenon_L1386_ *) % 30.22/30.34 assert (zenon_L1387_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.22/30.34 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_H37 zenon_Hb1 zenon_Hb6 zenon_He1 zenon_H90 zenon_H89. % 30.22/30.34 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.22/30.34 apply (zenon_L386_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.22/30.34 apply (zenon_L320_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.22/30.34 apply (zenon_L204_); trivial. % 30.22/30.34 apply (zenon_L538_); trivial. % 30.22/30.34 (* end of lemma zenon_L1387_ *) % 30.22/30.34 assert (zenon_L1388_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H23b zenon_He1 zenon_Hb1 zenon_H37 zenon_Hcd zenon_Hf9 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H60 zenon_Hcc zenon_Hd6 zenon_H222 zenon_H5e zenon_H3c zenon_H1e zenon_H1ca zenon_Hb6 zenon_H6f zenon_He2 zenon_H89. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.34 apply (zenon_L1387_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.34 apply (zenon_L1381_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.34 apply (zenon_L540_); trivial. % 30.22/30.34 apply (zenon_L252_); trivial. % 30.22/30.34 (* end of lemma zenon_L1388_ *) % 30.22/30.34 assert (zenon_L1389_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H23b zenon_Hcd zenon_H40 zenon_H6f zenon_H26 zenon_H10d zenon_He2 zenon_H89. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.34 apply (zenon_L386_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.34 apply (zenon_L80_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.34 apply (zenon_L699_); trivial. % 30.22/30.34 apply (zenon_L252_); trivial. % 30.22/30.34 (* end of lemma zenon_L1389_ *) % 30.22/30.34 assert (zenon_L1390_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H42 zenon_H35 zenon_Hb6 zenon_H1ca zenon_H1e zenon_H3c zenon_H5e zenon_H222 zenon_Hd6 zenon_Hcc zenon_H60 zenon_Hf9 zenon_Hb1 zenon_He1 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H23b zenon_Hcd zenon_H6f zenon_H26 zenon_H10d zenon_He2 zenon_H89. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.34 apply (zenon_L1331_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.34 apply (zenon_L1388_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.34 apply (zenon_L1333_); trivial. % 30.22/30.34 apply (zenon_L1389_); trivial. % 30.22/30.34 (* end of lemma zenon_L1390_ *) % 30.22/30.34 assert (zenon_L1391_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.22/30.34 do 0 intro. intros zenon_He4 zenon_H74 zenon_Hde zenon_H174 zenon_Hf9 zenon_H35 zenon_H124 zenon_He1 zenon_Hb1 zenon_H2d zenon_H42 zenon_H208 zenon_H18c zenon_Had zenon_H3f zenon_Hb6 zenon_H6f zenon_H101 zenon_H218 zenon_H1af zenon_H108 zenon_Hf6 zenon_H20d zenon_Hdf zenon_H1e6 zenon_H10d zenon_H26 zenon_Hcd zenon_H23b zenon_H1ca zenon_H1e zenon_H3c zenon_H5e zenon_H222 zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H19e. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.22/30.34 exact (zenon_H74 zenon_H73). % 30.22/30.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.22/30.34 apply (zenon_L48_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.22/30.34 apply (zenon_L49_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.34 apply (zenon_L1390_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.34 apply (zenon_L4_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.34 apply (zenon_L598_); trivial. % 30.22/30.34 apply (zenon_L1382_); trivial. % 30.22/30.34 (* end of lemma zenon_L1391_ *) % 30.22/30.34 assert (zenon_L1392_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H23b zenon_Hcd zenon_H33 zenon_H218 zenon_H60 zenon_He9 zenon_H3c zenon_H222 zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_Hb6 zenon_H6f zenon_He2 zenon_H89. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.34 apply (zenon_L386_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.34 apply (zenon_L1372_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.34 apply (zenon_L540_); trivial. % 30.22/30.34 apply (zenon_L252_); trivial. % 30.22/30.34 (* end of lemma zenon_L1392_ *) % 30.22/30.34 assert (zenon_L1393_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.34 do 0 intro. intros zenon_H23b zenon_Had zenon_H33 zenon_He9 zenon_H3c zenon_H222 zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_Hb6 zenon_H6f zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.34 apply (zenon_L639_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.34 apply (zenon_L1372_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.34 apply (zenon_L540_); trivial. % 30.22/30.34 apply (zenon_L551_); trivial. % 30.22/30.34 (* end of lemma zenon_L1393_ *) % 30.22/30.34 assert (zenon_L1394_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.34 do 0 intro. intros zenon_H174 zenon_He2 zenon_H113 zenon_Hb1 zenon_H1bd zenon_Hcd zenon_H19f zenon_H2d zenon_H296 zenon_H10d zenon_H23b zenon_Had zenon_H33 zenon_He9 zenon_H3c zenon_H222 zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_Hb6 zenon_H6f zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H218. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.34 apply (zenon_L1392_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.34 apply (zenon_L1371_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.34 apply (zenon_L151_); trivial. % 30.22/30.34 apply (zenon_L1393_); trivial. % 30.22/30.34 (* end of lemma zenon_L1394_ *) % 30.22/30.34 assert (zenon_L1395_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H98 zenon_H5e zenon_H222 zenon_H1c7 zenon_H3d zenon_H1af zenon_H17b zenon_H108 zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H218 zenon_H33. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.22/30.34 apply (zenon_L120_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.22/30.34 apply (zenon_L514_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.22/30.34 apply (zenon_L1345_); trivial. % 30.22/30.34 apply (zenon_L870_); trivial. % 30.22/30.34 (* end of lemma zenon_L1395_ *) % 30.22/30.34 assert (zenon_L1396_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H23b zenon_Hcd zenon_H33 zenon_H218 zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H108 zenon_H17b zenon_H1af zenon_H3d zenon_H1c7 zenon_H222 zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_Hb6 zenon_H6f zenon_He2 zenon_H89. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.34 apply (zenon_L386_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.34 apply (zenon_L1395_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.34 apply (zenon_L540_); trivial. % 30.22/30.34 apply (zenon_L252_); trivial. % 30.22/30.34 (* end of lemma zenon_L1396_ *) % 30.22/30.34 assert (zenon_L1397_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H42 zenon_H113 zenon_H1bd zenon_Hcc zenon_H19f zenon_H2d zenon_H296 zenon_H89 zenon_He2 zenon_H6f zenon_Hb6 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_H1c7 zenon_H1af zenon_H17b zenon_H108 zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H218 zenon_H33 zenon_Hcd zenon_H23b zenon_He1 zenon_H9d. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.34 apply (zenon_L1371_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.34 apply (zenon_L320_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.34 apply (zenon_L1396_); trivial. % 30.22/30.34 apply (zenon_L1354_); trivial. % 30.22/30.34 (* end of lemma zenon_L1397_ *) % 30.22/30.34 assert (zenon_L1398_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 30.22/30.34 do 0 intro. intros zenon_H101 zenon_H60 zenon_H20d zenon_Hdf zenon_H3c zenon_Had zenon_H10d zenon_H174 zenon_H13b zenon_Hd6 zenon_H42 zenon_H113 zenon_H1bd zenon_Hcc zenon_H19f zenon_H2d zenon_H296 zenon_H89 zenon_He2 zenon_H6f zenon_Hb6 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_H1c7 zenon_H1af zenon_H17b zenon_H108 zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H218 zenon_H33 zenon_Hcd zenon_H23b zenon_He1. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.34 apply (zenon_L1394_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.34 exact (zenon_H13b zenon_Hfd). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.34 apply (zenon_L555_); trivial. % 30.22/30.34 apply (zenon_L1397_); trivial. % 30.22/30.34 (* end of lemma zenon_L1398_ *) % 30.22/30.34 assert (zenon_L1399_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.34 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_H33 zenon_Hb1 zenon_H17b zenon_H3d zenon_H1c7 zenon_H222 zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_Hb6 zenon_H6f zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.34 apply (zenon_L386_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.34 apply (zenon_L1395_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.34 apply (zenon_L540_); trivial. % 30.22/30.34 apply (zenon_L551_); trivial. % 30.22/30.34 (* end of lemma zenon_L1399_ *) % 30.22/30.34 assert (zenon_L1400_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H218 zenon_H16b zenon_H1af zenon_H108 zenon_H60 zenon_Hcc zenon_Hf6 zenon_H20d zenon_Hdf zenon_H1e6 zenon_H6f zenon_Hb6 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_H1c7 zenon_H17b zenon_Hb1 zenon_H33 zenon_He2 zenon_Hcd zenon_H23b zenon_He1 zenon_H9d. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.34 apply (zenon_L4_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.34 apply (zenon_L320_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.34 apply (zenon_L1399_); trivial. % 30.22/30.34 apply (zenon_L1354_); trivial. % 30.22/30.34 (* end of lemma zenon_L1400_ *) % 30.22/30.34 assert (zenon_L1401_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H98 zenon_H5e zenon_H222 zenon_H3c zenon_He9 zenon_H60 zenon_H218 zenon_H33. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.22/30.34 apply (zenon_L157_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.22/30.34 apply (zenon_L514_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.22/30.34 apply (zenon_L219_); trivial. % 30.22/30.34 apply (zenon_L870_); trivial. % 30.22/30.34 (* end of lemma zenon_L1401_ *) % 30.22/30.34 assert (zenon_L1402_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.34 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_H33 zenon_He9 zenon_H3c zenon_H222 zenon_H5e zenon_H76 zenon_H208 zenon_Hb6 zenon_H6f zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.34 apply (zenon_L386_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.34 apply (zenon_L1401_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.34 apply (zenon_L540_); trivial. % 30.22/30.34 apply (zenon_L551_); trivial. % 30.22/30.34 (* end of lemma zenon_L1402_ *) % 30.22/30.34 assert (zenon_L1403_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.34 do 0 intro. intros zenon_H1d5 zenon_H3c zenon_He9 zenon_H218 zenon_H16b zenon_H108 zenon_H60 zenon_Hcc zenon_Hf6 zenon_H20d zenon_Hdf zenon_H1e6 zenon_H6f zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_H1c7 zenon_H17b zenon_Hb1 zenon_H33 zenon_He2 zenon_Hcd zenon_H23b zenon_H1dc zenon_Hb6 zenon_H1af zenon_H16c zenon_H156. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.22/30.34 apply (zenon_L1402_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.22/30.34 apply (zenon_L1399_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.22/30.34 apply (zenon_L200_); trivial. % 30.22/30.34 apply (zenon_L290_); trivial. % 30.22/30.34 (* end of lemma zenon_L1403_ *) % 30.22/30.34 assert (zenon_L1404_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 30.22/30.34 do 0 intro. intros zenon_H101 zenon_H76 zenon_H3c zenon_H13b zenon_Hd5 zenon_H42 zenon_H2d zenon_H1e zenon_H218 zenon_H16b zenon_H1af zenon_H108 zenon_H60 zenon_Hcc zenon_Hf6 zenon_H20d zenon_Hdf zenon_H1e6 zenon_H6f zenon_Hb6 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_H1c7 zenon_H17b zenon_Hb1 zenon_H33 zenon_He2 zenon_Hcd zenon_H23b zenon_He1. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.34 apply (zenon_L1402_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.34 exact (zenon_H13b zenon_Hfd). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.34 apply (zenon_L212_); trivial. % 30.22/30.34 apply (zenon_L1400_); trivial. % 30.22/30.34 (* end of lemma zenon_L1404_ *) % 30.22/30.34 assert (zenon_L1405_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.34 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_H23b zenon_Hcd zenon_He2 zenon_H33 zenon_Hb1 zenon_H1c7 zenon_H222 zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_Hb6 zenon_H6f zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_Hcc zenon_H108 zenon_H1e zenon_H2d zenon_H42 zenon_Hd5 zenon_H13b zenon_H3c zenon_H101 zenon_H37 zenon_H19e zenon_H17b zenon_H60 zenon_H1af zenon_H16b zenon_H218. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.22/30.34 apply (zenon_L1404_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.22/30.34 apply (zenon_L131_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.22/30.34 apply (zenon_L259_); trivial. % 30.22/30.34 apply (zenon_L245_); trivial. % 30.22/30.34 (* end of lemma zenon_L1405_ *) % 30.22/30.34 assert (zenon_L1406_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.22/30.34 do 0 intro. intros zenon_H8d zenon_H124 zenon_Had zenon_H3f zenon_H16f zenon_H15a zenon_H19e zenon_Hee zenon_H1d5 zenon_H1dc zenon_H156 zenon_H113 zenon_Hb1 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H1bd zenon_Hcd zenon_Hcc zenon_H218 zenon_H33 zenon_H19f zenon_H101 zenon_H3c zenon_H13b zenon_Hd6 zenon_H42 zenon_H2d zenon_H16b zenon_H1af zenon_H108 zenon_H60 zenon_Hf6 zenon_H20d zenon_Hdf zenon_H1e6 zenon_H6f zenon_Hb6 zenon_H222 zenon_H1c7 zenon_H17b zenon_He2 zenon_H23b zenon_He1 zenon_H296 zenon_H2fb. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.34 apply (zenon_L641_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.34 exact (zenon_H13b zenon_Hfd). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.34 apply (zenon_L575_); trivial. % 30.22/30.34 apply (zenon_L1400_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.22/30.34 apply (zenon_L241_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.22/30.34 apply (zenon_L125_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.22/30.34 apply (zenon_L490_); trivial. % 30.22/30.34 apply (zenon_L1403_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.34 exact (zenon_H13b zenon_Hfd). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.34 apply (zenon_L555_); trivial. % 30.22/30.34 apply (zenon_L1400_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.22/30.34 apply (zenon_L241_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.22/30.34 apply (zenon_L1405_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.22/30.34 apply (zenon_L490_); trivial. % 30.22/30.34 apply (zenon_L1403_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.34 exact (zenon_H13b zenon_Hfd). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.34 apply (zenon_L212_); trivial. % 30.22/30.34 apply (zenon_L1400_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.34 apply (zenon_L1372_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.34 exact (zenon_H13b zenon_Hfd). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.34 apply (zenon_L555_); trivial. % 30.22/30.34 apply (zenon_L1400_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.22/30.34 exact (zenon_H19f zenon_Hc3). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.22/30.34 apply (zenon_L1370_); trivial. % 30.22/30.34 apply (zenon_L798_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.22/30.34 apply (zenon_L18_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.34 apply (zenon_L1402_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.34 exact (zenon_H13b zenon_Hfd). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.34 apply (zenon_L575_); trivial. % 30.22/30.34 apply (zenon_L1400_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.22/30.34 exact (zenon_H19f zenon_Hc3). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.22/30.34 apply (zenon_L1370_); trivial. % 30.22/30.34 apply (zenon_L798_); trivial. % 30.22/30.34 exact (zenon_H2fb zenon_H8a). % 30.22/30.34 (* end of lemma zenon_L1406_ *) % 30.22/30.34 assert (zenon_L1407_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.22/30.34 do 0 intro. intros zenon_H301 zenon_H17d zenon_Hc0 zenon_H1a2 zenon_Hd1 zenon_H102 zenon_H1ca zenon_H35 zenon_Hf9 zenon_H225 zenon_H6b zenon_H27 zenon_He4 zenon_H74 zenon_Hde zenon_H174 zenon_H10d zenon_H8d zenon_H124 zenon_Had zenon_H3f zenon_H16f zenon_H15a zenon_H19e zenon_Hee zenon_H1d5 zenon_H1dc zenon_H156 zenon_H113 zenon_H208 zenon_H18c zenon_H5e zenon_H1bd zenon_Hcd zenon_Hcc zenon_H218 zenon_H101 zenon_H3c zenon_H13b zenon_Hd6 zenon_H42 zenon_H2d zenon_H1af zenon_H108 zenon_H60 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_H6f zenon_Hb6 zenon_H222 zenon_H1c7 zenon_H23b zenon_He1 zenon_H296 zenon_H2fb zenon_H20e zenon_H200 zenon_H246 zenon_H14e zenon_H1a5 zenon_H19f zenon_H20 zenon_H68 zenon_H172 zenon_Ha4 zenon_Hb1. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.22/30.34 exact (zenon_H74 zenon_H73). % 30.22/30.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.22/30.34 apply (zenon_L48_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.22/30.34 apply (zenon_L552_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.34 apply (zenon_L148_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.34 apply (zenon_L1331_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.34 apply (zenon_L151_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.22/30.34 apply (zenon_L148_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.22/30.34 apply (zenon_L18_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.22/30.34 apply (zenon_L16_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.22/30.34 exact (zenon_H19f zenon_Hc3). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.22/30.34 apply (zenon_L1385_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.22/30.34 exact (zenon_H19f zenon_Hc3). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.22/30.34 apply (zenon_L1366_); trivial. % 30.22/30.34 apply (zenon_L798_); trivial. % 30.22/30.34 apply (zenon_L84_); trivial. % 30.22/30.34 exact (zenon_H2fb zenon_H8a). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.22/30.34 exact (zenon_H74 zenon_H73). % 30.22/30.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.22/30.34 apply (zenon_L48_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.22/30.34 apply (zenon_L552_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.34 apply (zenon_L148_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.34 apply (zenon_L1331_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.34 apply (zenon_L151_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.22/30.34 apply (zenon_L16_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.22/30.34 exact (zenon_H19f zenon_Hc3). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.22/30.34 apply (zenon_L1385_); trivial. % 30.22/30.34 apply (zenon_L84_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.22/30.34 apply (zenon_L16_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.22/30.34 exact (zenon_H74 zenon_H73). % 30.22/30.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.22/30.34 apply (zenon_L48_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.22/30.34 apply (zenon_L552_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.34 apply (zenon_L734_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.34 apply (zenon_L4_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.34 apply (zenon_L151_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.22/30.34 apply (zenon_L1380_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.22/30.34 apply (zenon_L45_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.22/30.34 apply (zenon_L1386_); trivial. % 30.22/30.34 apply (zenon_L1381_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.22/30.34 apply (zenon_L1380_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.22/30.34 apply (zenon_L1391_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.22/30.34 exact (zenon_H74 zenon_H73). % 30.22/30.34 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.22/30.34 exact (zenon_H74 zenon_H73). % 30.22/30.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.22/30.34 apply (zenon_L48_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.22/30.34 apply (zenon_L552_); trivial. % 30.22/30.34 apply (zenon_L1394_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.22/30.34 apply (zenon_L554_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.22/30.34 exact (zenon_H74 zenon_H73). % 30.22/30.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.22/30.34 apply (zenon_L48_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.22/30.34 apply (zenon_L49_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.34 apply (zenon_L1398_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.34 apply (zenon_L1371_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.34 apply (zenon_L151_); trivial. % 30.22/30.34 apply (zenon_L1406_); trivial. % 30.22/30.34 apply (zenon_L772_); trivial. % 30.22/30.34 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.22/30.34 apply (zenon_L1330_); trivial. % 30.22/30.34 apply (zenon_L869_); trivial. % 30.22/30.34 (* end of lemma zenon_L1407_ *) % 30.22/30.34 assert (zenon_L1408_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.22/30.35 do 0 intro. intros zenon_Hb8 zenon_H16b zenon_H1a0 zenon_Ha4 zenon_H172 zenon_H68 zenon_H20 zenon_H19f zenon_H1a5 zenon_H14e zenon_H246 zenon_H200 zenon_H20e zenon_H2fb zenon_H296 zenon_He1 zenon_H23b zenon_H1c7 zenon_H222 zenon_H6f zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H60 zenon_H108 zenon_H1af zenon_H42 zenon_Hd6 zenon_H13b zenon_H3c zenon_H101 zenon_H218 zenon_Hcc zenon_Hcd zenon_H1bd zenon_H5e zenon_H18c zenon_H208 zenon_H113 zenon_H156 zenon_H1dc zenon_H1d5 zenon_Hee zenon_H19e zenon_H15a zenon_H16f zenon_H3f zenon_Had zenon_H124 zenon_H8d zenon_H10d zenon_H174 zenon_Hde zenon_H74 zenon_He4 zenon_H27 zenon_H6b zenon_H225 zenon_Hf9 zenon_H35 zenon_H1ca zenon_H102 zenon_Hd1 zenon_H1a2 zenon_Hc0 zenon_H17d zenon_H301 zenon_Hb1 zenon_H2d. % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.22/30.35 exact (zenon_H2fb zenon_H8a). % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.22/30.35 apply (zenon_L1379_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.22/30.35 apply (zenon_L1407_); trivial. % 30.22/30.35 apply (zenon_L107_); trivial. % 30.22/30.35 (* end of lemma zenon_L1408_ *) % 30.22/30.35 assert (zenon_L1409_ : ((op (e2) (e1)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.22/30.35 do 0 intro. intros zenon_Hd5 zenon_H33 zenon_H173 zenon_He2 zenon_Hfc zenon_H100 zenon_H159 zenon_Hdf zenon_He9 zenon_Hb8 zenon_H16b zenon_Ha4 zenon_H172 zenon_H68 zenon_H20 zenon_H19f zenon_H1a5 zenon_H14e zenon_H246 zenon_H200 zenon_H20e zenon_H2fb zenon_H296 zenon_He1 zenon_H23b zenon_H1c7 zenon_H222 zenon_H6f zenon_H1e6 zenon_H20d zenon_Hf6 zenon_H60 zenon_H108 zenon_H1af zenon_H42 zenon_Hd6 zenon_H13b zenon_H3c zenon_H101 zenon_H218 zenon_Hcc zenon_Hcd zenon_H1bd zenon_H5e zenon_H18c zenon_H208 zenon_H113 zenon_H156 zenon_H1dc zenon_H1d5 zenon_Hee zenon_H19e zenon_H15a zenon_H16f zenon_H3f zenon_Had zenon_H124 zenon_H8d zenon_H10d zenon_H174 zenon_Hde zenon_H74 zenon_He4 zenon_H27 zenon_H6b zenon_H225 zenon_Hf9 zenon_H35 zenon_H1ca zenon_H102 zenon_Hd1 zenon_H1a2 zenon_Hc0 zenon_H17d zenon_H301 zenon_Hb1 zenon_H2d. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.22/30.35 apply (zenon_L700_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.22/30.35 apply (zenon_L1378_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.22/30.35 apply (zenon_L219_); trivial. % 30.22/30.35 apply (zenon_L1408_); trivial. % 30.22/30.35 (* end of lemma zenon_L1409_ *) % 30.22/30.35 assert (zenon_L1410_ : (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H2d zenon_Hb1 zenon_H301 zenon_H17d zenon_Hc0 zenon_H1a2 zenon_Hd1 zenon_H102 zenon_H1ca zenon_H35 zenon_Hf9 zenon_H225 zenon_H6b zenon_H27 zenon_He4 zenon_H74 zenon_Hde zenon_H174 zenon_H10d zenon_H8d zenon_H124 zenon_Had zenon_H3f zenon_H16f zenon_H15a zenon_Hee zenon_H1d5 zenon_H1dc zenon_H156 zenon_H113 zenon_H208 zenon_H18c zenon_H5e zenon_H1bd zenon_Hcd zenon_Hcc zenon_H218 zenon_H101 zenon_H13b zenon_Hd6 zenon_H42 zenon_H108 zenon_Hf6 zenon_H20d zenon_H1e6 zenon_H6f zenon_H222 zenon_H1c7 zenon_H23b zenon_He1 zenon_H296 zenon_H2fb zenon_H20e zenon_H200 zenon_H246 zenon_H14e zenon_H1a5 zenon_H19f zenon_H20 zenon_H68 zenon_H172 zenon_Ha4 zenon_H16b zenon_Hb8 zenon_Hdf zenon_H159 zenon_H100 zenon_Hfc zenon_He2 zenon_H173 zenon_H33 zenon_H3c zenon_He9 zenon_H60 zenon_H1af zenon_H37 zenon_H19e. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.22/30.35 apply (zenon_L120_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.22/30.35 apply (zenon_L1409_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.22/30.35 apply (zenon_L219_); trivial. % 30.22/30.35 apply (zenon_L214_); trivial. % 30.22/30.35 (* end of lemma zenon_L1410_ *) % 30.22/30.35 assert (zenon_L1411_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.22/30.35 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H98 zenon_H5e zenon_H9d zenon_H60 zenon_H222 zenon_H218 zenon_H33. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.22/30.35 apply (zenon_L157_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.22/30.35 apply (zenon_L514_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.22/30.35 apply (zenon_L256_); trivial. % 30.22/30.35 apply (zenon_L870_); trivial. % 30.22/30.35 (* end of lemma zenon_L1411_ *) % 30.22/30.35 assert (zenon_L1412_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.22/30.35 do 0 intro. intros zenon_H101 zenon_H3c zenon_H18c zenon_H68 zenon_H13b zenon_Hcc zenon_Hd6 zenon_H208 zenon_H6f zenon_H76 zenon_H98 zenon_H5e zenon_H60 zenon_H222 zenon_H218 zenon_H33. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.35 apply (zenon_L1372_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.35 exact (zenon_H13b zenon_Hfd). % 30.22/30.35 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.35 apply (zenon_L555_); trivial. % 30.22/30.35 apply (zenon_L1411_); trivial. % 30.22/30.35 (* end of lemma zenon_L1412_ *) % 30.22/30.35 assert (zenon_L1413_ : (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.22/30.35 do 0 intro. intros zenon_He1 zenon_H102 zenon_H19f zenon_Hd1 zenon_H19e zenon_Hb1 zenon_H1e zenon_H2d zenon_H42 zenon_Hf6 zenon_Hfe zenon_H20e zenon_H1bd zenon_H301 zenon_H17d zenon_Hc0 zenon_H1a2 zenon_H1ca zenon_H35 zenon_Hf9 zenon_H225 zenon_H6b zenon_H27 zenon_He4 zenon_H74 zenon_Hde zenon_H174 zenon_H10d zenon_H8d zenon_H124 zenon_Had zenon_H3f zenon_H16f zenon_H15a zenon_Hee zenon_H1d5 zenon_H1dc zenon_H156 zenon_H113 zenon_Hcd zenon_H108 zenon_H20d zenon_H1e6 zenon_H1c7 zenon_H23b zenon_H296 zenon_H2fb zenon_H200 zenon_H246 zenon_H14e zenon_H1a5 zenon_H20 zenon_H172 zenon_Ha4 zenon_H16b zenon_Hb8 zenon_H159 zenon_Hfc zenon_He2 zenon_H173 zenon_H1af zenon_H100 zenon_H101 zenon_H3c zenon_H18c zenon_H68 zenon_H13b zenon_Hcc zenon_Hd6 zenon_H208 zenon_H6f zenon_H76 zenon_H5e zenon_H60 zenon_H222 zenon_H218 zenon_H33. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.22/30.35 apply (zenon_L1364_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.22/30.35 apply (zenon_L45_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.35 apply (zenon_L1371_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.35 apply (zenon_L1410_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.35 apply (zenon_L608_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.35 apply (zenon_L350_); trivial. % 30.22/30.35 apply (zenon_L690_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.35 apply (zenon_L1333_); trivial. % 30.22/30.35 apply (zenon_L1334_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.35 exact (zenon_H13b zenon_Hfd). % 30.22/30.35 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.35 apply (zenon_L575_); trivial. % 30.22/30.35 apply (zenon_L1355_); trivial. % 30.22/30.35 apply (zenon_L1412_); trivial. % 30.22/30.35 (* end of lemma zenon_L1413_ *) % 30.22/30.35 assert (zenon_L1414_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H218 zenon_H17b zenon_H60 zenon_H1af zenon_H16c zenon_H156. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.22/30.35 apply (zenon_L332_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.22/30.35 apply (zenon_L1333_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.22/30.35 apply (zenon_L259_); trivial. % 30.22/30.35 apply (zenon_L290_); trivial. % 30.22/30.35 (* end of lemma zenon_L1414_ *) % 30.22/30.35 assert (zenon_L1415_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H225 zenon_H74 zenon_H27 zenon_H174 zenon_Hb8 zenon_H10d zenon_H8d zenon_H16f zenon_H15a zenon_H18c zenon_H20e zenon_H222 zenon_Hf6 zenon_H1e6 zenon_Hfc zenon_H1d5 zenon_Hc8 zenon_H218 zenon_H156 zenon_He1 zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H19e zenon_Hb1 zenon_H1e zenon_H2d zenon_H42 zenon_Hd6 zenon_Hcc zenon_H35 zenon_H1af zenon_H60 zenon_H3c zenon_H5e zenon_H1f zenon_H6f zenon_H208 zenon_H100 zenon_H101 zenon_H2fb. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.22/30.35 exact (zenon_H74 zenon_H73). % 30.22/30.35 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.22/30.35 apply (zenon_L1336_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.22/30.35 apply (zenon_L554_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.22/30.35 apply (zenon_L241_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.22/30.35 apply (zenon_L454_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.22/30.35 apply (zenon_L1361_); trivial. % 30.22/30.35 apply (zenon_L1414_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.35 exact (zenon_H13b zenon_Hfd). % 30.22/30.35 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.35 apply (zenon_L575_); trivial. % 30.22/30.35 apply (zenon_L1355_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.35 apply (zenon_L4_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.35 apply (zenon_L1335_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.22/30.35 apply (zenon_L241_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.22/30.35 apply (zenon_L454_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.22/30.35 apply (zenon_L1339_); trivial. % 30.22/30.35 apply (zenon_L1414_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.35 exact (zenon_H13b zenon_Hfd). % 30.22/30.35 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.35 apply (zenon_L575_); trivial. % 30.22/30.35 apply (zenon_L1355_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.22/30.35 apply (zenon_L18_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.22/30.35 apply (zenon_L1364_); trivial. % 30.22/30.35 exact (zenon_H2fb zenon_H8a). % 30.22/30.35 (* end of lemma zenon_L1415_ *) % 30.22/30.35 assert (zenon_L1416_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.22/30.35 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H100 zenon_H2fb zenon_Hb8 zenon_H37 zenon_Hfc zenon_H1c5 zenon_H108 zenon_H42 zenon_H35 zenon_H1ca zenon_H1e zenon_H3c zenon_H5e zenon_H222 zenon_Hd6 zenon_Hcc zenon_H60 zenon_Hf9 zenon_Hb1 zenon_He1 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H23b zenon_Hcd zenon_H6f zenon_H26 zenon_H10d zenon_He2 zenon_H89. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.22/30.35 apply (zenon_L1332_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.22/30.35 apply (zenon_L203_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.22/30.35 apply (zenon_L171_); trivial. % 30.22/30.35 apply (zenon_L1390_); trivial. % 30.22/30.35 (* end of lemma zenon_L1416_ *) % 30.22/30.35 assert (zenon_L1417_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.22/30.35 do 0 intro. intros zenon_H1d5 zenon_Hc8 zenon_H1fd zenon_H2d zenon_H100 zenon_H2fb zenon_Hb8 zenon_H37 zenon_Hfc zenon_H108 zenon_H42 zenon_H35 zenon_H1ca zenon_H1e zenon_H3c zenon_H5e zenon_H222 zenon_Hd6 zenon_Hcc zenon_H60 zenon_Hf9 zenon_Hb1 zenon_He1 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H23b zenon_Hcd zenon_H6f zenon_H26 zenon_H10d zenon_He2 zenon_H89. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.22/30.35 apply (zenon_L332_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.22/30.35 apply (zenon_L131_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.22/30.35 apply (zenon_L544_); trivial. % 30.22/30.35 apply (zenon_L1416_); trivial. % 30.22/30.35 (* end of lemma zenon_L1417_ *) % 30.22/30.35 assert (zenon_L1418_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H40 zenon_H222 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.22/30.35 apply (zenon_L690_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.22/30.35 apply (zenon_L1337_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.22/30.35 apply (zenon_L550_); trivial. % 30.22/30.35 apply (zenon_L245_); trivial. % 30.22/30.35 (* end of lemma zenon_L1418_ *) % 30.22/30.35 assert (zenon_L1419_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.22/30.35 do 0 intro. intros zenon_H42 zenon_H35 zenon_H15e zenon_Hfc zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H23b zenon_Hcd zenon_H6f zenon_H26 zenon_H10d zenon_He2 zenon_H89. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.35 apply (zenon_L1331_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.35 apply (zenon_L203_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.35 apply (zenon_L1333_); trivial. % 30.22/30.35 apply (zenon_L1389_); trivial. % 30.22/30.35 (* end of lemma zenon_L1419_ *) % 30.22/30.35 assert (zenon_L1420_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H218 zenon_H16b zenon_H108 zenon_H60 zenon_Hf6 zenon_H20d zenon_Hdf zenon_H1e6 zenon_H10d zenon_H26 zenon_H222 zenon_H5e zenon_He2 zenon_H23b zenon_Hcd zenon_Hcc zenon_H1af zenon_H37 zenon_H19e. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.22/30.35 apply (zenon_L157_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.22/30.35 apply (zenon_L700_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.22/30.35 apply (zenon_L44_); trivial. % 30.22/30.35 apply (zenon_L214_); trivial. % 30.22/30.35 (* end of lemma zenon_L1420_ *) % 30.22/30.35 assert (zenon_L1421_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H1af zenon_Hcc zenon_Hcd zenon_H23b zenon_He2 zenon_H5e zenon_H222 zenon_H26 zenon_H10d zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_H60 zenon_H108 zenon_H16b zenon_H218 zenon_H76 zenon_H6f zenon_H208 zenon_H19e zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H100. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.35 apply (zenon_L4_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.35 apply (zenon_L1420_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.35 apply (zenon_L1333_); trivial. % 30.22/30.35 apply (zenon_L1334_); trivial. % 30.22/30.35 (* end of lemma zenon_L1421_ *) % 30.22/30.35 assert (zenon_L1422_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H42 zenon_H113 zenon_Hb1 zenon_H208 zenon_H18c zenon_H5e zenon_H1bd zenon_Hcd zenon_Hcc zenon_H218 zenon_H33 zenon_H2d zenon_H296 zenon_H15e zenon_Hfc zenon_H19e zenon_H102 zenon_H19f zenon_H68 zenon_Hd1 zenon_H13b zenon_H100. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.35 apply (zenon_L1371_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.35 apply (zenon_L203_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.35 apply (zenon_L1333_); trivial. % 30.22/30.35 apply (zenon_L1334_); trivial. % 30.22/30.35 (* end of lemma zenon_L1422_ *) % 30.22/30.35 assert (zenon_L1423_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> False). % 30.22/30.35 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H1fd zenon_H2d zenon_Hb1 zenon_H10d zenon_H100 zenon_H2fb zenon_Hb8 zenon_H37 zenon_Hfc zenon_H108 zenon_H6f zenon_H1a0. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.22/30.35 apply (zenon_L332_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.22/30.35 apply (zenon_L1333_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.22/30.35 apply (zenon_L751_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.22/30.35 apply (zenon_L1332_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.22/30.35 apply (zenon_L203_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.22/30.35 apply (zenon_L171_); trivial. % 30.22/30.35 apply (zenon_L540_); trivial. % 30.22/30.35 (* end of lemma zenon_L1423_ *) % 30.22/30.35 assert (zenon_L1424_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H1a2 zenon_Hcc zenon_Hd6 zenon_H222 zenon_H5e zenon_H1e zenon_H1ca zenon_H23b zenon_Hcd zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_H1af zenon_H218 zenon_H101 zenon_H3f zenon_Had zenon_H18c zenon_H208 zenon_H42 zenon_He1 zenon_H124 zenon_H35 zenon_Hf9 zenon_H174 zenon_Hde zenon_H74 zenon_He4 zenon_H113 zenon_H1bd zenon_H33 zenon_H296 zenon_H1b1 zenon_H3c zenon_He9 zenon_H60 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H1fd zenon_H2d zenon_Hb1 zenon_H10d zenon_H100 zenon_H2fb zenon_Hb8 zenon_H37 zenon_Hfc zenon_H108 zenon_H6f. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.22/30.35 apply (zenon_L332_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.22/30.35 apply (zenon_L131_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.22/30.35 apply (zenon_L544_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.22/30.35 apply (zenon_L598_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.22/30.35 apply (zenon_L1422_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.22/30.35 apply (zenon_L171_); trivial. % 30.22/30.35 apply (zenon_L1391_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.22/30.35 apply (zenon_L147_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.22/30.35 apply (zenon_L219_); trivial. % 30.22/30.35 apply (zenon_L1423_); trivial. % 30.22/30.35 (* end of lemma zenon_L1424_ *) % 30.22/30.35 assert (zenon_L1425_ : ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.35 do 0 intro. intros zenon_He9 zenon_H3c zenon_H33 zenon_H173 zenon_He2 zenon_Hfc zenon_H100 zenon_H159 zenon_Hdf zenon_Hb8 zenon_Ha4 zenon_H172 zenon_H20 zenon_H1a5 zenon_H14e zenon_H246 zenon_H200 zenon_H20e zenon_H2fb zenon_H296 zenon_He1 zenon_H23b zenon_H1c7 zenon_H6f zenon_H20d zenon_H42 zenon_Hd6 zenon_H101 zenon_Hcd zenon_H1bd zenon_H5e zenon_H18c zenon_H208 zenon_H113 zenon_H156 zenon_H1dc zenon_H1d5 zenon_Hee zenon_H15a zenon_H16f zenon_H3f zenon_Had zenon_H124 zenon_H8d zenon_H10d zenon_H174 zenon_Hde zenon_H74 zenon_He4 zenon_H27 zenon_H6b zenon_H225 zenon_Hf9 zenon_H35 zenon_H1ca zenon_H1a2 zenon_Hc0 zenon_H17d zenon_H301 zenon_H2d zenon_H19e zenon_H13b zenon_Hd1 zenon_H68 zenon_H19f zenon_H102 zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H222 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.35 apply (zenon_L1371_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.35 apply (zenon_L1410_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.35 apply (zenon_L1333_); trivial. % 30.22/30.35 apply (zenon_L1418_); trivial. % 30.22/30.35 (* end of lemma zenon_L1425_ *) % 30.22/30.35 assert (zenon_L1426_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.22/30.35 do 0 intro. intros zenon_Hb8 zenon_H2fb zenon_Hb1 zenon_Hb3 zenon_H97 zenon_H10d zenon_H117 zenon_Hb9. % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.22/30.35 exact (zenon_H2fb zenon_H8a). % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.22/30.35 apply (zenon_L36_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.22/30.35 apply (zenon_L151_); trivial. % 30.22/30.35 exact (zenon_Hb9 zenon_Hbc). % 30.22/30.35 (* end of lemma zenon_L1426_ *) % 30.22/30.35 assert (zenon_L1427_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.22/30.35 do 0 intro. intros zenon_Hb8 zenon_H2fb zenon_H3f zenon_H2c zenon_Hee zenon_H15e zenon_Hb9. % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.22/30.35 exact (zenon_H2fb zenon_H8a). % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.22/30.35 apply (zenon_L746_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.22/30.35 apply (zenon_L490_); trivial. % 30.22/30.35 exact (zenon_Hb9 zenon_Hbc). % 30.22/30.35 (* end of lemma zenon_L1427_ *) % 30.22/30.35 assert (zenon_L1428_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.22/30.35 do 0 intro. intros zenon_Hb8 zenon_H2fb zenon_H222 zenon_H3d zenon_Hee zenon_H15e zenon_Hb9. % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.22/30.35 exact (zenon_H2fb zenon_H8a). % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.22/30.35 apply (zenon_L775_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.22/30.35 apply (zenon_L490_); trivial. % 30.22/30.35 exact (zenon_Hb9 zenon_Hbc). % 30.22/30.35 (* end of lemma zenon_L1428_ *) % 30.22/30.35 assert (zenon_L1429_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e0)) -> False). % 30.22/30.35 do 0 intro. intros zenon_H42 zenon_H3f zenon_Hfc zenon_Hb9 zenon_H15e zenon_Hee zenon_H222 zenon_H2fb zenon_Hb8 zenon_H97 zenon_Hb3 zenon_Hb1. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.35 apply (zenon_L1427_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.35 apply (zenon_L203_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.35 apply (zenon_L1428_); trivial. % 30.22/30.35 apply (zenon_L36_); trivial. % 30.22/30.35 (* end of lemma zenon_L1429_ *) % 30.22/30.35 assert (zenon_L1430_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> False). % 30.22/30.35 do 0 intro. intros zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_H16a zenon_H198 zenon_H117. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.35 apply (zenon_L94_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.35 exact (zenon_H13b zenon_Hfd). % 30.22/30.35 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.35 apply (zenon_L159_); trivial. % 30.22/30.35 apply (zenon_L1004_); trivial. % 30.22/30.35 (* end of lemma zenon_L1430_ *) % 30.22/30.35 assert (zenon_L1431_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H1fd zenon_H198 zenon_H16a zenon_Hcd zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_H6f zenon_H19a zenon_Hcc zenon_He1 zenon_H8a zenon_Hb5. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.22/30.35 apply (zenon_L1430_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.22/30.35 apply (zenon_L235_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.22/30.35 apply (zenon_L544_); trivial. % 30.22/30.35 apply (zenon_L461_); trivial. % 30.22/30.35 (* end of lemma zenon_L1431_ *) % 30.22/30.35 assert (zenon_L1432_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_Hf5 zenon_H156. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.35 apply (zenon_L94_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.35 exact (zenon_H13b zenon_Hfd). % 30.22/30.35 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.35 apply (zenon_L159_); trivial. % 30.22/30.35 apply (zenon_L90_); trivial. % 30.22/30.35 (* end of lemma zenon_L1432_ *) % 30.22/30.35 assert (zenon_L1433_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e3)) -> False). % 30.22/30.35 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H156 zenon_Hcd zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_H1fd zenon_H198 zenon_H16a zenon_H6f zenon_He1 zenon_H8a zenon_Hb5 zenon_Hc8 zenon_H135 zenon_H20e zenon_H19a zenon_H218 zenon_H188 zenon_H2c. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.22/30.35 apply (zenon_L120_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.35 apply (zenon_L43_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.35 apply (zenon_L212_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.35 apply (zenon_L1431_); trivial. % 30.22/30.35 apply (zenon_L1432_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.22/30.35 apply (zenon_L225_); trivial. % 30.22/30.35 apply (zenon_L1132_); trivial. % 30.22/30.35 (* end of lemma zenon_L1433_ *) % 30.22/30.35 assert (zenon_L1434_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.22/30.35 do 0 intro. intros zenon_H174 zenon_H188 zenon_H218 zenon_H20e zenon_H135 zenon_Hc8 zenon_Hb5 zenon_He1 zenon_H6f zenon_H1fd zenon_H156 zenon_H18c zenon_H68 zenon_H208 zenon_H36 zenon_H8d zenon_H198 zenon_H16a zenon_H19a zenon_Hcd zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_H185 zenon_H2d. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.35 apply (zenon_L232_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.22/30.35 apply (zenon_L232_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.22/30.35 apply (zenon_L1000_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.22/30.35 apply (zenon_L1001_); trivial. % 30.22/30.35 apply (zenon_L1433_); trivial. % 30.22/30.35 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.35 apply (zenon_L1430_); trivial. % 30.22/30.35 apply (zenon_L848_); trivial. % 30.22/30.35 (* end of lemma zenon_L1434_ *) % 30.22/30.36 assert (zenon_L1435_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H301 zenon_H1b3 zenon_H304 zenon_H174 zenon_H188 zenon_H218 zenon_H20e zenon_H135 zenon_Hc8 zenon_Hb5 zenon_He1 zenon_H6f zenon_H1fd zenon_H156 zenon_H18c zenon_H68 zenon_H208 zenon_H36 zenon_H8d zenon_H198 zenon_H16a zenon_H19a zenon_Hcd zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_H2d. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.22/30.36 exact (zenon_H1b3 zenon_H64). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.22/30.36 apply (zenon_L119_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.22/30.36 exact (zenon_H304 zenon_H10e). % 30.22/30.36 apply (zenon_L1434_); trivial. % 30.22/30.36 (* end of lemma zenon_L1435_ *) % 30.22/30.36 assert (zenon_L1436_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H11e zenon_Hfe zenon_H1a5 zenon_H19a zenon_H138 zenon_He9 zenon_H198 zenon_Hb6 zenon_H10d. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H10e | zenon_intro zenon_H11f ]. % 30.22/30.36 apply (zenon_L764_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H26 | zenon_intro zenon_H120 ]. % 30.22/30.36 apply (zenon_L136_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hda | zenon_intro zenon_H117 ]. % 30.22/30.36 apply (zenon_L1041_); trivial. % 30.22/30.36 apply (zenon_L151_); trivial. % 30.22/30.36 (* end of lemma zenon_L1436_ *) % 30.22/30.36 assert (zenon_L1437_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H1fd zenon_H16a zenon_Hcd zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_H6f zenon_Hcc zenon_He1 zenon_H11e zenon_Hfe zenon_H1a5 zenon_H19a zenon_H138 zenon_He9 zenon_H198 zenon_H10d. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.22/30.36 apply (zenon_L1430_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.22/30.36 apply (zenon_L235_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.22/30.36 apply (zenon_L544_); trivial. % 30.22/30.36 apply (zenon_L1436_); trivial. % 30.22/30.36 (* end of lemma zenon_L1437_ *) % 30.22/30.36 assert (zenon_L1438_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H135 zenon_Hc8 zenon_H3c zenon_H10d zenon_H198 zenon_He9 zenon_H138 zenon_H1a5 zenon_Hfe zenon_H11e zenon_He1 zenon_H6f zenon_H16a zenon_H1fd zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_H156. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.36 apply (zenon_L43_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.36 apply (zenon_L88_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.36 apply (zenon_L1437_); trivial. % 30.22/30.36 apply (zenon_L1432_); trivial. % 30.22/30.36 (* end of lemma zenon_L1438_ *) % 30.22/30.36 assert (zenon_L1439_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e2)) = (e0)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H10d zenon_H2d6 zenon_H73 zenon_H9c. % 30.22/30.36 cut (((op (e0) (op (e0) (e0))) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 30.22/30.36 intro zenon_D_pnotp. % 30.22/30.36 apply zenon_H10d. % 30.22/30.36 rewrite <- zenon_D_pnotp. % 30.22/30.36 exact zenon_H2d6. % 30.22/30.36 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 30.22/30.36 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H305]. % 30.22/30.36 congruence. % 30.22/30.36 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H10f ]. % 30.22/30.36 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (op (e0) (e0))) = (op (e0) (e2)))). % 30.22/30.36 intro zenon_D_pnotp. % 30.22/30.36 apply zenon_H305. % 30.22/30.36 rewrite <- zenon_D_pnotp. % 30.22/30.36 exact zenon_H211. % 30.22/30.36 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.22/30.36 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H306]. % 30.22/30.36 congruence. % 30.22/30.36 cut (((e2) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 30.22/30.36 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.22/30.36 congruence. % 30.22/30.36 apply zenon_H1d. apply refl_equal. % 30.22/30.36 apply zenon_H82. apply sym_equal. exact zenon_H73. % 30.22/30.36 apply zenon_H10f. apply refl_equal. % 30.22/30.36 apply zenon_H10f. apply refl_equal. % 30.22/30.36 apply zenon_Ha2. apply sym_equal. exact zenon_H9c. % 30.22/30.36 (* end of lemma zenon_L1439_ *) % 30.22/30.36 assert (zenon_L1440_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H1d5 zenon_H6f zenon_He1 zenon_H55 zenon_H73 zenon_H6c zenon_H218 zenon_H36 zenon_H16b. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.22/30.36 apply (zenon_L157_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.22/30.36 apply (zenon_L126_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.22/30.36 apply (zenon_L244_); trivial. % 30.22/30.36 apply (zenon_L1038_); trivial. % 30.22/30.36 (* end of lemma zenon_L1440_ *) % 30.22/30.36 assert (zenon_L1441_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H11e zenon_H304 zenon_H9d zenon_H198 zenon_H3f zenon_H73 zenon_Hd9 zenon_Hb6 zenon_H10d. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H10e | zenon_intro zenon_H11f ]. % 30.22/30.36 exact (zenon_H304 zenon_H10e). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H26 | zenon_intro zenon_H120 ]. % 30.22/30.36 apply (zenon_L129_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hda | zenon_intro zenon_H117 ]. % 30.22/30.36 apply (zenon_L47_); trivial. % 30.22/30.36 apply (zenon_L151_); trivial. % 30.22/30.36 (* end of lemma zenon_L1441_ *) % 30.22/30.36 assert (zenon_L1442_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H1fd zenon_H155 zenon_H16a zenon_H6f zenon_H19a zenon_Hcc zenon_He1 zenon_H11e zenon_H304 zenon_H9d zenon_H198 zenon_H3f zenon_H73 zenon_Hd9 zenon_H10d. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.22/30.36 apply (zenon_L1004_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.22/30.36 apply (zenon_L235_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.22/30.36 apply (zenon_L544_); trivial. % 30.22/30.36 apply (zenon_L1441_); trivial. % 30.22/30.36 (* end of lemma zenon_L1442_ *) % 30.22/30.36 assert (zenon_L1443_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H135 zenon_Hc8 zenon_H222 zenon_H10d zenon_Hd9 zenon_H3f zenon_H198 zenon_H9d zenon_H304 zenon_H11e zenon_He1 zenon_H6f zenon_H16a zenon_H155 zenon_H1fd zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_H156. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.36 apply (zenon_L43_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.36 apply (zenon_L264_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.36 apply (zenon_L1442_); trivial. % 30.22/30.36 apply (zenon_L1432_); trivial. % 30.22/30.36 (* end of lemma zenon_L1443_ *) % 30.22/30.36 assert (zenon_L1444_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> False). % 30.22/30.36 do 0 intro. intros zenon_He7 zenon_H188 zenon_H1e zenon_H90. % 30.22/30.36 cut (((op (e0) (op (e0) (e1))) = (e1)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 30.22/30.36 intro zenon_D_pnotp. % 30.22/30.36 apply zenon_He7. % 30.22/30.36 rewrite <- zenon_D_pnotp. % 30.22/30.36 exact zenon_H188. % 30.22/30.36 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H26a]. % 30.22/30.36 cut (((op (e0) (op (e0) (e1))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 30.22/30.36 congruence. % 30.22/30.36 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H18b | zenon_intro zenon_Hcb ]. % 30.22/30.36 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (e0) (op (e0) (e1))) = (op (e0) (e0)))). % 30.22/30.36 intro zenon_D_pnotp. % 30.22/30.36 apply zenon_H18a. % 30.22/30.36 rewrite <- zenon_D_pnotp. % 30.22/30.36 exact zenon_H18b. % 30.22/30.36 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.22/30.36 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 30.22/30.36 congruence. % 30.22/30.36 apply (zenon_L118_); trivial. % 30.22/30.36 apply zenon_Hcb. apply refl_equal. % 30.22/30.36 apply zenon_Hcb. apply refl_equal. % 30.22/30.36 apply zenon_H26a. apply sym_equal. exact zenon_H90. % 30.22/30.36 (* end of lemma zenon_L1444_ *) % 30.22/30.36 assert (zenon_L1445_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H102 zenon_H19f zenon_Hfc zenon_H19a zenon_H13b zenon_H2c zenon_H35. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.36 exact (zenon_H19f zenon_Hc3). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.36 apply (zenon_L130_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_L1002_); trivial. % 30.22/30.36 (* end of lemma zenon_L1445_ *) % 30.22/30.36 assert (zenon_L1446_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H23b zenon_H88 zenon_He7 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.36 apply (zenon_L1053_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.36 apply (zenon_L336_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.36 apply (zenon_L337_); trivial. % 30.22/30.36 exact (zenon_H1ab zenon_H112). % 30.22/30.36 (* end of lemma zenon_L1446_ *) % 30.22/30.36 assert (zenon_L1447_ : (((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 (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H23b zenon_H68 zenon_Had zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.36 apply (zenon_L639_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.36 apply (zenon_L336_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.36 apply (zenon_L337_); trivial. % 30.22/30.36 exact (zenon_H1ab zenon_H112). % 30.22/30.36 (* end of lemma zenon_L1447_ *) % 30.22/30.36 assert (zenon_L1448_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H13b zenon_H4a zenon_H33 zenon_H16a. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.36 apply (zenon_L42_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.36 exact (zenon_H18f zenon_Hd2). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_L839_); trivial. % 30.22/30.36 (* end of lemma zenon_L1448_ *) % 30.22/30.36 assert (zenon_L1449_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H2b1 zenon_H16a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Hd1 zenon_H6e zenon_H4e zenon_H37 zenon_H4a zenon_H156 zenon_H1ab. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.22/30.36 apply (zenon_L1448_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.22/30.36 apply (zenon_L729_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.22/30.36 apply (zenon_L841_); trivial. % 30.22/30.36 exact (zenon_H1ab zenon_H112). % 30.22/30.36 (* end of lemma zenon_L1449_ *) % 30.22/30.36 assert (zenon_L1450_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.36 apply (zenon_L763_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.36 exact (zenon_H18f zenon_Hd2). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_L150_); trivial. % 30.22/30.36 (* end of lemma zenon_L1450_ *) % 30.22/30.36 assert (zenon_L1451_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1ab zenon_H156 zenon_H4e zenon_H6e zenon_Hd1 zenon_H1e zenon_H16a zenon_H2b1 zenon_H19e zenon_He9 zenon_H35 zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H13b zenon_H100. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.36 apply (zenon_L4_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.36 apply (zenon_L1449_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.36 apply (zenon_L922_); trivial. % 30.22/30.36 apply (zenon_L1450_); trivial. % 30.22/30.36 (* end of lemma zenon_L1451_ *) % 30.22/30.36 assert (zenon_L1452_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H101 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_H35 zenon_H2b1 zenon_H16a zenon_H1e zenon_Hd1 zenon_H6e zenon_H4e zenon_H156 zenon_H1ab zenon_H2d zenon_H42 zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.36 apply (zenon_L1451_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.36 apply (zenon_L824_); trivial. % 30.22/30.36 apply (zenon_L1184_); trivial. % 30.22/30.36 (* end of lemma zenon_L1452_ *) % 30.22/30.36 assert (zenon_L1453_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H16f zenon_H100 zenon_H13b zenon_H18f zenon_H18c zenon_H6c zenon_H102 zenon_H35 zenon_He9 zenon_H19e zenon_H1e zenon_Hd1 zenon_H2d zenon_H42 zenon_H1ab zenon_H156 zenon_H4a zenon_H2b0 zenon_H2b1 zenon_H6f zenon_H19a zenon_H4e zenon_H16b zenon_H16a. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.22/30.36 apply (zenon_L1451_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.22/30.36 apply (zenon_L842_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.22/30.36 apply (zenon_L235_); trivial. % 30.22/30.36 apply (zenon_L859_); trivial. % 30.22/30.36 (* end of lemma zenon_L1453_ *) % 30.22/30.36 assert (zenon_L1454_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H101 zenon_H16a zenon_H16b zenon_H4e zenon_H6f zenon_H2b1 zenon_H2b0 zenon_H4a zenon_H156 zenon_H1ab zenon_H42 zenon_H2d zenon_Hd1 zenon_H1e zenon_H35 zenon_H102 zenon_H6c zenon_H18c zenon_H18f zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.36 apply (zenon_L1453_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.36 apply (zenon_L824_); trivial. % 30.22/30.36 apply (zenon_L1184_); trivial. % 30.22/30.36 (* end of lemma zenon_L1454_ *) % 30.22/30.36 assert (zenon_L1455_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H174 zenon_He1 zenon_H73 zenon_Hee zenon_H3f zenon_H1f zenon_H23b zenon_Hd9 zenon_H8d zenon_H101 zenon_H16a zenon_H4e zenon_H6f zenon_H2b1 zenon_H2b0 zenon_H4a zenon_H156 zenon_H1ab zenon_H42 zenon_H2d zenon_Hd1 zenon_H1e zenon_H35 zenon_H102 zenon_H6c zenon_H18c zenon_H18f zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.36 apply (zenon_L232_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.36 apply (zenon_L4_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.22/30.36 apply (zenon_L149_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.22/30.36 apply (zenon_L1452_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.22/30.36 apply (zenon_L157_); trivial. % 30.22/30.36 apply (zenon_L1187_); trivial. % 30.22/30.36 apply (zenon_L1454_); trivial. % 30.22/30.36 (* end of lemma zenon_L1455_ *) % 30.22/30.36 assert (zenon_L1456_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_H4e zenon_H117 zenon_H1a5. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.36 apply (zenon_L94_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.36 apply (zenon_L159_); trivial. % 30.22/30.36 apply (zenon_L828_); trivial. % 30.22/30.36 (* end of lemma zenon_L1456_ *) % 30.22/30.36 assert (zenon_L1457_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hfe zenon_H4c zenon_H1b1 zenon_H4e zenon_H117 zenon_H1a5. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.36 apply (zenon_L94_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.36 apply (zenon_L1177_); trivial. % 30.22/30.36 apply (zenon_L828_); trivial. % 30.22/30.36 (* end of lemma zenon_L1457_ *) % 30.22/30.36 assert (zenon_L1458_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H159 zenon_Hc3 zenon_H14f. % 30.22/30.36 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 30.22/30.36 intro zenon_D_pnotp. % 30.22/30.36 apply zenon_H159. % 30.22/30.36 rewrite <- zenon_D_pnotp. % 30.22/30.36 exact zenon_Hc3. % 30.22/30.36 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H284]. % 30.22/30.36 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.22/30.36 congruence. % 30.22/30.36 apply zenon_Hc5. apply refl_equal. % 30.22/30.36 apply zenon_H284. apply sym_equal. exact zenon_H14f. % 30.22/30.36 (* end of lemma zenon_L1458_ *) % 30.22/30.36 assert (zenon_L1459_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H102 zenon_H14f zenon_H159 zenon_H18f zenon_H13b zenon_H4a zenon_H33 zenon_H16a. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.36 apply (zenon_L1458_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.36 exact (zenon_H18f zenon_Hd2). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_L839_); trivial. % 30.22/30.36 (* end of lemma zenon_L1459_ *) % 30.22/30.36 assert (zenon_L1460_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H2b4 zenon_H20 zenon_H16a zenon_H33 zenon_H4a zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H156 zenon_H14e zenon_H48 zenon_H6e. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.22/30.36 apply (zenon_L117_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.22/30.36 apply (zenon_L1459_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.22/30.36 apply (zenon_L737_); trivial. % 30.22/30.36 apply (zenon_L770_); trivial. % 30.22/30.36 (* end of lemma zenon_L1460_ *) % 30.22/30.36 assert (zenon_L1461_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H102 zenon_H14f zenon_H159 zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H1e5. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.36 apply (zenon_L1458_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.36 exact (zenon_H18f zenon_Hd2). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_L841_); trivial. % 30.22/30.36 (* end of lemma zenon_L1461_ *) % 30.22/30.36 assert (zenon_L1462_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H2b1 zenon_H6e zenon_H48 zenon_H14e zenon_H16a zenon_H20 zenon_H2b4 zenon_H3d zenon_H4e zenon_H19e zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H159 zenon_H14f zenon_H102 zenon_H1ab. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.22/30.36 apply (zenon_L1460_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.22/30.36 apply (zenon_L731_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.22/30.36 apply (zenon_L1461_); trivial. % 30.22/30.36 exact (zenon_H1ab zenon_H112). % 30.22/30.36 (* end of lemma zenon_L1462_ *) % 30.22/30.36 assert (zenon_L1463_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H102 zenon_H14f zenon_H159 zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.36 apply (zenon_L1458_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.36 exact (zenon_H18f zenon_Hd2). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_L150_); trivial. % 30.22/30.36 (* end of lemma zenon_L1463_ *) % 30.22/30.36 assert (zenon_L1464_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H42 zenon_H2d zenon_Hd1 zenon_H35 zenon_H1e zenon_H1ab zenon_H156 zenon_H4a zenon_H19e zenon_H4e zenon_H2b4 zenon_H20 zenon_H16a zenon_H14e zenon_H48 zenon_H6e zenon_H2b1 zenon_H102 zenon_H14f zenon_H159 zenon_H18f zenon_H13b zenon_H100. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.36 apply (zenon_L4_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.36 apply (zenon_L1449_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.36 apply (zenon_L1462_); trivial. % 30.22/30.36 apply (zenon_L1463_); trivial. % 30.22/30.36 (* end of lemma zenon_L1464_ *) % 30.22/30.36 assert (zenon_L1465_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H18c zenon_H90 zenon_Had zenon_H1a5 zenon_H117 zenon_H1b1 zenon_H4c zenon_H15a zenon_H73 zenon_H173 zenon_H42 zenon_H2d zenon_Hd1 zenon_H35 zenon_H1e zenon_H1ab zenon_H156 zenon_H4a zenon_H19e zenon_H4e zenon_H2b4 zenon_H20 zenon_H16a zenon_H14e zenon_H48 zenon_H6e zenon_H2b1 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H100. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.22/30.36 apply (zenon_L740_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.22/30.36 apply (zenon_L769_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.22/30.36 apply (zenon_L1457_); trivial. % 30.22/30.36 apply (zenon_L1464_); trivial. % 30.22/30.36 (* end of lemma zenon_L1465_ *) % 30.22/30.36 assert (zenon_L1466_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H142 zenon_H19e zenon_H3d. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.36 apply (zenon_L42_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.36 exact (zenon_H18f zenon_Hd2). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.36 apply (zenon_L79_); trivial. % 30.22/30.36 apply (zenon_L131_); trivial. % 30.22/30.36 (* end of lemma zenon_L1466_ *) % 30.22/30.36 assert (zenon_L1467_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H200 zenon_H100 zenon_H13b zenon_H159 zenon_H2b1 zenon_H14e zenon_H16a zenon_H20 zenon_H2b4 zenon_H4e zenon_H4a zenon_H1ab zenon_Hd1 zenon_H2d zenon_H42 zenon_H173 zenon_H73 zenon_H15a zenon_H4c zenon_H1b1 zenon_H117 zenon_H1a5 zenon_Had zenon_H90 zenon_H18c zenon_H172 zenon_H3c zenon_H3d zenon_H19e zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_H156 zenon_H48 zenon_H6e. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.36 apply (zenon_L1465_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.36 apply (zenon_L207_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.36 apply (zenon_L1466_); trivial. % 30.22/30.36 apply (zenon_L737_); trivial. % 30.22/30.36 (* end of lemma zenon_L1467_ *) % 30.22/30.36 assert (zenon_L1468_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> False). % 30.22/30.36 do 0 intro. intros zenon_Hee zenon_H4e zenon_H155 zenon_Hb6. % 30.22/30.36 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 30.22/30.36 intro zenon_D_pnotp. % 30.22/30.36 apply zenon_Hee. % 30.22/30.36 rewrite <- zenon_D_pnotp. % 30.22/30.36 exact zenon_H4e. % 30.22/30.36 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 30.22/30.36 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 30.22/30.36 congruence. % 30.22/30.36 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 30.22/30.36 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e2)))). % 30.22/30.36 intro zenon_D_pnotp. % 30.22/30.36 apply zenon_H2ad. % 30.22/30.36 rewrite <- zenon_D_pnotp. % 30.22/30.36 exact zenon_H19b. % 30.22/30.36 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 30.22/30.36 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2ac]. % 30.22/30.36 congruence. % 30.22/30.36 apply (zenon_L827_); trivial. % 30.22/30.36 apply zenon_H19c. apply refl_equal. % 30.22/30.36 apply zenon_H19c. apply refl_equal. % 30.22/30.36 apply zenon_Hb7. apply sym_equal. exact zenon_Hb6. % 30.22/30.36 (* end of lemma zenon_L1468_ *) % 30.22/30.36 assert (zenon_L1469_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e2)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H1fd zenon_H6e zenon_H48 zenon_H156 zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H19e zenon_H3d zenon_H3c zenon_H172 zenon_H18c zenon_H90 zenon_Had zenon_H1a5 zenon_H1b1 zenon_H4c zenon_H15a zenon_H73 zenon_H173 zenon_H42 zenon_H2d zenon_Hd1 zenon_H1ab zenon_H4a zenon_H2b4 zenon_H20 zenon_H16a zenon_H14e zenon_H2b1 zenon_H159 zenon_H13b zenon_H100 zenon_H200 zenon_H6f zenon_H19a zenon_H20e zenon_Hee zenon_H4e zenon_H155. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.22/30.36 apply (zenon_L1467_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.22/30.36 apply (zenon_L235_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.22/30.36 apply (zenon_L829_); trivial. % 30.22/30.36 apply (zenon_L1468_); trivial. % 30.22/30.36 (* end of lemma zenon_L1469_ *) % 30.22/30.36 assert (zenon_L1470_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H2b4 zenon_H2d zenon_H16b zenon_H100 zenon_H40 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H156 zenon_H14e zenon_H48 zenon_H6e. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.22/30.36 apply (zenon_L848_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.22/30.36 apply (zenon_L1463_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.22/30.36 apply (zenon_L737_); trivial. % 30.22/30.36 apply (zenon_L770_); trivial. % 30.22/30.36 (* end of lemma zenon_L1470_ *) % 30.22/30.36 assert (zenon_L1471_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H18c zenon_H76 zenon_H2d zenon_H2b4 zenon_H100 zenon_H40 zenon_H6f zenon_H19a zenon_H4e zenon_H16b zenon_H16a. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.22/30.36 apply (zenon_L865_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.22/30.36 apply (zenon_L150_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.22/30.36 apply (zenon_L235_); trivial. % 30.22/30.36 apply (zenon_L859_); trivial. % 30.22/30.36 (* end of lemma zenon_L1471_ *) % 30.22/30.36 assert (zenon_L1472_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H8d zenon_H15a zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H16b zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.22/30.36 apply (zenon_L860_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.22/30.36 apply (zenon_L1470_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.22/30.36 apply (zenon_L1471_); trivial. % 30.22/30.36 apply (zenon_L862_); trivial. % 30.22/30.36 (* end of lemma zenon_L1472_ *) % 30.22/30.36 assert (zenon_L1473_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H102 zenon_H90 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.36 apply (zenon_L769_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.36 exact (zenon_H18f zenon_Hd2). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_L150_); trivial. % 30.22/30.36 (* end of lemma zenon_L1473_ *) % 30.22/30.36 assert (zenon_L1474_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H92 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H4e zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_H173 zenon_Hcd zenon_H1a5 zenon_H1e zenon_H73 zenon_He1 zenon_H174 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.22/30.36 apply (zenon_L998_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.36 apply (zenon_L232_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.36 apply (zenon_L4_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.36 apply (zenon_L48_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.36 apply (zenon_L159_); trivial. % 30.22/30.36 apply (zenon_L828_); trivial. % 30.22/30.36 apply (zenon_L1472_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.22/30.36 apply (zenon_L1450_); trivial. % 30.22/30.36 apply (zenon_L1473_); trivial. % 30.22/30.36 (* end of lemma zenon_L1474_ *) % 30.22/30.36 assert (zenon_L1475_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H52 zenon_Hfc zenon_Hc0 zenon_H23b zenon_H19a zenon_Hee zenon_H3f zenon_He7 zenon_Had zenon_H174 zenon_H16f zenon_H2b0 zenon_Hd9 zenon_H101 zenon_H4c zenon_H2b1 zenon_H156 zenon_H4e zenon_Hd1 zenon_H35 zenon_H13b zenon_H16a zenon_H4a zenon_H102 zenon_H19e zenon_H18c zenon_H100 zenon_H42 zenon_H6f zenon_H8d zenon_H1e zenon_H2d zenon_He1 zenon_H1fd zenon_H20e zenon_H172 zenon_H20 zenon_H159 zenon_H14e zenon_H2b4 zenon_H1b1 zenon_H48 zenon_H3c zenon_H200 zenon_H92 zenon_H97 zenon_H15a zenon_H1a5 zenon_H173 zenon_H73 zenon_Hcd zenon_H53. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.22/30.36 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.22/30.36 apply (zenon_L998_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.22/30.36 apply (zenon_L1446_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.22/30.36 apply (zenon_L1447_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.22/30.36 apply (zenon_L1455_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.36 apply (zenon_L232_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.36 apply (zenon_L4_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.36 apply (zenon_L1456_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.22/30.36 apply (zenon_L232_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.36 apply (zenon_L94_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.36 apply (zenon_L159_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.36 apply (zenon_L4_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.36 apply (zenon_L842_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.36 apply (zenon_L1469_); trivial. % 30.22/30.36 apply (zenon_L1474_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.22/30.36 apply (zenon_L865_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.22/30.36 apply (zenon_L842_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.22/30.36 apply (zenon_L235_); trivial. % 30.22/30.36 apply (zenon_L859_); trivial. % 30.22/30.36 apply (zenon_L39_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.22/30.36 apply (zenon_L136_); trivial. % 30.22/30.36 apply (zenon_L1448_); trivial. % 30.22/30.36 apply (zenon_L1474_); trivial. % 30.22/30.36 apply (zenon_L130_); trivial. % 30.22/30.36 (* end of lemma zenon_L1475_ *) % 30.22/30.36 assert (zenon_L1476_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 30.22/30.36 do 0 intro. intros zenon_H102 zenon_Hfe zenon_Hfc zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H1e5. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.36 apply (zenon_L59_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.36 exact (zenon_H18f zenon_Hd2). % 30.22/30.36 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.36 exact (zenon_H13b zenon_Hfd). % 30.22/30.36 apply (zenon_L841_); trivial. % 30.22/30.36 (* end of lemma zenon_L1476_ *) % 30.22/30.36 assert (zenon_L1477_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.22/30.36 do 0 intro. intros zenon_H2b1 zenon_H20 zenon_H185 zenon_H19a zenon_H2b0 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_Hfc zenon_Hfe zenon_H102 zenon_H1ab. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.22/30.36 apply (zenon_L117_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.22/30.36 apply (zenon_L840_); trivial. % 30.22/30.36 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.22/30.36 apply (zenon_L1476_); trivial. % 30.22/30.36 exact (zenon_H1ab zenon_H112). % 30.22/30.36 (* end of lemma zenon_L1477_ *) % 30.22/30.36 assert (zenon_L1478_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H2b1 zenon_H6e zenon_H48 zenon_H14e zenon_H16a zenon_H2b4 zenon_H20 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H159 zenon_H14f zenon_H102 zenon_H1ab. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.22/30.37 apply (zenon_L1460_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.22/30.37 apply (zenon_L658_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.22/30.37 apply (zenon_L1461_); trivial. % 30.22/30.37 exact (zenon_H1ab zenon_H112). % 30.22/30.37 (* end of lemma zenon_L1478_ *) % 30.22/30.37 assert (zenon_L1479_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H6c zenon_H18c zenon_Hfc zenon_H2b0 zenon_H19a zenon_H185 zenon_H2b1 zenon_H6e zenon_H48 zenon_H14e zenon_H16a zenon_H2b4 zenon_H20 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H1ab. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.22/30.37 apply (zenon_L740_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.22/30.37 apply (zenon_L763_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.22/30.37 apply (zenon_L1477_); trivial. % 30.22/30.37 apply (zenon_L1478_); trivial. % 30.22/30.37 (* end of lemma zenon_L1479_ *) % 30.22/30.37 assert (zenon_L1480_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H102 zenon_H1ba zenon_H19e zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H1e5. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.37 apply (zenon_L347_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.37 exact (zenon_H18f zenon_Hd2). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 apply (zenon_L841_); trivial. % 30.22/30.37 (* end of lemma zenon_L1480_ *) % 30.22/30.37 assert (zenon_L1481_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H2b1 zenon_H48 zenon_H14e zenon_H159 zenon_H16a zenon_H20 zenon_H2b4 zenon_Hd1 zenon_H6e zenon_H4e zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H19e zenon_H1ba zenon_H102 zenon_H1ab. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.22/30.37 apply (zenon_L1460_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.22/30.37 apply (zenon_L729_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.22/30.37 apply (zenon_L1480_); trivial. % 30.22/30.37 exact (zenon_H1ab zenon_H112). % 30.22/30.37 (* end of lemma zenon_L1481_ *) % 30.22/30.37 assert (zenon_L1482_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H18c zenon_H90 zenon_Had zenon_Hfc zenon_H2b0 zenon_H19a zenon_H185 zenon_H2b1 zenon_H6e zenon_H48 zenon_H14e zenon_H16a zenon_H2b4 zenon_H20 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H1ab. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.22/30.37 apply (zenon_L740_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.22/30.37 apply (zenon_L769_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.22/30.37 apply (zenon_L1477_); trivial. % 30.22/30.37 apply (zenon_L1478_); trivial. % 30.22/30.37 (* end of lemma zenon_L1482_ *) % 30.22/30.37 assert (zenon_L1483_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H135 zenon_Hc8 zenon_Hd5 zenon_Hde zenon_H142 zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_H156. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.37 apply (zenon_L43_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.37 apply (zenon_L212_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.37 apply (zenon_L89_); trivial. % 30.22/30.37 apply (zenon_L1432_); trivial. % 30.22/30.37 (* end of lemma zenon_L1483_ *) % 30.22/30.37 assert (zenon_L1484_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H208 zenon_H6f zenon_H156 zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_Hc8 zenon_H56 zenon_H135 zenon_He1 zenon_H76 zenon_H19a zenon_H4c zenon_H19e zenon_Hde zenon_H142 zenon_Hcd. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.22/30.37 apply (zenon_L157_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.22/30.37 apply (zenon_L1483_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.22/30.37 exact (zenon_H56 zenon_H25). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.37 apply (zenon_L273_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.37 apply (zenon_L824_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.37 apply (zenon_L89_); trivial. % 30.22/30.37 apply (zenon_L1017_); trivial. % 30.22/30.37 (* end of lemma zenon_L1484_ *) % 30.22/30.37 assert (zenon_L1485_ : (((op (e2) (op (e2) (e0))) = (e0))/\(((op (e2) (op (e2) (e1))) = (e1))/\(((op (e2) (op (e2) (e2))) = (e2))/\(((op (e2) (op (e2) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0)))/\(((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3)))))))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e0) (e0)) = (e2)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H5a zenon_H304 zenon_H73. % 30.22/30.37 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.22/30.37 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.22/30.37 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.22/30.37 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.22/30.37 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H29b); [ zenon_intro zenon_H74 | zenon_intro zenon_H10e ]. % 30.22/30.37 exact (zenon_H74 zenon_H73). % 30.22/30.37 exact (zenon_H304 zenon_H10e). % 30.22/30.37 (* end of lemma zenon_L1485_ *) % 30.22/30.37 assert (zenon_L1486_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H102 zenon_H35 zenon_H1e zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.37 apply (zenon_L42_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.37 apply (zenon_L130_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 exact (zenon_H103 zenon_H37). % 30.22/30.37 (* end of lemma zenon_L1486_ *) % 30.22/30.37 assert (zenon_L1487_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H102 zenon_Hfe zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.37 apply (zenon_L59_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.37 apply (zenon_L130_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 exact (zenon_H103 zenon_H37). % 30.22/30.37 (* end of lemma zenon_L1487_ *) % 30.22/30.37 assert (zenon_L1488_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_Hf4 zenon_H14e. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.37 apply (zenon_L94_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.37 apply (zenon_L159_); trivial. % 30.22/30.37 apply (zenon_L525_); trivial. % 30.22/30.37 (* end of lemma zenon_L1488_ *) % 30.22/30.37 assert (zenon_L1489_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H11b zenon_H110 zenon_H9c zenon_H1e5 zenon_Hf6 zenon_H14e zenon_H19a zenon_Hcd zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_Hb9. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.22/30.37 apply (zenon_L65_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.22/30.37 apply (zenon_L187_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.22/30.37 apply (zenon_L1488_); trivial. % 30.22/30.37 exact (zenon_Hb9 zenon_Hbc). % 30.22/30.37 (* end of lemma zenon_L1489_ *) % 30.22/30.37 assert (zenon_L1490_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H102 zenon_H112 zenon_H155 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.37 apply (zenon_L279_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.37 apply (zenon_L130_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 exact (zenon_H103 zenon_H37). % 30.22/30.37 (* end of lemma zenon_L1490_ *) % 30.22/30.37 assert (zenon_L1491_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H2b1 zenon_H20 zenon_H185 zenon_Hb9 zenon_H173 zenon_H73 zenon_H15a zenon_Hcd zenon_H14e zenon_Hf6 zenon_H9c zenon_H110 zenon_H11b zenon_H102 zenon_H155 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.22/30.37 apply (zenon_L117_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.22/30.37 apply (zenon_L1135_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.22/30.37 apply (zenon_L1489_); trivial. % 30.22/30.37 apply (zenon_L1490_); trivial. % 30.22/30.37 (* end of lemma zenon_L1491_ *) % 30.22/30.37 assert (zenon_L1492_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H14b zenon_H304 zenon_H6b zenon_Hdf zenon_H2b1 zenon_H20 zenon_H185 zenon_Hb9 zenon_H173 zenon_H73 zenon_H15a zenon_Hcd zenon_H14e zenon_Hf6 zenon_H110 zenon_H11b zenon_H102 zenon_H155 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.22/30.37 exact (zenon_H304 zenon_H10e). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.22/30.37 apply (zenon_L1487_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.22/30.37 apply (zenon_L303_); trivial. % 30.22/30.37 apply (zenon_L1491_); trivial. % 30.22/30.37 (* end of lemma zenon_L1492_ *) % 30.22/30.37 assert (zenon_L1493_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H14b zenon_H304 zenon_Hd6 zenon_H1ba zenon_H2b1 zenon_H20 zenon_H185 zenon_Hb9 zenon_H173 zenon_H73 zenon_H15a zenon_Hcd zenon_H14e zenon_Hf6 zenon_H110 zenon_H11b zenon_H102 zenon_H155 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.22/30.37 exact (zenon_H304 zenon_H10e). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.22/30.37 apply (zenon_L1487_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.22/30.37 apply (zenon_L161_); trivial. % 30.22/30.37 apply (zenon_L1491_); trivial. % 30.22/30.37 (* end of lemma zenon_L1493_ *) % 30.22/30.37 assert (zenon_L1494_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_Hb8 zenon_Had zenon_H6e zenon_H98 zenon_H6f zenon_H10d zenon_H117 zenon_Hb9. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.22/30.37 apply (zenon_L34_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.22/30.37 apply (zenon_L80_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.22/30.37 apply (zenon_L151_); trivial. % 30.22/30.37 exact (zenon_Hb9 zenon_Hbc). % 30.22/30.37 (* end of lemma zenon_L1494_ *) % 30.22/30.37 assert (zenon_L1495_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e2)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H1fd zenon_Hb9 zenon_H10d zenon_H98 zenon_H6e zenon_Had zenon_Hb8 zenon_H6f zenon_H19a zenon_H1db zenon_He1 zenon_Heb. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.22/30.37 apply (zenon_L1494_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.22/30.37 apply (zenon_L235_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.22/30.37 exact (zenon_H1db zenon_H1b9). % 30.22/30.37 apply (zenon_L204_); trivial. % 30.22/30.37 (* end of lemma zenon_L1495_ *) % 30.22/30.37 assert (zenon_L1496_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H23b zenon_H20 zenon_H8b zenon_Heb zenon_He1 zenon_H1db zenon_H6f zenon_Hb8 zenon_Had zenon_H6e zenon_H10d zenon_Hb9 zenon_H1fd zenon_Hee zenon_H102 zenon_H155 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.37 apply (zenon_L27_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.37 apply (zenon_L1495_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.37 apply (zenon_L337_); trivial. % 30.22/30.37 apply (zenon_L1490_); trivial. % 30.22/30.37 (* end of lemma zenon_L1496_ *) % 30.22/30.37 assert (zenon_L1497_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H100 zenon_Hc3 zenon_H95. % 30.22/30.37 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 30.22/30.37 intro zenon_D_pnotp. % 30.22/30.37 apply zenon_H100. % 30.22/30.37 rewrite <- zenon_D_pnotp. % 30.22/30.37 exact zenon_Hc3. % 30.22/30.37 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 30.22/30.37 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.22/30.37 congruence. % 30.22/30.37 apply zenon_Hc5. apply refl_equal. % 30.22/30.37 apply zenon_H96. apply sym_equal. exact zenon_H95. % 30.22/30.37 (* end of lemma zenon_L1497_ *) % 30.22/30.37 assert (zenon_L1498_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H102 zenon_H95 zenon_H100 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.37 apply (zenon_L1497_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.37 apply (zenon_L130_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 exact (zenon_H103 zenon_H37). % 30.22/30.37 (* end of lemma zenon_L1498_ *) % 30.22/30.37 assert (zenon_L1499_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H125 zenon_H73 zenon_Hd9 zenon_Hcd zenon_Hde zenon_Hbd zenon_H155 zenon_Hee zenon_H1fd zenon_Hb9 zenon_H10d zenon_H6e zenon_Had zenon_Hb8 zenon_H6f zenon_H1db zenon_He1 zenon_H20 zenon_H23b zenon_H103 zenon_H13b zenon_H19a zenon_Hfc zenon_H100 zenon_H102 zenon_H142 zenon_H1dc zenon_Ha4 zenon_H185. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.22/30.37 apply (zenon_L47_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.22/30.37 apply (zenon_L159_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.22/30.37 apply (zenon_L89_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.22/30.37 apply (zenon_L1496_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.22/30.37 apply (zenon_L1498_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.22/30.37 apply (zenon_L177_); trivial. % 30.22/30.37 apply (zenon_L869_); trivial. % 30.22/30.37 (* end of lemma zenon_L1499_ *) % 30.22/30.37 assert (zenon_L1500_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (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))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H200 zenon_H6b zenon_H11b zenon_H110 zenon_Hf6 zenon_H14e zenon_H15a zenon_H173 zenon_H2b1 zenon_Hd6 zenon_H304 zenon_H14b zenon_Ha4 zenon_H1dc zenon_H102 zenon_H100 zenon_Hfc zenon_H19a zenon_H13b zenon_H103 zenon_H23b zenon_H20 zenon_He1 zenon_H1db zenon_H6f zenon_Hb8 zenon_Had zenon_H6e zenon_H10d zenon_Hb9 zenon_H1fd zenon_Hee zenon_Hbd zenon_Hde zenon_Hcd zenon_Hd9 zenon_H73 zenon_H125 zenon_H218 zenon_H185. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.37 apply (zenon_L94_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.37 apply (zenon_L159_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.37 apply (zenon_L1492_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.37 apply (zenon_L1493_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.37 apply (zenon_L1499_); trivial. % 30.22/30.37 apply (zenon_L1088_); trivial. % 30.22/30.37 (* end of lemma zenon_L1500_ *) % 30.22/30.37 assert (zenon_L1501_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H14b zenon_H304 zenon_H6b zenon_Hdf zenon_H2b1 zenon_H20 zenon_H185 zenon_Hb9 zenon_H173 zenon_H73 zenon_H15a zenon_Hcd zenon_H14e zenon_Hf6 zenon_H110 zenon_H11b zenon_H102 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.37 apply (zenon_L94_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.37 apply (zenon_L159_); trivial. % 30.22/30.37 apply (zenon_L1492_); trivial. % 30.22/30.37 (* end of lemma zenon_L1501_ *) % 30.22/30.37 assert (zenon_L1502_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H135 zenon_H73 zenon_Hc8 zenon_He1 zenon_H3d zenon_Hde zenon_H142 zenon_Hcd zenon_H1e5. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.37 apply (zenon_L43_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.37 apply (zenon_L126_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.37 apply (zenon_L89_); trivial. % 30.22/30.37 apply (zenon_L1017_); trivial. % 30.22/30.37 (* end of lemma zenon_L1502_ *) % 30.22/30.37 assert (zenon_L1503_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H200 zenon_H103 zenon_Hfc zenon_H102 zenon_H11b zenon_H110 zenon_Hf6 zenon_H14e zenon_Hb9 zenon_H20 zenon_H2b1 zenon_H6b zenon_H304 zenon_H14b zenon_H1e zenon_H3c zenon_Hcd zenon_Hde zenon_H3d zenon_He1 zenon_Hc8 zenon_H73 zenon_H135 zenon_H76 zenon_H173 zenon_H15a zenon_H13b zenon_H19a zenon_H156 zenon_H6f zenon_H208 zenon_H218 zenon_H185. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.37 apply (zenon_L1501_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.37 apply (zenon_L207_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.22/30.37 apply (zenon_L157_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.22/30.37 apply (zenon_L1483_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.22/30.37 apply (zenon_L23_); trivial. % 30.22/30.37 apply (zenon_L1502_); trivial. % 30.22/30.37 apply (zenon_L1088_); trivial. % 30.22/30.37 (* end of lemma zenon_L1503_ *) % 30.22/30.37 assert (zenon_L1504_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H23b zenon_H20 zenon_H8b zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hf6 zenon_H1e5. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.37 apply (zenon_L27_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.37 apply (zenon_L336_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.37 apply (zenon_L337_); trivial. % 30.22/30.37 apply (zenon_L187_); trivial. % 30.22/30.37 (* end of lemma zenon_L1504_ *) % 30.22/30.37 assert (zenon_L1505_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_Hbd zenon_Hee zenon_H3f zenon_H1f zenon_H20 zenon_H23b zenon_H40 zenon_H2d zenon_Hb9 zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_H14e zenon_Hf6 zenon_H1e5 zenon_H110 zenon_H11b zenon_Ha4 zenon_H185. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.22/30.37 apply (zenon_L1504_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.22/30.37 apply (zenon_L766_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.22/30.37 apply (zenon_L1489_); trivial. % 30.22/30.37 apply (zenon_L869_); trivial. % 30.22/30.37 (* end of lemma zenon_L1505_ *) % 30.22/30.37 assert (zenon_L1506_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H208 zenon_H6f zenon_H76 zenon_H156 zenon_H142 zenon_Hde zenon_Hc8 zenon_H135 zenon_H20e zenon_Hbd zenon_Hee zenon_H3f zenon_H1f zenon_H20 zenon_H23b zenon_H40 zenon_H2d zenon_Hb9 zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_H14e zenon_Hf6 zenon_H110 zenon_H11b zenon_Ha4 zenon_H185. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.22/30.37 apply (zenon_L157_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.22/30.37 apply (zenon_L1483_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.22/30.37 apply (zenon_L225_); trivial. % 30.22/30.37 apply (zenon_L1505_); trivial. % 30.22/30.37 (* end of lemma zenon_L1506_ *) % 30.22/30.37 assert (zenon_L1507_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H42 zenon_He1 zenon_H3c zenon_H1e zenon_H200 zenon_H6b zenon_H103 zenon_Hfc zenon_H102 zenon_H2b1 zenon_Hd6 zenon_H304 zenon_H14b zenon_Ha4 zenon_H11b zenon_H110 zenon_Hf6 zenon_H14e zenon_H19a zenon_Hcd zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_Hb9 zenon_H2d zenon_H23b zenon_H20 zenon_H1f zenon_H3f zenon_Hee zenon_Hbd zenon_H20e zenon_H135 zenon_Hc8 zenon_Hde zenon_H156 zenon_H76 zenon_H6f zenon_H208 zenon_H218 zenon_H185. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.37 apply (zenon_L94_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.37 apply (zenon_L159_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.37 apply (zenon_L4_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.37 exact (zenon_H103 zenon_H37). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.37 apply (zenon_L1503_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.37 apply (zenon_L1492_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.37 apply (zenon_L1493_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.37 apply (zenon_L1506_); trivial. % 30.22/30.37 apply (zenon_L1088_); trivial. % 30.22/30.37 (* end of lemma zenon_L1507_ *) % 30.22/30.37 assert (zenon_L1508_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H14b zenon_H304 zenon_Hd6 zenon_H1ba zenon_H2b1 zenon_H20 zenon_H185 zenon_Hb9 zenon_H173 zenon_H73 zenon_H15a zenon_Hcd zenon_H14e zenon_Hf6 zenon_H110 zenon_H11b zenon_H102 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.37 apply (zenon_L94_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.37 apply (zenon_L159_); trivial. % 30.22/30.37 apply (zenon_L1493_); trivial. % 30.22/30.37 (* end of lemma zenon_L1508_ *) % 30.22/30.37 assert (zenon_L1509_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_Hbd zenon_Hee zenon_H3f zenon_H1f zenon_H20 zenon_H23b zenon_Hc3 zenon_H100 zenon_Hb9 zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_H14e zenon_Hf6 zenon_H1e5 zenon_H110 zenon_H11b zenon_Ha4 zenon_H185. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.22/30.37 apply (zenon_L1504_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.22/30.37 apply (zenon_L1497_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.22/30.37 apply (zenon_L1489_); trivial. % 30.22/30.37 apply (zenon_L869_); trivial. % 30.22/30.37 (* end of lemma zenon_L1509_ *) % 30.22/30.37 assert (zenon_L1510_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H208 zenon_H6f zenon_H156 zenon_H142 zenon_Hde zenon_Hc8 zenon_H135 zenon_H76 zenon_Hbd zenon_Hee zenon_H3f zenon_H1f zenon_H20 zenon_H23b zenon_Hc3 zenon_H100 zenon_Hb9 zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_H14e zenon_Hf6 zenon_H110 zenon_H11b zenon_Ha4 zenon_H185. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.22/30.37 apply (zenon_L157_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.22/30.37 apply (zenon_L1483_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.22/30.37 apply (zenon_L23_); trivial. % 30.22/30.37 apply (zenon_L1509_); trivial. % 30.22/30.37 (* end of lemma zenon_L1510_ *) % 30.22/30.37 assert (zenon_L1511_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H200 zenon_H6b zenon_H103 zenon_Hfc zenon_H102 zenon_H2b1 zenon_Hd6 zenon_H304 zenon_H14b zenon_Ha4 zenon_H11b zenon_H110 zenon_Hf6 zenon_H14e zenon_H19a zenon_Hcd zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_Hb9 zenon_H100 zenon_Hc3 zenon_H23b zenon_H20 zenon_H1f zenon_H3f zenon_Hee zenon_Hbd zenon_H76 zenon_H135 zenon_Hc8 zenon_Hde zenon_H156 zenon_H6f zenon_H208 zenon_H218 zenon_H185. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.37 apply (zenon_L1501_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.37 apply (zenon_L1508_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.37 apply (zenon_L1510_); trivial. % 30.22/30.37 apply (zenon_L1088_); trivial. % 30.22/30.37 (* end of lemma zenon_L1511_ *) % 30.22/30.37 assert (zenon_L1512_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H296 zenon_H20e zenon_H2d zenon_H3c zenon_He1 zenon_H42 zenon_H218 zenon_H208 zenon_H6f zenon_H156 zenon_Hde zenon_Hc8 zenon_H135 zenon_H76 zenon_Hbd zenon_Hee zenon_H3f zenon_H1f zenon_H23b zenon_Ha4 zenon_H6b zenon_H200 zenon_H11b zenon_H110 zenon_Hf6 zenon_H14e zenon_Hcd zenon_H15a zenon_H73 zenon_H173 zenon_Hb9 zenon_H185 zenon_H20 zenon_H2b1 zenon_Hd6 zenon_H304 zenon_H14b zenon_H102 zenon_H100 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.22/30.37 apply (zenon_L1507_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.22/30.37 apply (zenon_L1511_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.22/30.37 apply (zenon_L1508_); trivial. % 30.22/30.37 apply (zenon_L1498_); trivial. % 30.22/30.37 (* end of lemma zenon_L1512_ *) % 30.22/30.37 assert (zenon_L1513_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H135 zenon_Hc8 zenon_He1 zenon_H3d zenon_Hde zenon_H142 zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_Hcd zenon_H19a zenon_H156. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.37 apply (zenon_L43_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.37 apply (zenon_L126_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.37 apply (zenon_L89_); trivial. % 30.22/30.37 apply (zenon_L1432_); trivial. % 30.22/30.37 (* end of lemma zenon_L1513_ *) % 30.22/30.37 assert (zenon_L1514_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H200 zenon_H6b zenon_H103 zenon_Hfc zenon_H155 zenon_H102 zenon_H11b zenon_H110 zenon_Hf6 zenon_H14e zenon_Hb9 zenon_H20 zenon_H2b1 zenon_Hd6 zenon_H304 zenon_H14b zenon_H156 zenon_H19a zenon_Hcd zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_Hde zenon_H3d zenon_He1 zenon_Hc8 zenon_H135 zenon_H218 zenon_H185. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.37 apply (zenon_L1492_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.37 apply (zenon_L1493_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.37 apply (zenon_L1513_); trivial. % 30.22/30.37 apply (zenon_L1088_); trivial. % 30.22/30.37 (* end of lemma zenon_L1514_ *) % 30.22/30.37 assert (zenon_L1515_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.22/30.37 do 0 intro. intros zenon_Haa zenon_Hc3 zenon_H100 zenon_H1f zenon_H3f zenon_H55 zenon_H222 zenon_H8a zenon_H97. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H95 | zenon_intro zenon_Hab ]. % 30.22/30.37 apply (zenon_L1497_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H98 | zenon_intro zenon_Hac ]. % 30.22/30.37 apply (zenon_L336_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9d | zenon_intro zenon_H40 ]. % 30.22/30.37 apply (zenon_L264_); trivial. % 30.22/30.37 apply (zenon_L862_); trivial. % 30.22/30.37 (* end of lemma zenon_L1515_ *) % 30.22/30.37 assert (zenon_L1516_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H296 zenon_He1 zenon_H2d zenon_H42 zenon_H218 zenon_H135 zenon_Hc8 zenon_H97 zenon_H8a zenon_H222 zenon_H3f zenon_H1f zenon_Haa zenon_Hde zenon_H156 zenon_H6b zenon_H200 zenon_H11b zenon_H110 zenon_Hf6 zenon_H14e zenon_Hcd zenon_H15a zenon_H73 zenon_H173 zenon_Hb9 zenon_H185 zenon_H20 zenon_H2b1 zenon_Hd6 zenon_H304 zenon_H14b zenon_H102 zenon_H100 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.37 apply (zenon_L94_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.37 apply (zenon_L159_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.37 apply (zenon_L4_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.37 exact (zenon_H103 zenon_H37). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.37 apply (zenon_L1514_); trivial. % 30.22/30.37 apply (zenon_L862_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.37 apply (zenon_L94_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.37 apply (zenon_L159_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.37 apply (zenon_L1501_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.37 apply (zenon_L1508_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.37 apply (zenon_L43_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.37 apply (zenon_L1515_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.37 apply (zenon_L89_); trivial. % 30.22/30.37 apply (zenon_L90_); trivial. % 30.22/30.37 apply (zenon_L1088_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.22/30.37 apply (zenon_L1508_); trivial. % 30.22/30.37 apply (zenon_L1498_); trivial. % 30.22/30.37 (* end of lemma zenon_L1516_ *) % 30.22/30.37 assert (zenon_L1517_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.22/30.37 do 0 intro. intros zenon_Hc0 zenon_H103 zenon_H13b zenon_Hfc zenon_H100 zenon_H102 zenon_H14b zenon_H304 zenon_Hd6 zenon_H2b1 zenon_Hb9 zenon_H173 zenon_H73 zenon_H15a zenon_Hcd zenon_H14e zenon_Hf6 zenon_H110 zenon_H11b zenon_H200 zenon_H6b zenon_H156 zenon_Hde zenon_Haa zenon_H3f zenon_H222 zenon_H97 zenon_Hc8 zenon_H135 zenon_H218 zenon_H42 zenon_H2d zenon_He1 zenon_H296 zenon_H20e zenon_H3c zenon_H208 zenon_H6f zenon_Hbd zenon_Hee zenon_H23b zenon_Ha4 zenon_H1dc zenon_H1db zenon_Hb8 zenon_Had zenon_H10d zenon_H1fd zenon_Hd9 zenon_H125 zenon_H8d zenon_H1a5 zenon_H19a zenon_H185 zenon_H20. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.22/30.37 apply (zenon_L998_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.22/30.37 apply (zenon_L232_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.22/30.37 apply (zenon_L1500_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.22/30.37 apply (zenon_L1512_); trivial. % 30.22/30.37 apply (zenon_L1516_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.22/30.37 apply (zenon_L136_); trivial. % 30.22/30.37 apply (zenon_L117_); trivial. % 30.22/30.37 (* end of lemma zenon_L1517_ *) % 30.22/30.37 assert (zenon_L1518_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 30.22/30.37 do 0 intro. intros zenon_Haa zenon_Hc3 zenon_H100 zenon_H90 zenon_H97 zenon_He9 zenon_H3f zenon_H113 zenon_Hbc. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H95 | zenon_intro zenon_Hab ]. % 30.22/30.37 apply (zenon_L1497_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H98 | zenon_intro zenon_Hac ]. % 30.22/30.37 apply (zenon_L30_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9d | zenon_intro zenon_H40 ]. % 30.22/30.37 apply (zenon_L53_); trivial. % 30.22/30.37 apply (zenon_L753_); trivial. % 30.22/30.37 (* end of lemma zenon_L1518_ *) % 30.22/30.37 assert (zenon_L1519_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H102 zenon_Hbc zenon_H113 zenon_H3f zenon_He9 zenon_H97 zenon_H90 zenon_H100 zenon_Haa zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.37 apply (zenon_L1518_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.37 apply (zenon_L130_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.37 exact (zenon_H13b zenon_Hfd). % 30.22/30.37 exact (zenon_H103 zenon_H37). % 30.22/30.37 (* end of lemma zenon_L1519_ *) % 30.22/30.37 assert (zenon_L1520_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H14b zenon_H304 zenon_H103 zenon_H13b zenon_H19a zenon_Hfc zenon_H102 zenon_H6b zenon_Hdf zenon_H97 zenon_H9b zenon_H9d. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.22/30.37 exact (zenon_H304 zenon_H10e). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.22/30.37 apply (zenon_L1487_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.22/30.37 apply (zenon_L303_); trivial. % 30.22/30.37 apply (zenon_L31_); trivial. % 30.22/30.37 (* end of lemma zenon_L1520_ *) % 30.22/30.37 assert (zenon_L1521_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 30.22/30.37 do 0 intro. intros zenon_H14b zenon_H304 zenon_H103 zenon_H13b zenon_H19a zenon_Hfc zenon_H102 zenon_Hd6 zenon_H1ba zenon_H97 zenon_H9b zenon_H9d. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.22/30.37 exact (zenon_H304 zenon_H10e). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.22/30.37 apply (zenon_L1487_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.22/30.37 apply (zenon_L161_); trivial. % 30.22/30.37 apply (zenon_L31_); trivial. % 30.22/30.37 (* end of lemma zenon_L1521_ *) % 30.22/30.37 assert (zenon_L1522_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H135 zenon_H73 zenon_Hc8 zenon_Hbc zenon_H113 zenon_He1 zenon_H103 zenon_H1e zenon_H2d zenon_H42 zenon_Hde zenon_H142 zenon_H155 zenon_H156. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.37 apply (zenon_L43_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.37 apply (zenon_L1308_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.37 apply (zenon_L89_); trivial. % 30.22/30.37 apply (zenon_L90_); trivial. % 30.22/30.37 (* end of lemma zenon_L1522_ *) % 30.22/30.37 assert (zenon_L1523_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H1d2 zenon_H9c zenon_H1dc zenon_H73 zenon_H76 zenon_H55 zenon_Hd6 zenon_H1db. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.22/30.37 apply (zenon_L177_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.22/30.37 apply (zenon_L23_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.22/30.37 apply (zenon_L555_); trivial. % 30.22/30.37 exact (zenon_H1db zenon_H1b9). % 30.22/30.37 (* end of lemma zenon_L1523_ *) % 30.22/30.37 assert (zenon_L1524_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((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 (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.22/30.37 do 0 intro. intros zenon_H14b zenon_H304 zenon_H103 zenon_H13b zenon_H19a zenon_Hfc zenon_H102 zenon_H6b zenon_Hdf zenon_H1d2 zenon_H1dc zenon_H73 zenon_H76 zenon_H55 zenon_Hd6 zenon_H1db. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.22/30.37 exact (zenon_H304 zenon_H10e). % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.22/30.37 apply (zenon_L1487_); trivial. % 30.22/30.37 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.22/30.37 apply (zenon_L303_); trivial. % 30.22/30.37 apply (zenon_L1523_); trivial. % 30.22/30.37 (* end of lemma zenon_L1524_ *) % 30.22/30.37 assert (zenon_L1525_ : ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.37 do 0 intro. intros zenon_Hb3 zenon_Hbc zenon_H1c5 zenon_Hf6. % 30.22/30.37 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.22/30.37 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 30.22/30.37 intro zenon_D_pnotp. % 30.22/30.37 apply zenon_Hf6. % 30.22/30.37 rewrite <- zenon_D_pnotp. % 30.22/30.37 exact zenon_Ha5. % 30.22/30.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.22/30.37 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 30.22/30.37 congruence. % 30.22/30.37 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 30.22/30.37 intro zenon_D_pnotp. % 30.22/30.37 apply zenon_Hf7. % 30.22/30.37 rewrite <- zenon_D_pnotp. % 30.22/30.37 exact zenon_Hb3. % 30.22/30.37 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 30.22/30.37 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 30.22/30.37 congruence. % 30.22/30.37 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.22/30.37 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e3)))). % 30.22/30.37 intro zenon_D_pnotp. % 30.22/30.37 apply zenon_H181. % 30.22/30.37 rewrite <- zenon_D_pnotp. % 30.22/30.37 exact zenon_Ha5. % 30.22/30.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.22/30.37 cut (((op (e3) (e3)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 30.22/30.37 congruence. % 30.22/30.37 apply (zenon_L112_); trivial. % 30.22/30.37 apply zenon_Ha6. apply refl_equal. % 30.22/30.38 apply zenon_Ha6. apply refl_equal. % 30.22/30.38 apply zenon_H1c6. apply sym_equal. exact zenon_H1c5. % 30.22/30.38 apply zenon_Ha6. apply refl_equal. % 30.22/30.38 apply zenon_Ha6. apply refl_equal. % 30.22/30.38 (* end of lemma zenon_L1525_ *) % 30.22/30.38 assert (zenon_L1526_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H1d5 zenon_Hd6 zenon_H73 zenon_H1dc zenon_H1d2 zenon_Hdf zenon_H6b zenon_H102 zenon_Hfc zenon_H19a zenon_H13b zenon_H103 zenon_H304 zenon_H14b zenon_He1 zenon_H55 zenon_H1db zenon_Hb3 zenon_Hbc zenon_Hf6. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.22/30.38 apply (zenon_L1524_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.22/30.38 apply (zenon_L126_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.22/30.38 exact (zenon_H1db zenon_H1b9). % 30.22/30.38 apply (zenon_L1525_); trivial. % 30.22/30.38 (* end of lemma zenon_L1526_ *) % 30.22/30.38 assert (zenon_L1527_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> False). % 30.22/30.38 do 0 intro. intros zenon_H101 zenon_Haa zenon_H100 zenon_H90 zenon_H3f zenon_H113 zenon_Hf6 zenon_Hbc zenon_Hb3 zenon_H1db zenon_He1 zenon_H1d2 zenon_H1dc zenon_H73 zenon_Hd6 zenon_H1d5 zenon_H14b zenon_H304 zenon_H103 zenon_H13b zenon_H19a zenon_Hfc zenon_H102 zenon_H6b zenon_Hdf zenon_H97 zenon_H9b. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.38 apply (zenon_L1519_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.38 exact (zenon_H13b zenon_Hfd). % 30.22/30.38 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.38 apply (zenon_L1526_); trivial. % 30.22/30.38 apply (zenon_L1520_); trivial. % 30.22/30.38 (* end of lemma zenon_L1527_ *) % 30.22/30.38 assert (zenon_L1528_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H23b zenon_H9b zenon_H97 zenon_Hdf zenon_H6b zenon_H102 zenon_Hfc zenon_H13b zenon_H103 zenon_H304 zenon_H14b zenon_H1d5 zenon_Hd6 zenon_H73 zenon_H1dc zenon_H1d2 zenon_He1 zenon_H1db zenon_Hb3 zenon_Hf6 zenon_H113 zenon_H100 zenon_Haa zenon_H101 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hbc zenon_H6f. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.38 apply (zenon_L1527_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.38 apply (zenon_L336_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.38 apply (zenon_L337_); trivial. % 30.22/30.38 apply (zenon_L152_); trivial. % 30.22/30.38 (* end of lemma zenon_L1528_ *) % 30.22/30.38 assert (zenon_L1529_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 30.22/30.38 do 0 intro. intros zenon_Hbd zenon_H6f zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_H20 zenon_H23b zenon_Hc3 zenon_H100 zenon_H142 zenon_H1dc zenon_Hbc zenon_H2d. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.22/30.38 apply (zenon_L1320_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.22/30.38 apply (zenon_L1497_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.22/30.38 apply (zenon_L177_); trivial. % 30.22/30.38 apply (zenon_L107_); trivial. % 30.22/30.38 (* end of lemma zenon_L1529_ *) % 30.22/30.38 assert (zenon_L1530_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H14b zenon_H304 zenon_H103 zenon_H13b zenon_H19a zenon_Hfc zenon_H102 zenon_H1ba zenon_H1d5 zenon_Hd6 zenon_H73 zenon_H1dc zenon_H1d2 zenon_He1 zenon_H55 zenon_H1db zenon_Hb3 zenon_Hbc zenon_Hf6. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.22/30.38 exact (zenon_H304 zenon_H10e). % 30.22/30.38 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.22/30.38 apply (zenon_L1487_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.22/30.38 apply (zenon_L161_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.22/30.38 apply (zenon_L1523_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.22/30.38 apply (zenon_L126_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.22/30.38 exact (zenon_H1db zenon_H1b9). % 30.22/30.38 apply (zenon_L1525_); trivial. % 30.22/30.38 (* end of lemma zenon_L1530_ *) % 30.22/30.38 assert (zenon_L1531_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> False). % 30.22/30.38 do 0 intro. intros zenon_H101 zenon_Haa zenon_H100 zenon_H90 zenon_H3f zenon_H113 zenon_Hf6 zenon_Hbc zenon_Hb3 zenon_H1db zenon_He1 zenon_H1d2 zenon_H1dc zenon_H73 zenon_H1d5 zenon_H14b zenon_H304 zenon_H103 zenon_H13b zenon_H19a zenon_Hfc zenon_H102 zenon_Hd6 zenon_H1ba zenon_H97 zenon_H9b. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.38 apply (zenon_L1519_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.38 exact (zenon_H13b zenon_Hfd). % 30.22/30.38 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.38 apply (zenon_L1530_); trivial. % 30.22/30.38 apply (zenon_L1521_); trivial. % 30.22/30.38 (* end of lemma zenon_L1531_ *) % 30.22/30.38 assert (zenon_L1532_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H296 zenon_H135 zenon_Hc8 zenon_H42 zenon_Hde zenon_H156 zenon_Hcd zenon_H15a zenon_H173 zenon_H185 zenon_H218 zenon_Hbd zenon_H6f zenon_Hee zenon_H1f zenon_H20 zenon_H23b zenon_H2d zenon_H19e zenon_H6b zenon_H200 zenon_H9b zenon_H97 zenon_Hd6 zenon_H304 zenon_H14b zenon_H1d5 zenon_H73 zenon_H1dc zenon_H1d2 zenon_He1 zenon_H1db zenon_Hb3 zenon_Hbc zenon_Hf6 zenon_H113 zenon_H3f zenon_H90 zenon_Haa zenon_H101 zenon_H102 zenon_H100 zenon_Hfc zenon_H19a zenon_H13b zenon_H103. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.38 apply (zenon_L94_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.38 exact (zenon_H13b zenon_Hfd). % 30.22/30.38 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.38 apply (zenon_L159_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.38 apply (zenon_L1519_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.38 exact (zenon_H13b zenon_Hfd). % 30.22/30.38 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.38 apply (zenon_L1308_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.38 apply (zenon_L1520_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.38 apply (zenon_L1521_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.38 apply (zenon_L1522_); trivial. % 30.22/30.38 apply (zenon_L1088_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.22/30.38 apply (zenon_L1528_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.22/30.38 apply (zenon_L347_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.22/30.38 apply (zenon_L1529_); trivial. % 30.22/30.38 apply (zenon_L1088_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.22/30.38 apply (zenon_L1531_); trivial. % 30.22/30.38 apply (zenon_L1498_); trivial. % 30.22/30.38 (* end of lemma zenon_L1532_ *) % 30.22/30.38 assert (zenon_L1533_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.22/30.38 do 0 intro. intros zenon_Hc0 zenon_H6f zenon_Hbc zenon_Hee zenon_H3f zenon_H296 zenon_H135 zenon_Hc8 zenon_H42 zenon_Hde zenon_H156 zenon_Hcd zenon_H15a zenon_H173 zenon_H218 zenon_Hbd zenon_H23b zenon_H2d zenon_H19e zenon_H6b zenon_H200 zenon_H9b zenon_H97 zenon_Hd6 zenon_H304 zenon_H14b zenon_H1d5 zenon_H73 zenon_H1dc zenon_H1d2 zenon_He1 zenon_H1db zenon_Hb3 zenon_Hf6 zenon_H113 zenon_Haa zenon_H101 zenon_H102 zenon_H100 zenon_Hfc zenon_H13b zenon_H103 zenon_H1a5 zenon_H19a zenon_H185 zenon_H20. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.22/30.38 apply (zenon_L998_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.38 apply (zenon_L1532_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.38 apply (zenon_L336_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.38 apply (zenon_L337_); trivial. % 30.22/30.38 apply (zenon_L152_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.22/30.38 apply (zenon_L136_); trivial. % 30.22/30.38 apply (zenon_L117_); trivial. % 30.22/30.38 (* end of lemma zenon_L1533_ *) % 30.22/30.38 assert (zenon_L1534_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H1fd zenon_Hf4 zenon_H198 zenon_Ha4 zenon_H6f zenon_H19a zenon_Hcc zenon_He1 zenon_H2a9. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.22/30.38 apply (zenon_L1006_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.22/30.38 apply (zenon_L235_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.22/30.38 apply (zenon_L544_); trivial. % 30.22/30.38 exact (zenon_H2a9 zenon_Hb6). % 30.22/30.38 (* end of lemma zenon_L1534_ *) % 30.22/30.38 assert (zenon_L1535_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_H3c zenon_He9 zenon_H2a9 zenon_He1 zenon_H19a zenon_H6f zenon_Ha4 zenon_H198 zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.38 apply (zenon_L142_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.38 apply (zenon_L88_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.38 apply (zenon_L1534_); trivial. % 30.22/30.38 apply (zenon_L56_); trivial. % 30.22/30.38 (* end of lemma zenon_L1535_ *) % 30.22/30.38 assert (zenon_L1536_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H173 zenon_Hf6 zenon_H1fd zenon_H198 zenon_Ha4 zenon_H6f zenon_He1 zenon_H2a9 zenon_He9 zenon_H3c zenon_H18c zenon_H135 zenon_H13b zenon_Hcd zenon_H19a zenon_Hf4 zenon_H14e. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.38 apply (zenon_L1535_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.38 exact (zenon_H13b zenon_Hfd). % 30.22/30.38 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.38 apply (zenon_L159_); trivial. % 30.22/30.38 apply (zenon_L525_); trivial. % 30.22/30.38 (* end of lemma zenon_L1536_ *) % 30.22/30.38 assert (zenon_L1537_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H1fd zenon_Hf4 zenon_H198 zenon_Ha4 zenon_H6f zenon_H19a zenon_H6b zenon_H76 zenon_H2a9. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.22/30.38 apply (zenon_L1006_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.22/30.38 apply (zenon_L235_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.22/30.38 apply (zenon_L1149_); trivial. % 30.22/30.38 exact (zenon_H2a9 zenon_Hb6). % 30.22/30.38 (* end of lemma zenon_L1537_ *) % 30.22/30.38 assert (zenon_L1538_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 30.22/30.38 do 0 intro. intros zenon_H10d zenon_H198 zenon_Hda zenon_Heb. % 30.22/30.38 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 30.22/30.38 intro zenon_D_pnotp. % 30.22/30.38 apply zenon_H10d. % 30.22/30.38 rewrite <- zenon_D_pnotp. % 30.22/30.38 exact zenon_H198. % 30.22/30.38 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 30.22/30.38 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2cf]. % 30.22/30.38 congruence. % 30.22/30.38 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H10f ]. % 30.22/30.38 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e2)))). % 30.22/30.38 intro zenon_D_pnotp. % 30.22/30.38 apply zenon_H2cf. % 30.22/30.38 rewrite <- zenon_D_pnotp. % 30.22/30.38 exact zenon_H211. % 30.22/30.38 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.22/30.38 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 30.22/30.38 congruence. % 30.22/30.38 apply (zenon_L1029_); trivial. % 30.22/30.38 apply zenon_H10f. apply refl_equal. % 30.22/30.38 apply zenon_H10f. apply refl_equal. % 30.22/30.38 apply zenon_Hec. apply sym_equal. exact zenon_Heb. % 30.22/30.38 (* end of lemma zenon_L1538_ *) % 30.22/30.38 assert (zenon_L1539_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 30.22/30.38 do 0 intro. intros zenon_Hf9 zenon_H8a zenon_He1 zenon_H55 zenon_H222 zenon_Hda zenon_H198 zenon_H10d zenon_H95 zenon_H37. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.22/30.38 apply (zenon_L50_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.22/30.38 apply (zenon_L264_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.22/30.38 apply (zenon_L1538_); trivial. % 30.22/30.38 apply (zenon_L513_); trivial. % 30.22/30.38 (* end of lemma zenon_L1539_ *) % 30.22/30.38 assert (zenon_L1540_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.22/30.38 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_H112 zenon_Hf6 zenon_H156 zenon_H155 zenon_H218 zenon_H36 zenon_H16b. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.22/30.38 apply (zenon_L690_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.22/30.38 apply (zenon_L187_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.22/30.38 apply (zenon_L90_); trivial. % 30.22/30.38 apply (zenon_L1038_); trivial. % 30.22/30.38 (* end of lemma zenon_L1540_ *) % 30.22/30.38 assert (zenon_L1541_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.22/30.38 do 0 intro. intros zenon_H16a zenon_H36 zenon_H16b zenon_H16c. % 30.22/30.38 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 30.22/30.38 intro zenon_D_pnotp. % 30.22/30.38 apply zenon_H16a. % 30.22/30.38 rewrite <- zenon_D_pnotp. % 30.22/30.38 exact zenon_H36. % 30.22/30.38 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 30.22/30.38 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d3]. % 30.22/30.38 congruence. % 30.22/30.38 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H16e ]. % 30.22/30.38 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e3)))). % 30.22/30.38 intro zenon_D_pnotp. % 30.22/30.38 apply zenon_H2d3. % 30.22/30.38 rewrite <- zenon_D_pnotp. % 30.22/30.38 exact zenon_H194. % 30.22/30.38 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.22/30.38 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2d2]. % 30.22/30.38 congruence. % 30.22/30.38 apply (zenon_L1037_); trivial. % 30.22/30.38 apply zenon_H16e. apply refl_equal. % 30.22/30.38 apply zenon_H16e. apply refl_equal. % 30.22/30.38 apply zenon_H16d. apply sym_equal. exact zenon_H16c. % 30.22/30.38 (* end of lemma zenon_L1541_ *) % 30.22/30.38 assert (zenon_L1542_ : (((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 (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.22/30.38 do 0 intro. intros zenon_H256 zenon_H14e zenon_H218 zenon_H156 zenon_Hf6 zenon_H112 zenon_Hb1 zenon_H1e6 zenon_H16a zenon_H36 zenon_H16b. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 30.22/30.38 apply (zenon_L84_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 30.22/30.38 apply (zenon_L137_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 30.22/30.38 apply (zenon_L1540_); trivial. % 30.22/30.38 apply (zenon_L1541_); trivial. % 30.22/30.38 (* end of lemma zenon_L1542_ *) % 30.22/30.38 assert (zenon_L1543_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (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 (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.22/30.38 do 0 intro. intros zenon_Hbd zenon_H2d zenon_H37 zenon_H10d zenon_H198 zenon_Hda zenon_H222 zenon_H55 zenon_He1 zenon_H8a zenon_Hf9 zenon_H1b9 zenon_H256 zenon_H14e zenon_H218 zenon_H156 zenon_Hf6 zenon_H112 zenon_H1e6 zenon_H16a zenon_H36 zenon_H16b. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.22/30.38 apply (zenon_L25_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.22/30.38 apply (zenon_L1539_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.22/30.38 apply (zenon_L198_); trivial. % 30.22/30.38 apply (zenon_L1542_); trivial. % 30.22/30.38 (* end of lemma zenon_L1543_ *) % 30.22/30.38 assert (zenon_L1544_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (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 (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.22/30.38 do 0 intro. intros zenon_H23b zenon_H6f zenon_H1f zenon_H188 zenon_H3f zenon_H19a zenon_Hee zenon_Hbd zenon_H2d zenon_H37 zenon_H10d zenon_H198 zenon_Hda zenon_H222 zenon_H55 zenon_He1 zenon_H8a zenon_Hf9 zenon_H1b9 zenon_H256 zenon_H14e zenon_H218 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H16a zenon_H36 zenon_H16b. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.22/30.38 apply (zenon_L39_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.22/30.38 apply (zenon_L1159_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.22/30.38 apply (zenon_L337_); trivial. % 30.22/30.38 apply (zenon_L1543_); trivial. % 30.22/30.38 (* end of lemma zenon_L1544_ *) % 30.22/30.38 assert (zenon_L1545_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.22/30.38 do 0 intro. intros zenon_Hb8 zenon_H16a zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H218 zenon_H14e zenon_H256 zenon_H1b9 zenon_Hf9 zenon_He1 zenon_H55 zenon_H222 zenon_Hda zenon_H198 zenon_H10d zenon_H2d zenon_Hbd zenon_Hee zenon_H19a zenon_H3f zenon_H188 zenon_H1f zenon_H6f zenon_H23b zenon_H100 zenon_H37 zenon_H2a9 zenon_Ha4 zenon_H36 zenon_H16b. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.22/30.38 apply (zenon_L1544_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.22/30.38 apply (zenon_L150_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.22/30.38 exact (zenon_H2a9 zenon_Hb6). % 30.22/30.38 apply (zenon_L1142_); trivial. % 30.22/30.38 (* end of lemma zenon_L1545_ *) % 30.22/30.38 assert (zenon_L1546_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H102 zenon_H19f zenon_Hfc zenon_H19a zenon_H13b zenon_H40 zenon_H100. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.22/30.38 exact (zenon_H19f zenon_Hc3). % 30.22/30.38 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.22/30.38 apply (zenon_L130_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.22/30.38 exact (zenon_H13b zenon_Hfd). % 30.22/30.38 apply (zenon_L150_); trivial. % 30.22/30.38 (* end of lemma zenon_L1546_ *) % 30.22/30.38 assert (zenon_L1547_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hc9 zenon_H13b zenon_Hcd zenon_H19a zenon_Hf4 zenon_H14e. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.38 apply (zenon_L142_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.38 exact (zenon_H13b zenon_Hfd). % 30.22/30.38 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.38 apply (zenon_L159_); trivial. % 30.22/30.38 apply (zenon_L525_); trivial. % 30.22/30.38 (* end of lemma zenon_L1547_ *) % 30.22/30.38 assert (zenon_L1548_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H135 zenon_H14e zenon_Hcd zenon_H13b zenon_H18c zenon_H173 zenon_H9d zenon_H222 zenon_H2a9 zenon_He1 zenon_H19a zenon_H6f zenon_Ha4 zenon_H198 zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.38 apply (zenon_L1547_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.38 apply (zenon_L264_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.38 apply (zenon_L1534_); trivial. % 30.22/30.38 apply (zenon_L56_); trivial. % 30.22/30.38 (* end of lemma zenon_L1548_ *) % 30.22/30.38 assert (zenon_L1549_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H101 zenon_H138 zenon_H100 zenon_Hfc zenon_H19f zenon_H102 zenon_H1d5 zenon_H6b zenon_H19e zenon_H23b zenon_H1f zenon_H188 zenon_H3f zenon_Hee zenon_Hbd zenon_H2d zenon_H10d zenon_Hda zenon_Hf9 zenon_H256 zenon_H156 zenon_H1e6 zenon_H16a zenon_Hb8 zenon_H218 zenon_H36 zenon_H16b zenon_H35 zenon_H42 zenon_H135 zenon_H14e zenon_Hcd zenon_H13b zenon_H18c zenon_H173 zenon_H222 zenon_H2a9 zenon_He1 zenon_H19a zenon_H6f zenon_Ha4 zenon_H198 zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.22/30.38 apply (zenon_L1041_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.22/30.38 exact (zenon_H13b zenon_Hfd). % 30.22/30.38 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.22/30.38 apply (zenon_L1445_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.22/30.38 apply (zenon_L1537_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.22/30.38 apply (zenon_L131_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.22/30.38 apply (zenon_L1545_); trivial. % 30.22/30.38 apply (zenon_L1038_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.22/30.38 apply (zenon_L126_); trivial. % 30.22/30.38 apply (zenon_L1546_); trivial. % 30.22/30.38 apply (zenon_L1548_); trivial. % 30.22/30.38 (* end of lemma zenon_L1549_ *) % 30.22/30.38 assert (zenon_L1550_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H135 zenon_H14e zenon_H13b zenon_H18c zenon_H173 zenon_Hd5 zenon_Hcd zenon_H2a9 zenon_He1 zenon_H19a zenon_H6f zenon_Ha4 zenon_H198 zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.22/30.38 apply (zenon_L1547_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.22/30.38 apply (zenon_L212_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.22/30.38 apply (zenon_L1534_); trivial. % 30.22/30.38 apply (zenon_L56_); trivial. % 30.22/30.38 (* end of lemma zenon_L1550_ *) % 30.22/30.38 assert (zenon_L1551_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hc9 zenon_H13b zenon_Hda zenon_H198 zenon_H1a5 zenon_Hf4 zenon_H14e. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.22/30.38 apply (zenon_L142_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.22/30.38 exact (zenon_H13b zenon_Hfd). % 30.22/30.38 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.22/30.38 apply (zenon_L1030_); trivial. % 30.22/30.38 apply (zenon_L525_); trivial. % 30.22/30.38 (* end of lemma zenon_L1551_ *) % 30.22/30.38 assert (zenon_L1552_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H174 zenon_H90 zenon_H101 zenon_H138 zenon_H100 zenon_Hfc zenon_H19f zenon_H102 zenon_H1d5 zenon_H6b zenon_H19e zenon_H23b zenon_H1f zenon_H188 zenon_H3f zenon_Hee zenon_Hbd zenon_H2d zenon_H10d zenon_Hda zenon_Hf9 zenon_H256 zenon_H156 zenon_H1e6 zenon_H16a zenon_Hb8 zenon_H218 zenon_H36 zenon_H35 zenon_H42 zenon_H135 zenon_H14e zenon_Hcd zenon_H13b zenon_H18c zenon_H173 zenon_H222 zenon_H2a9 zenon_He1 zenon_H19a zenon_H6f zenon_Ha4 zenon_H198 zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.22/30.38 apply (zenon_L538_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.22/30.38 apply (zenon_L1445_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.22/30.38 apply (zenon_L1006_); trivial. % 30.22/30.38 apply (zenon_L1549_); trivial. % 30.22/30.38 (* end of lemma zenon_L1552_ *) % 30.22/30.38 assert (zenon_L1553_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.22/30.38 do 0 intro. intros zenon_H2b7 zenon_H1b9 zenon_H110 zenon_H112 zenon_Hda zenon_H10d zenon_H2a9. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.22/30.38 apply (zenon_L198_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.22/30.38 apply (zenon_L133_); trivial. % 30.22/30.38 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.22/30.38 apply (zenon_L64_); trivial. % 30.22/30.38 exact (zenon_H2a9 zenon_Hb6). % 30.22/30.38 (* end of lemma zenon_L1553_ *) % 30.22/30.38 assert (zenon_L1554_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.27/30.38 do 0 intro. intros zenon_Hf6 zenon_Hf4 zenon_H1fd zenon_H198 zenon_Ha4 zenon_H6f zenon_He1 zenon_H222 zenon_H173 zenon_H18c zenon_H13b zenon_Hcd zenon_H14e zenon_H135 zenon_H42 zenon_H35 zenon_H36 zenon_H218 zenon_Hb8 zenon_H16a zenon_H1e6 zenon_H156 zenon_H256 zenon_Hf9 zenon_H2d zenon_Hbd zenon_H188 zenon_H23b zenon_H19e zenon_H6b zenon_H1d5 zenon_H102 zenon_H19f zenon_Hfc zenon_H100 zenon_H138 zenon_H101 zenon_H174 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H2b7 zenon_H1b9 zenon_H110 zenon_Hda zenon_H10d zenon_H2a9. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.27/30.38 apply (zenon_L1552_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.27/30.38 apply (zenon_L336_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.27/30.38 apply (zenon_L337_); trivial. % 30.27/30.38 apply (zenon_L1553_); trivial. % 30.27/30.38 (* end of lemma zenon_L1554_ *) % 30.27/30.38 assert (zenon_L1555_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H1fd zenon_Hf4 zenon_H198 zenon_Ha4 zenon_H6f zenon_H19a zenon_H1c5 zenon_H108 zenon_H2a9. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.27/30.38 apply (zenon_L1006_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.27/30.38 apply (zenon_L235_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.27/30.38 apply (zenon_L171_); trivial. % 30.27/30.38 exact (zenon_H2a9 zenon_Hb6). % 30.27/30.38 (* end of lemma zenon_L1555_ *) % 30.27/30.38 assert (zenon_L1556_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H174 zenon_H6f zenon_H88 zenon_H35 zenon_H13b zenon_H19a zenon_Hfc zenon_H19f zenon_H102 zenon_Hf4 zenon_H198 zenon_Ha4 zenon_H185 zenon_H2d. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.38 apply (zenon_L734_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.38 apply (zenon_L1445_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.38 apply (zenon_L1006_); trivial. % 30.27/30.38 apply (zenon_L848_); trivial. % 30.27/30.38 (* end of lemma zenon_L1556_ *) % 30.27/30.38 assert (zenon_L1557_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H174 zenon_He1 zenon_H73 zenon_H35 zenon_H13b zenon_H19a zenon_Hfc zenon_H19f zenon_H102 zenon_Hf4 zenon_H198 zenon_Ha4 zenon_H185 zenon_H2d. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.38 apply (zenon_L232_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.38 apply (zenon_L1445_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.38 apply (zenon_L1006_); trivial. % 30.27/30.38 apply (zenon_L848_); trivial. % 30.27/30.38 (* end of lemma zenon_L1557_ *) % 30.27/30.38 assert (zenon_L1558_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H108 zenon_Hd9 zenon_H174 zenon_H2b7 zenon_H110 zenon_Hc8 zenon_H185 zenon_H101 zenon_H138 zenon_H100 zenon_Hfc zenon_H19f zenon_H102 zenon_H1d5 zenon_H6b zenon_H19e zenon_H23b zenon_H1f zenon_H188 zenon_H3f zenon_Hee zenon_Hbd zenon_H2d zenon_H10d zenon_Hda zenon_Hf9 zenon_H256 zenon_H156 zenon_H1e6 zenon_H16a zenon_Hb8 zenon_H218 zenon_H36 zenon_H35 zenon_H42 zenon_H135 zenon_H14e zenon_Hcd zenon_H13b zenon_H18c zenon_H173 zenon_H222 zenon_H2a9 zenon_He1 zenon_H19a zenon_H6f zenon_Ha4 zenon_H198 zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.27/30.38 apply (zenon_L1041_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.27/30.38 exact (zenon_H13b zenon_Hfd). % 30.27/30.38 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.38 apply (zenon_L1445_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.27/30.38 apply (zenon_L1001_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.27/30.38 apply (zenon_L131_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.27/30.38 apply (zenon_L1554_); trivial. % 30.27/30.38 apply (zenon_L948_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.38 apply (zenon_L126_); trivial. % 30.27/30.38 apply (zenon_L1546_); trivial. % 30.27/30.38 apply (zenon_L1548_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.38 apply (zenon_L1445_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.38 apply (zenon_L1006_); trivial. % 30.27/30.38 apply (zenon_L1549_); trivial. % 30.27/30.38 (* end of lemma zenon_L1558_ *) % 30.27/30.38 assert (zenon_L1559_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H173 zenon_H68 zenon_H13b zenon_Hcd zenon_H19a zenon_Hf4 zenon_H14e. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.27/30.38 apply (zenon_L48_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.27/30.38 exact (zenon_H13b zenon_Hfd). % 30.27/30.38 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.27/30.38 apply (zenon_L159_); trivial. % 30.27/30.38 apply (zenon_L525_); trivial. % 30.27/30.38 (* end of lemma zenon_L1559_ *) % 30.27/30.38 assert (zenon_L1560_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.27/30.38 do 0 intro. intros zenon_He4 zenon_H64 zenon_Hde zenon_Hf6 zenon_H1fd zenon_H198 zenon_Ha4 zenon_H6f zenon_He1 zenon_H2a9 zenon_He9 zenon_H3c zenon_H135 zenon_H14e zenon_H19a zenon_Hcd zenon_H13b zenon_H18c zenon_H173 zenon_Hf4 zenon_H17d. % 30.27/30.38 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.27/30.38 apply (zenon_L1209_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.27/30.38 apply (zenon_L1535_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.27/30.38 apply (zenon_L1547_); trivial. % 30.27/30.38 apply (zenon_L847_); trivial. % 30.27/30.38 (* end of lemma zenon_L1560_ *) % 30.27/30.38 assert (zenon_L1561_ : (~((op (e0) (e3)) = (op (e0) (op (e0) (e0))))) -> ((op (e0) (e0)) = (e3)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H307 zenon_H89. % 30.27/30.38 cut (((e3) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 30.27/30.38 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.27/30.38 congruence. % 30.27/30.38 apply zenon_H1d. apply refl_equal. % 30.27/30.38 apply zenon_H1f9. apply sym_equal. exact zenon_H89. % 30.27/30.38 (* end of lemma zenon_L1561_ *) % 30.27/30.38 assert (zenon_L1562_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H16a zenon_H2d6 zenon_H89 zenon_H14f. % 30.27/30.38 cut (((op (e0) (op (e0) (e0))) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 30.27/30.38 intro zenon_D_pnotp. % 30.27/30.38 apply zenon_H16a. % 30.27/30.38 rewrite <- zenon_D_pnotp. % 30.27/30.38 exact zenon_H2d6. % 30.27/30.38 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H284]. % 30.27/30.38 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H308]. % 30.27/30.38 congruence. % 30.27/30.38 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H16e ]. % 30.27/30.38 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (op (e0) (e0))) = (op (e0) (e3)))). % 30.27/30.38 intro zenon_D_pnotp. % 30.27/30.38 apply zenon_H308. % 30.27/30.38 rewrite <- zenon_D_pnotp. % 30.27/30.38 exact zenon_H194. % 30.27/30.38 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.27/30.38 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H307]. % 30.27/30.38 congruence. % 30.27/30.38 apply (zenon_L1561_); trivial. % 30.27/30.38 apply zenon_H16e. apply refl_equal. % 30.27/30.38 apply zenon_H16e. apply refl_equal. % 30.27/30.38 apply zenon_H284. apply sym_equal. exact zenon_H14f. % 30.27/30.38 (* end of lemma zenon_L1562_ *) % 30.27/30.38 assert (zenon_L1563_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e3)) = (e0)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H218 zenon_H2d6 zenon_H89 zenon_H1e1. % 30.27/30.38 cut (((op (e0) (op (e0) (e0))) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 30.27/30.38 intro zenon_D_pnotp. % 30.27/30.38 apply zenon_H218. % 30.27/30.38 rewrite <- zenon_D_pnotp. % 30.27/30.38 exact zenon_H2d6. % 30.27/30.38 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 30.27/30.38 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H308]. % 30.27/30.38 congruence. % 30.27/30.38 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H16e ]. % 30.27/30.38 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (op (e0) (e0))) = (op (e0) (e3)))). % 30.27/30.38 intro zenon_D_pnotp. % 30.27/30.38 apply zenon_H308. % 30.27/30.38 rewrite <- zenon_D_pnotp. % 30.27/30.38 exact zenon_H194. % 30.27/30.38 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 30.27/30.38 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H307]. % 30.27/30.38 congruence. % 30.27/30.38 apply (zenon_L1561_); trivial. % 30.27/30.38 apply zenon_H16e. apply refl_equal. % 30.27/30.38 apply zenon_H16e. apply refl_equal. % 30.27/30.38 apply zenon_H1e2. apply sym_equal. exact zenon_H1e1. % 30.27/30.38 (* end of lemma zenon_L1563_ *) % 30.27/30.38 assert (zenon_L1564_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H2b4 zenon_H64 zenon_H2c1 zenon_H16a zenon_H89 zenon_H2d6 zenon_H218 zenon_H122. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.27/30.38 apply (zenon_L1050_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.27/30.38 apply (zenon_L1562_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.27/30.38 apply (zenon_L1563_); trivial. % 30.27/30.38 exact (zenon_H122 zenon_Hb1). % 30.27/30.38 (* end of lemma zenon_L1564_ *) % 30.27/30.38 assert (zenon_L1565_ : (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H309 zenon_H36 zenon_H33 zenon_H16b. % 30.27/30.38 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e1)) = (op (e0) (e3)))). % 30.27/30.38 intro zenon_D_pnotp. % 30.27/30.38 apply zenon_H309. % 30.27/30.38 rewrite <- zenon_D_pnotp. % 30.27/30.38 exact zenon_H36. % 30.27/30.38 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 30.27/30.38 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 30.27/30.38 congruence. % 30.27/30.38 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 30.27/30.38 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e1)))). % 30.27/30.38 intro zenon_D_pnotp. % 30.27/30.38 apply zenon_H39. % 30.27/30.38 rewrite <- zenon_D_pnotp. % 30.27/30.38 exact zenon_H3a. % 30.27/30.38 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 30.27/30.38 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 30.27/30.38 congruence. % 30.27/30.38 apply (zenon_L5_); trivial. % 30.27/30.38 apply zenon_H3b. apply refl_equal. % 30.27/30.38 apply zenon_H3b. apply refl_equal. % 30.27/30.38 apply zenon_H21a. apply sym_equal. exact zenon_H16b. % 30.27/30.38 (* end of lemma zenon_L1565_ *) % 30.27/30.38 assert (zenon_L1566_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_Hcc zenon_He1 zenon_H218 zenon_H36 zenon_H16b. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.27/30.38 apply (zenon_L174_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.27/30.38 apply (zenon_L131_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.27/30.38 apply (zenon_L544_); trivial. % 30.27/30.38 apply (zenon_L1038_); trivial. % 30.27/30.38 (* end of lemma zenon_L1566_ *) % 30.27/30.38 assert (zenon_L1567_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H174 zenon_He7 zenon_H35 zenon_H13b zenon_Hfc zenon_H19f zenon_H102 zenon_H198 zenon_Ha4 zenon_H16f zenon_Had zenon_Hf6 zenon_Hf4 zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H19e zenon_He1 zenon_H218 zenon_He9 zenon_H3c zenon_Hdc zenon_H18c zenon_H135 zenon_H6f zenon_H19a zenon_H16a zenon_H36. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.38 apply (zenon_L199_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.38 apply (zenon_L1445_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.38 apply (zenon_L1006_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.38 apply (zenon_L34_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.27/30.38 apply (zenon_L142_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.27/30.38 apply (zenon_L88_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.27/30.38 apply (zenon_L1566_); trivial. % 30.27/30.38 apply (zenon_L56_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.38 apply (zenon_L235_); trivial. % 30.27/30.38 apply (zenon_L1541_); trivial. % 30.27/30.38 (* end of lemma zenon_L1567_ *) % 30.27/30.38 assert (zenon_L1568_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.27/30.38 do 0 intro. intros zenon_He4 zenon_H64 zenon_Hde zenon_H36 zenon_H16a zenon_H6f zenon_H135 zenon_H3c zenon_He9 zenon_H218 zenon_H19e zenon_H1d8 zenon_H1d5 zenon_Hf6 zenon_Had zenon_H16f zenon_Ha4 zenon_H198 zenon_H102 zenon_H19f zenon_Hfc zenon_H35 zenon_He7 zenon_H174 zenon_H14e zenon_Hf4 zenon_H19a zenon_Hcd zenon_H13b zenon_H18c zenon_H173 zenon_He1 zenon_H8a. % 30.27/30.38 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.27/30.38 apply (zenon_L1209_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.27/30.38 apply (zenon_L1567_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.27/30.38 apply (zenon_L1547_); trivial. % 30.27/30.38 apply (zenon_L50_); trivial. % 30.27/30.38 (* end of lemma zenon_L1568_ *) % 30.27/30.38 assert (zenon_L1569_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H2f6 zenon_He7 zenon_H2c1 zenon_H2d6 zenon_H64 zenon_H16a zenon_H89 zenon_H218 zenon_H2b4. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.27/30.38 apply (zenon_L1564_); trivial. % 30.27/30.38 apply (zenon_L199_); trivial. % 30.27/30.38 (* end of lemma zenon_L1569_ *) % 30.27/30.38 assert (zenon_L1570_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H16f zenon_Had zenon_Hf6 zenon_Hf4 zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H19e zenon_He1 zenon_H218 zenon_H222 zenon_H9d zenon_H173 zenon_H18c zenon_H13b zenon_Hda zenon_H198 zenon_H1a5 zenon_H14e zenon_H135 zenon_H6f zenon_H19a zenon_H16a zenon_H36 zenon_H16b. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.38 apply (zenon_L34_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.27/30.38 apply (zenon_L1551_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.27/30.38 apply (zenon_L264_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.27/30.38 apply (zenon_L1566_); trivial. % 30.27/30.38 apply (zenon_L56_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.38 apply (zenon_L235_); trivial. % 30.27/30.38 apply (zenon_L1541_); trivial. % 30.27/30.38 (* end of lemma zenon_L1570_ *) % 30.27/30.38 assert (zenon_L1571_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H225 zenon_Hcd zenon_H3c zenon_Hde zenon_He4 zenon_H36 zenon_H16a zenon_H19a zenon_H6f zenon_H135 zenon_H14e zenon_H1a5 zenon_H198 zenon_H13b zenon_H18c zenon_H173 zenon_H222 zenon_H218 zenon_He1 zenon_H19e zenon_H8a zenon_H1d8 zenon_H1d5 zenon_Hf6 zenon_Had zenon_H16f zenon_H2a9 zenon_H108 zenon_H1fd zenon_H23b zenon_H1f zenon_H188 zenon_H3f zenon_Hee zenon_Hbd zenon_H2d zenon_H10d zenon_Hf9 zenon_H256 zenon_H156 zenon_H1e6 zenon_H138 zenon_H101 zenon_H102 zenon_H19f zenon_Hfc zenon_H35 zenon_H2f6 zenon_He7 zenon_H2c1 zenon_H2d6 zenon_H64 zenon_H2b4 zenon_H174 zenon_Hf4 zenon_Ha4. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.27/30.38 apply (zenon_L1209_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.27/30.38 apply (zenon_L1568_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.38 apply (zenon_L1569_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.38 apply (zenon_L1445_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.38 apply (zenon_L1006_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.27/30.38 apply (zenon_L1041_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.27/30.38 exact (zenon_H13b zenon_Hfd). % 30.27/30.38 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.38 apply (zenon_L34_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.27/30.38 apply (zenon_L174_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.27/30.38 apply (zenon_L131_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.27/30.38 apply (zenon_L1544_); trivial. % 30.27/30.38 apply (zenon_L1555_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.38 apply (zenon_L235_); trivial. % 30.27/30.38 apply (zenon_L1541_); trivial. % 30.27/30.38 apply (zenon_L1570_); trivial. % 30.27/30.38 apply (zenon_L819_); trivial. % 30.27/30.38 (* end of lemma zenon_L1571_ *) % 30.27/30.38 assert (zenon_L1572_ : (((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)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e1)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H174 zenon_He7 zenon_H8a zenon_H35 zenon_H13b zenon_H19a zenon_Hfc zenon_H19f zenon_H102 zenon_Hf4 zenon_H198 zenon_Ha4 zenon_H309 zenon_H36 zenon_H33. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.38 apply (zenon_L199_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.38 apply (zenon_L1445_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.38 apply (zenon_L1006_); trivial. % 30.27/30.38 apply (zenon_L1565_); trivial. % 30.27/30.38 (* end of lemma zenon_L1572_ *) % 30.27/30.38 assert (zenon_L1573_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H173 zenon_H68 zenon_H13b zenon_Hcd zenon_H19a zenon_H1fd zenon_H1a5 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H20e zenon_H2a9. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.27/30.38 apply (zenon_L48_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.27/30.38 exact (zenon_H13b zenon_Hfd). % 30.27/30.38 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.27/30.38 apply (zenon_L159_); trivial. % 30.27/30.38 apply (zenon_L830_); trivial. % 30.27/30.38 (* end of lemma zenon_L1573_ *) % 30.27/30.38 assert (zenon_L1574_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H200 zenon_H69 zenon_H18c zenon_H3c zenon_H3d zenon_H19e zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_H156 zenon_H48 zenon_H6e. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.38 apply (zenon_L740_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.38 apply (zenon_L207_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.38 apply (zenon_L1466_); trivial. % 30.27/30.38 apply (zenon_L737_); trivial. % 30.27/30.38 (* end of lemma zenon_L1574_ *) % 30.27/30.38 assert (zenon_L1575_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H102 zenon_Hfe zenon_Hfc zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.27/30.38 apply (zenon_L59_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.27/30.38 exact (zenon_H18f zenon_Hd2). % 30.27/30.38 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.27/30.38 exact (zenon_H13b zenon_Hfd). % 30.27/30.38 apply (zenon_L150_); trivial. % 30.27/30.38 (* end of lemma zenon_L1575_ *) % 30.27/30.38 assert (zenon_L1576_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H35 zenon_H1e zenon_H100 zenon_H40 zenon_H13b zenon_H18f zenon_Hfc zenon_H102 zenon_H18c zenon_H4e zenon_H76. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.38 apply (zenon_L740_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.38 apply (zenon_L42_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.38 apply (zenon_L1575_); trivial. % 30.27/30.38 apply (zenon_L864_); trivial. % 30.27/30.38 (* end of lemma zenon_L1576_ *) % 30.27/30.38 assert (zenon_L1577_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H135 zenon_He1 zenon_H76 zenon_Hd5 zenon_Hcd zenon_Hde zenon_H142 zenon_Hf4 zenon_Hf6. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.27/30.38 apply (zenon_L273_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.27/30.38 apply (zenon_L212_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.27/30.38 apply (zenon_L89_); trivial. % 30.27/30.38 apply (zenon_L56_); trivial. % 30.27/30.38 (* end of lemma zenon_L1577_ *) % 30.27/30.38 assert (zenon_L1578_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 30.27/30.38 do 0 intro. intros zenon_H208 zenon_H100 zenon_H40 zenon_H13b zenon_H18f zenon_H18c zenon_H4a zenon_H102 zenon_Hf6 zenon_Hde zenon_Hcd zenon_H76 zenon_He1 zenon_H135 zenon_H56 zenon_H142 zenon_Hf4. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.27/30.38 apply (zenon_L1450_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.27/30.38 apply (zenon_L1577_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.27/30.38 exact (zenon_H56 zenon_H25). % 30.27/30.38 apply (zenon_L944_); trivial. % 30.27/30.38 (* end of lemma zenon_L1578_ *) % 30.27/30.38 assert (zenon_L1579_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H2bd zenon_H1e1 zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16c zenon_H16a. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H185 | zenon_intro zenon_H2be ]. % 30.27/30.38 apply (zenon_L1088_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H33 | zenon_intro zenon_H2bf ]. % 30.27/30.38 apply (zenon_L1448_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H17b | zenon_intro zenon_H16b ]. % 30.27/30.38 apply (zenon_L819_); trivial. % 30.27/30.38 apply (zenon_L859_); trivial. % 30.27/30.38 (* end of lemma zenon_L1579_ *) % 30.27/30.38 assert (zenon_L1580_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.38 do 0 intro. intros zenon_H200 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_H76 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H18c zenon_H40 zenon_H100 zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16c zenon_H16a. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.38 apply (zenon_L1576_); trivial. % 30.27/30.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.39 apply (zenon_L207_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.39 apply (zenon_L1578_); trivial. % 30.27/30.39 apply (zenon_L1579_); trivial. % 30.27/30.39 (* end of lemma zenon_L1580_ *) % 30.27/30.39 assert (zenon_L1581_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H16f zenon_H156 zenon_Hbd zenon_H2a9 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_Hee zenon_H20 zenon_H23b zenon_H3f zenon_H1dc zenon_H14e zenon_H69 zenon_H6f zenon_H19a zenon_H200 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_H76 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H18c zenon_H40 zenon_H100 zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16a. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.39 apply (zenon_L969_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.39 apply (zenon_L150_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.39 apply (zenon_L235_); trivial. % 30.27/30.39 apply (zenon_L1580_); trivial. % 30.27/30.39 (* end of lemma zenon_L1581_ *) % 30.27/30.39 assert (zenon_L1582_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H8d zenon_H117 zenon_Hd9 zenon_H16a zenon_H4e zenon_Hf4 zenon_Ha4 zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H13b zenon_H4a zenon_H218 zenon_H2bd zenon_H208 zenon_H100 zenon_H18c zenon_Hf6 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_H48 zenon_Hfc zenon_H200 zenon_H19a zenon_H6f zenon_H69 zenon_H14e zenon_H1dc zenon_H3f zenon_H23b zenon_H20 zenon_Hee zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H2a9 zenon_Hbd zenon_H156 zenon_H16f zenon_H40 zenon_H97. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.39 apply (zenon_L149_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.39 apply (zenon_L969_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.39 apply (zenon_L1581_); trivial. % 30.27/30.39 apply (zenon_L862_); trivial. % 30.27/30.39 (* end of lemma zenon_L1582_ *) % 30.27/30.39 assert (zenon_L1583_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1ab zenon_Hd1 zenon_H2b1 zenon_H6e zenon_H19e zenon_H8d zenon_H117 zenon_Hd9 zenon_H16a zenon_H4e zenon_Hf4 zenon_Ha4 zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H13b zenon_H4a zenon_H218 zenon_H2bd zenon_H208 zenon_H100 zenon_H18c zenon_Hf6 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_H48 zenon_Hfc zenon_H200 zenon_H19a zenon_H6f zenon_H69 zenon_H14e zenon_H1dc zenon_H3f zenon_H23b zenon_H20 zenon_Hee zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H2a9 zenon_Hbd zenon_H156 zenon_H16f zenon_H97. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.39 apply (zenon_L4_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.39 apply (zenon_L1449_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.39 apply (zenon_L1574_); trivial. % 30.27/30.39 apply (zenon_L1582_); trivial. % 30.27/30.39 (* end of lemma zenon_L1583_ *) % 30.27/30.39 assert (zenon_L1584_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H200 zenon_H69 zenon_H48 zenon_H18c zenon_H3c zenon_H3d zenon_H19e zenon_H2bd zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16c zenon_H16a. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.39 apply (zenon_L740_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.39 apply (zenon_L207_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.39 apply (zenon_L1466_); trivial. % 30.27/30.39 apply (zenon_L1579_); trivial. % 30.27/30.39 (* end of lemma zenon_L1584_ *) % 30.27/30.39 assert (zenon_L1585_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H8d zenon_H88 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H16b zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.39 apply (zenon_L734_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.39 apply (zenon_L1470_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.39 apply (zenon_L1471_); trivial. % 30.27/30.39 apply (zenon_L862_); trivial. % 30.27/30.39 (* end of lemma zenon_L1585_ *) % 30.27/30.39 assert (zenon_L1586_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H174 zenon_Hbd zenon_H2a9 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_Hee zenon_H20 zenon_H23b zenon_H3f zenon_H1dc zenon_H69 zenon_H200 zenon_Hfc zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H1e zenon_H35 zenon_Ha4 zenon_Hf4 zenon_Hd9 zenon_H8d zenon_H88 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.39 apply (zenon_L734_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.39 apply (zenon_L4_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.39 apply (zenon_L1582_); trivial. % 30.27/30.39 apply (zenon_L1585_); trivial. % 30.27/30.39 (* end of lemma zenon_L1586_ *) % 30.27/30.39 assert (zenon_L1587_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H8d zenon_He1 zenon_H73 zenon_H68 zenon_H16a zenon_H16b zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.39 apply (zenon_L232_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.39 apply (zenon_L18_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.39 apply (zenon_L1471_); trivial. % 30.27/30.39 apply (zenon_L862_); trivial. % 30.27/30.39 (* end of lemma zenon_L1587_ *) % 30.27/30.39 assert (zenon_L1588_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H174 zenon_H3f zenon_H4c zenon_H200 zenon_Hfc zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_Hd9 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H8d zenon_He1 zenon_H73 zenon_H68 zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.39 apply (zenon_L232_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.39 apply (zenon_L746_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.39 apply (zenon_L149_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.39 apply (zenon_L18_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.39 apply (zenon_L18_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.39 apply (zenon_L150_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.39 apply (zenon_L752_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.39 apply (zenon_L1576_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.39 apply (zenon_L207_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.27/30.39 apply (zenon_L120_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.27/30.39 apply (zenon_L958_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.27/30.39 apply (zenon_L212_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.27/30.39 apply (zenon_L89_); trivial. % 30.27/30.39 apply (zenon_L56_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.27/30.39 exact (zenon_H56 zenon_H25). % 30.27/30.39 apply (zenon_L944_); trivial. % 30.27/30.39 apply (zenon_L1579_); trivial. % 30.27/30.39 apply (zenon_L862_); trivial. % 30.27/30.39 apply (zenon_L1587_); trivial. % 30.27/30.39 (* end of lemma zenon_L1588_ *) % 30.27/30.39 assert (zenon_L1589_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.27/30.39 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H35 zenon_H1e zenon_H1a5 zenon_H117 zenon_H1b1 zenon_H4c zenon_H13b zenon_H15a zenon_H73 zenon_H173 zenon_H18c zenon_H4e zenon_H76. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.39 apply (zenon_L740_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.39 apply (zenon_L42_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.39 apply (zenon_L1457_); trivial. % 30.27/30.39 apply (zenon_L864_); trivial. % 30.27/30.39 (* end of lemma zenon_L1589_ *) % 30.27/30.39 assert (zenon_L1590_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.27/30.39 do 0 intro. intros zenon_H8d zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_Hcd zenon_H23b zenon_H6f zenon_H68 zenon_H4e zenon_H18c zenon_Had zenon_H4c zenon_H1e zenon_H35 zenon_H48 zenon_Hdf zenon_H172 zenon_He1 zenon_He2. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.39 apply (zenon_L387_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.39 apply (zenon_L18_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.39 apply (zenon_L1327_); trivial. % 30.27/30.39 apply (zenon_L50_); trivial. % 30.27/30.39 (* end of lemma zenon_L1590_ *) % 30.27/30.39 assert (zenon_L1591_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.27/30.39 do 0 intro. intros zenon_He4 zenon_H97 zenon_H40 zenon_H16f zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H100 zenon_H16a zenon_H173 zenon_H15a zenon_H13b zenon_H1b1 zenon_H1a5 zenon_H174 zenon_Hde zenon_H8d zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_Hcd zenon_H23b zenon_H6f zenon_H68 zenon_H4e zenon_H18c zenon_Had zenon_H4c zenon_H1e zenon_H35 zenon_H48 zenon_Hdf zenon_H172 zenon_He1. % 30.27/30.39 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.39 apply (zenon_L232_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.39 apply (zenon_L4_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.39 apply (zenon_L232_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.39 apply (zenon_L18_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.39 apply (zenon_L1589_); trivial. % 30.27/30.39 apply (zenon_L862_); trivial. % 30.27/30.39 apply (zenon_L1587_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.27/30.39 apply (zenon_L48_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.27/30.39 apply (zenon_L49_); trivial. % 30.27/30.39 apply (zenon_L1590_); trivial. % 30.27/30.39 (* end of lemma zenon_L1591_ *) % 30.27/30.39 assert (zenon_L1592_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.27/30.39 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_H40 zenon_He1 zenon_Hed zenon_H4c zenon_Hee zenon_H90 zenon_H89. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.27/30.39 apply (zenon_L386_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.27/30.39 apply (zenon_L1354_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.27/30.39 apply (zenon_L1207_); trivial. % 30.27/30.39 apply (zenon_L538_); trivial. % 30.27/30.39 (* end of lemma zenon_L1592_ *) % 30.27/30.39 assert (zenon_L1593_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.27/30.39 do 0 intro. intros zenon_H23b zenon_H89 zenon_H4c zenon_Hed zenon_He1 zenon_H40 zenon_Hcd zenon_Hf9 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H9c zenon_H1b9. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.27/30.39 apply (zenon_L1592_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.27/30.39 apply (zenon_L336_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.27/30.39 apply (zenon_L337_); trivial. % 30.27/30.39 apply (zenon_L198_); trivial. % 30.27/30.39 (* end of lemma zenon_L1593_ *) % 30.27/30.39 assert (zenon_L1594_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.27/30.39 do 0 intro. intros zenon_H1d5 zenon_Hc9 zenon_H222 zenon_H1e1 zenon_Hf6 zenon_H23b zenon_H89 zenon_H4c zenon_Hed zenon_He1 zenon_H40 zenon_Hcd zenon_Hf9 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H2d zenon_Had zenon_H48 zenon_H69 zenon_Hbd zenon_H156 zenon_H4e zenon_H16c. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.27/30.39 apply (zenon_L273_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.27/30.39 apply (zenon_L775_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.27/30.39 apply (zenon_L749_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.27/30.39 apply (zenon_L766_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.27/30.39 apply (zenon_L1593_); trivial. % 30.27/30.39 apply (zenon_L690_); trivial. % 30.27/30.39 apply (zenon_L779_); trivial. % 30.27/30.39 (* end of lemma zenon_L1594_ *) % 30.27/30.39 assert (zenon_L1595_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H156 zenon_Hbd zenon_H69 zenon_H48 zenon_Had zenon_H2d zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_Hf9 zenon_Hcd zenon_He1 zenon_H23b zenon_Hf6 zenon_Hc9 zenon_H19e zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_H3c zenon_He4 zenon_H97 zenon_H16f zenon_H2b4 zenon_H100 zenon_H16a zenon_H173 zenon_H15a zenon_H13b zenon_H1b1 zenon_H174 zenon_Hde zenon_H8d zenon_H6f zenon_H68 zenon_H18c zenon_H172 zenon_H200 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H40 zenon_H20e zenon_H1fd zenon_H1a5 zenon_H4e zenon_Hf4 zenon_H4c zenon_H14e zenon_H108 zenon_H2a9. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.27/30.39 apply (zenon_L142_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.27/30.39 exact (zenon_H13b zenon_Hfd). % 30.27/30.39 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.39 apply (zenon_L241_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.39 apply (zenon_L150_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.39 apply (zenon_L235_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.39 apply (zenon_L1591_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.39 apply (zenon_L207_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.27/30.39 apply (zenon_L332_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.27/30.39 apply (zenon_L1466_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.27/30.39 apply (zenon_L175_); trivial. % 30.27/30.39 apply (zenon_L779_); trivial. % 30.27/30.39 apply (zenon_L1594_); trivial. % 30.27/30.39 apply (zenon_L857_); trivial. % 30.27/30.39 (* end of lemma zenon_L1595_ *) % 30.27/30.39 assert (zenon_L1596_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 30.27/30.39 do 0 intro. intros zenon_H208 zenon_H100 zenon_H40 zenon_H13b zenon_H18f zenon_H18c zenon_H4a zenon_H102 zenon_Hf6 zenon_Hde zenon_Hcd zenon_H1d8 zenon_He2 zenon_H135 zenon_H56 zenon_H142 zenon_Hf4. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.27/30.39 apply (zenon_L1450_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.27/30.39 apply (zenon_L307_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.27/30.39 apply (zenon_L212_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.27/30.39 apply (zenon_L89_); trivial. % 30.27/30.39 apply (zenon_L56_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.27/30.39 exact (zenon_H56 zenon_H25). % 30.27/30.39 apply (zenon_L944_); trivial. % 30.27/30.39 (* end of lemma zenon_L1596_ *) % 30.27/30.39 assert (zenon_L1597_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H8d zenon_He2 zenon_Hee zenon_H3f zenon_H1f zenon_Hcd zenon_H23b zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H16b zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.39 apply (zenon_L387_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.39 apply (zenon_L1470_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.39 apply (zenon_L1471_); trivial. % 30.27/30.39 apply (zenon_L862_); trivial. % 30.27/30.39 (* end of lemma zenon_L1597_ *) % 30.27/30.39 assert (zenon_L1598_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H2bd zenon_H1e1 zenon_H218 zenon_H4a zenon_H1e zenon_H35 zenon_Ha4 zenon_Hf4 zenon_H8d zenon_He2 zenon_Hee zenon_H3f zenon_H1f zenon_Hcd zenon_H23b zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H185 | zenon_intro zenon_H2be ]. % 30.27/30.39 apply (zenon_L1088_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H33 | zenon_intro zenon_H2bf ]. % 30.27/30.39 apply (zenon_L1448_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H17b | zenon_intro zenon_H16b ]. % 30.27/30.39 apply (zenon_L819_); trivial. % 30.27/30.39 apply (zenon_L1597_); trivial. % 30.27/30.39 (* end of lemma zenon_L1598_ *) % 30.27/30.39 assert (zenon_L1599_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H200 zenon_He1 zenon_H172 zenon_H4c zenon_Had zenon_H68 zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_Hf6 zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H1e zenon_H35 zenon_Ha4 zenon_Hf4 zenon_H8d zenon_He2 zenon_Hee zenon_H3f zenon_H1f zenon_Hcd zenon_H23b zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.39 apply (zenon_L1590_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.39 apply (zenon_L207_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.39 apply (zenon_L1596_); trivial. % 30.27/30.39 apply (zenon_L1598_); trivial. % 30.27/30.39 (* end of lemma zenon_L1599_ *) % 30.27/30.39 assert (zenon_L1600_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H92 zenon_H1dc zenon_H20 zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H4e zenon_H16a zenon_H159 zenon_H23b zenon_Hcd zenon_H1f zenon_H3f zenon_Hee zenon_H8d zenon_Hf4 zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H4c zenon_H172 zenon_He1 zenon_H200 zenon_H2a9 zenon_H108 zenon_H1a5 zenon_H1fd zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H174 zenon_H1b1 zenon_H173 zenon_He4 zenon_H19e zenon_Hf9 zenon_H69 zenon_Hbd zenon_Hd9 zenon_H15a zenon_Hfc zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.27/30.39 apply (zenon_L1586_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.27/30.39 apply (zenon_L1588_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.27/30.39 apply (zenon_L48_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.39 apply (zenon_L1595_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.39 apply (zenon_L4_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.39 apply (zenon_L958_); trivial. % 30.27/30.39 apply (zenon_L1472_); trivial. % 30.27/30.39 apply (zenon_L1599_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.27/30.39 apply (zenon_L1450_); trivial. % 30.27/30.39 apply (zenon_L1473_); trivial. % 30.27/30.39 (* end of lemma zenon_L1600_ *) % 30.27/30.39 assert (zenon_L1601_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_Hc0 zenon_H100 zenon_H40 zenon_Had zenon_H18c zenon_Hfc zenon_H15a zenon_Hd9 zenon_Hbd zenon_H69 zenon_Hf9 zenon_H19e zenon_He4 zenon_H173 zenon_H1b1 zenon_H174 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_H20e zenon_H1fd zenon_H108 zenon_H2a9 zenon_H200 zenon_He1 zenon_H172 zenon_H4c zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_Hf6 zenon_H208 zenon_H2bd zenon_H218 zenon_Ha4 zenon_Hf4 zenon_H8d zenon_Hee zenon_H3f zenon_Hcd zenon_H23b zenon_H159 zenon_H4e zenon_H6f zenon_H2b4 zenon_H2d zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H97 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H20 zenon_H1dc zenon_H92 zenon_H1a5 zenon_H19a zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H13b zenon_H4a zenon_H16a. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.27/30.39 apply (zenon_L1586_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.27/30.39 apply (zenon_L1600_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.27/30.39 apply (zenon_L136_); trivial. % 30.27/30.39 apply (zenon_L1448_); trivial. % 30.27/30.39 (* end of lemma zenon_L1601_ *) % 30.27/30.39 assert (zenon_L1602_ : ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H117 zenon_Hd1 zenon_H42 zenon_H1ab zenon_H2b0 zenon_H2b1 zenon_Hc0 zenon_H100 zenon_Had zenon_H18c zenon_Hfc zenon_H15a zenon_Hd9 zenon_Hbd zenon_H69 zenon_Hf9 zenon_H19e zenon_He4 zenon_H173 zenon_H1b1 zenon_H174 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_H20e zenon_H1fd zenon_H108 zenon_H2a9 zenon_H200 zenon_He1 zenon_H172 zenon_H4c zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_Hf6 zenon_H208 zenon_H2bd zenon_H218 zenon_Ha4 zenon_Hf4 zenon_H8d zenon_Hee zenon_H3f zenon_Hcd zenon_H23b zenon_H159 zenon_H4e zenon_H6f zenon_H2b4 zenon_H2d zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H97 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H20 zenon_H1dc zenon_H92 zenon_H1a5 zenon_H19a zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H13b zenon_H4a zenon_H16a. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.39 apply (zenon_L1583_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.39 apply (zenon_L842_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.39 apply (zenon_L235_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.39 apply (zenon_L4_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.39 apply (zenon_L842_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.39 apply (zenon_L1584_); trivial. % 30.27/30.39 apply (zenon_L1601_); trivial. % 30.27/30.39 (* end of lemma zenon_L1602_ *) % 30.27/30.39 assert (zenon_L1603_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.27/30.39 do 0 intro. intros zenon_Hbd zenon_H2a9 zenon_Hf4 zenon_Hee zenon_H19a zenon_Hb5 zenon_H2b7 zenon_H1e zenon_H3f zenon_H110 zenon_H156 zenon_H2b1 zenon_H16a zenon_H20 zenon_H2b4 zenon_H3d zenon_H4e zenon_H19e zenon_H4a zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H1ab zenon_H16b zenon_H2d zenon_H14e zenon_H48 zenon_H6e. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.27/30.39 apply (zenon_L853_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.27/30.39 apply (zenon_L29_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.27/30.39 apply (zenon_L848_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.27/30.39 apply (zenon_L1462_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.27/30.39 apply (zenon_L737_); trivial. % 30.27/30.39 apply (zenon_L65_); trivial. % 30.27/30.39 apply (zenon_L770_); trivial. % 30.27/30.39 (* end of lemma zenon_L1603_ *) % 30.27/30.39 assert (zenon_L1604_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.27/30.39 do 0 intro. intros zenon_H42 zenon_Hd1 zenon_H35 zenon_H2d zenon_H16b zenon_H1ab zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H4a zenon_H19e zenon_H4e zenon_H2b4 zenon_H16a zenon_H2b1 zenon_H200 zenon_H69 zenon_H18c zenon_H3c zenon_H14e zenon_H1dc zenon_H3f zenon_H1e zenon_H23b zenon_H20 zenon_H6f zenon_H19a zenon_Hee zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hf4 zenon_H2a9 zenon_Hbd zenon_H156 zenon_H48 zenon_H6e. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.39 apply (zenon_L4_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.39 apply (zenon_L1449_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.39 apply (zenon_L1603_); trivial. % 30.27/30.39 apply (zenon_L969_); trivial. % 30.27/30.39 (* end of lemma zenon_L1604_ *) % 30.27/30.39 assert (zenon_L1605_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H8d zenon_H88 zenon_Hbd zenon_H2a9 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_Hee zenon_H6f zenon_H20 zenon_H23b zenon_H1e zenon_H3f zenon_H1dc zenon_H3c zenon_H69 zenon_H200 zenon_H19e zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H35 zenon_Hd1 zenon_H42 zenon_H2b4 zenon_H2d zenon_H18c zenon_H48 zenon_H16f zenon_Had zenon_H1ab zenon_H156 zenon_H4a zenon_H2b0 zenon_H19a zenon_H2b1 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.39 apply (zenon_L734_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.39 apply (zenon_L1604_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.39 apply (zenon_L929_); trivial. % 30.27/30.39 apply (zenon_L917_); trivial. % 30.27/30.39 (* end of lemma zenon_L1605_ *) % 30.27/30.39 assert (zenon_L1606_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.39 do 0 intro. intros zenon_H102 zenon_Hfe zenon_Hfc zenon_H18f zenon_H13b zenon_H4a zenon_H33 zenon_H16a. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.27/30.39 apply (zenon_L59_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.27/30.39 exact (zenon_H18f zenon_Hd2). % 30.27/30.39 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.27/30.39 exact (zenon_H13b zenon_Hfd). % 30.27/30.39 apply (zenon_L839_); trivial. % 30.27/30.39 (* end of lemma zenon_L1606_ *) % 30.27/30.39 assert (zenon_L1607_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.27/30.39 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H35 zenon_H1e zenon_H16a zenon_H33 zenon_H4a zenon_H13b zenon_H18f zenon_Hfc zenon_H102 zenon_H18c zenon_H4e zenon_H76. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.39 apply (zenon_L740_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.39 apply (zenon_L42_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.39 apply (zenon_L1606_); trivial. % 30.27/30.39 apply (zenon_L864_); trivial. % 30.27/30.39 (* end of lemma zenon_L1607_ *) % 30.27/30.39 assert (zenon_L1608_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> False). % 30.27/30.39 do 0 intro. intros zenon_H23b zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H40 zenon_H6f zenon_H19a zenon_Hee zenon_Hf6 zenon_H1e5. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.27/30.39 apply (zenon_L1473_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.27/30.39 apply (zenon_L80_); trivial. % 30.27/30.39 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.27/30.39 apply (zenon_L337_); trivial. % 30.27/30.39 apply (zenon_L187_); trivial. % 30.27/30.39 (* end of lemma zenon_L1608_ *) % 30.27/30.39 assert (zenon_L1609_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.27/30.40 do 0 intro. intros zenon_Hb8 zenon_H1ab zenon_H3f zenon_H1f zenon_H1e5 zenon_Hf6 zenon_Hee zenon_H19a zenon_H6f zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H100 zenon_H23b zenon_H2a9 zenon_H14e zenon_H4e zenon_H16c. % 30.27/30.40 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.27/30.40 apply (zenon_L1187_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.27/30.40 apply (zenon_L1608_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.27/30.40 exact (zenon_H2a9 zenon_Hb6). % 30.27/30.40 apply (zenon_L875_); trivial. % 30.27/30.40 (* end of lemma zenon_L1609_ *) % 30.27/30.40 assert (zenon_L1610_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H2b1 zenon_H76 zenon_H18c zenon_Hfc zenon_H16a zenon_H1e zenon_H35 zenon_H48 zenon_Hdf zenon_H172 zenon_H16c zenon_H4e zenon_H14e zenon_H2a9 zenon_H23b zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H6f zenon_H19a zenon_Hee zenon_Hf6 zenon_H1f zenon_H3f zenon_Hb8 zenon_H1ab. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.27/30.40 apply (zenon_L1607_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.27/30.40 apply (zenon_L758_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.27/30.40 apply (zenon_L1609_); trivial. % 30.27/30.40 exact (zenon_H1ab zenon_H112). % 30.27/30.40 (* end of lemma zenon_L1610_ *) % 30.27/30.40 assert (zenon_L1611_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H42 zenon_H2d zenon_H156 zenon_H2b0 zenon_H19e zenon_H2b1 zenon_H14e zenon_H2a9 zenon_H23b zenon_Had zenon_H6f zenon_H19a zenon_Hee zenon_H1f zenon_H3f zenon_Hb8 zenon_H1ab zenon_H200 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_H76 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H18c zenon_H100 zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16c zenon_H16a. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.40 apply (zenon_L4_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.40 apply (zenon_L842_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.40 apply (zenon_L1610_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.40 apply (zenon_L207_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.40 apply (zenon_L1466_); trivial. % 30.27/30.40 apply (zenon_L1579_); trivial. % 30.27/30.40 apply (zenon_L1580_); trivial. % 30.27/30.40 (* end of lemma zenon_L1611_ *) % 30.27/30.40 assert (zenon_L1612_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H16f zenon_H68 zenon_H42 zenon_H2d zenon_H156 zenon_H2b0 zenon_H19e zenon_H2b1 zenon_H14e zenon_H2a9 zenon_H23b zenon_Had zenon_H6f zenon_H19a zenon_Hee zenon_H1f zenon_H3f zenon_Hb8 zenon_H1ab zenon_H200 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_H76 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H18c zenon_H100 zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16a. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.40 apply (zenon_L18_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.40 apply (zenon_L842_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.40 apply (zenon_L235_); trivial. % 30.27/30.40 apply (zenon_L1611_); trivial. % 30.27/30.40 (* end of lemma zenon_L1612_ *) % 30.27/30.40 assert (zenon_L1613_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H8d zenon_H117 zenon_Hd9 zenon_H16a zenon_H4e zenon_Hf4 zenon_Ha4 zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H13b zenon_H4a zenon_H218 zenon_H2bd zenon_H208 zenon_H100 zenon_H18c zenon_Hf6 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_H48 zenon_Hfc zenon_H200 zenon_Hb8 zenon_Had zenon_H2a9 zenon_H14e zenon_H2b1 zenon_H19e zenon_H2b0 zenon_H156 zenon_H2d zenon_H42 zenon_H68 zenon_H16f zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.40 apply (zenon_L149_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.40 apply (zenon_L18_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.40 apply (zenon_L1612_); trivial. % 30.27/30.40 apply (zenon_L1187_); trivial. % 30.27/30.40 (* end of lemma zenon_L1613_ *) % 30.27/30.40 assert (zenon_L1614_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H16f zenon_H6f zenon_H68 zenon_H1ab zenon_H156 zenon_H4a zenon_H2b0 zenon_H19a zenon_H2b1 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16b zenon_H16a. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.40 apply (zenon_L18_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.40 apply (zenon_L842_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.40 apply (zenon_L752_); trivial. % 30.27/30.40 apply (zenon_L859_); trivial. % 30.27/30.40 (* end of lemma zenon_L1614_ *) % 30.27/30.40 assert (zenon_L1615_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H174 zenon_H73 zenon_Hee zenon_H3f zenon_H1f zenon_H23b zenon_H42 zenon_H2d zenon_H19e zenon_H2a9 zenon_Had zenon_Hb8 zenon_H200 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H18c zenon_H100 zenon_H208 zenon_H2bd zenon_H218 zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hd9 zenon_H8d zenon_H16f zenon_H6f zenon_H68 zenon_H1ab zenon_H156 zenon_H4a zenon_H2b0 zenon_H19a zenon_H2b1 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H16a. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.40 apply (zenon_L232_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.40 apply (zenon_L4_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.40 apply (zenon_L1613_); trivial. % 30.27/30.40 apply (zenon_L1614_); trivial. % 30.27/30.40 (* end of lemma zenon_L1615_ *) % 30.27/30.40 assert (zenon_L1616_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_H3c zenon_H3d zenon_H19e zenon_H2bd zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16c zenon_H16a. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.40 apply (zenon_L49_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.40 apply (zenon_L207_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.40 apply (zenon_L1466_); trivial. % 30.27/30.40 apply (zenon_L1579_); trivial. % 30.27/30.40 (* end of lemma zenon_L1616_ *) % 30.27/30.40 assert (zenon_L1617_ : ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H89 zenon_H42 zenon_H1ab zenon_H2b0 zenon_H2b1 zenon_Hc9 zenon_H92 zenon_H1dc zenon_H20 zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H4e zenon_H16a zenon_H159 zenon_H23b zenon_Hcd zenon_H1f zenon_H3f zenon_Hee zenon_H8d zenon_Hf4 zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H4c zenon_H172 zenon_He1 zenon_H200 zenon_H2a9 zenon_H108 zenon_H1a5 zenon_H1fd zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H174 zenon_H1b1 zenon_H173 zenon_He4 zenon_H19e zenon_Hf9 zenon_H69 zenon_Hbd zenon_Hd9 zenon_H15a zenon_Hfc zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H100. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.40 apply (zenon_L241_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.40 apply (zenon_L842_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.40 apply (zenon_L752_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.40 apply (zenon_L4_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.40 apply (zenon_L842_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.40 apply (zenon_L1616_); trivial. % 30.27/30.40 apply (zenon_L1600_); trivial. % 30.27/30.40 (* end of lemma zenon_L1617_ *) % 30.27/30.40 assert (zenon_L1618_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.27/30.40 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_H3c zenon_H1ab zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_Hbd zenon_H20 zenon_H1e zenon_H1dc zenon_H14e zenon_H23b zenon_H156 zenon_H48 zenon_H6e. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.40 apply (zenon_L49_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.40 apply (zenon_L207_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.27/30.40 apply (zenon_L991_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.27/30.40 apply (zenon_L336_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.27/30.40 apply (zenon_L337_); trivial. % 30.27/30.40 exact (zenon_H1ab zenon_H112). % 30.27/30.40 apply (zenon_L737_); trivial. % 30.27/30.40 (* end of lemma zenon_L1618_ *) % 30.27/30.40 assert (zenon_L1619_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H8d zenon_H117 zenon_Hd9 zenon_H1dc zenon_H20 zenon_Hbd zenon_Hc9 zenon_H16a zenon_H4e zenon_Hf4 zenon_Ha4 zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H13b zenon_H4a zenon_H218 zenon_H2bd zenon_H208 zenon_H100 zenon_H18c zenon_Hf6 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_H48 zenon_Hfc zenon_H200 zenon_Hb8 zenon_Had zenon_H2a9 zenon_H14e zenon_H2b1 zenon_H19e zenon_H2b0 zenon_H156 zenon_H2d zenon_H42 zenon_H68 zenon_H16f zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.40 apply (zenon_L149_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.40 apply (zenon_L1618_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.40 apply (zenon_L1612_); trivial. % 30.27/30.40 apply (zenon_L1187_); trivial. % 30.27/30.40 (* end of lemma zenon_L1619_ *) % 30.27/30.40 assert (zenon_L1620_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.27/30.40 do 0 intro. intros zenon_H8d zenon_H1f zenon_Hcd zenon_Hbd zenon_H2a9 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_Hee zenon_H6f zenon_H20 zenon_H23b zenon_H1e zenon_H3f zenon_H1dc zenon_H3c zenon_H69 zenon_H200 zenon_H19e zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H35 zenon_Hd1 zenon_H42 zenon_H16a zenon_H16b zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H2b1 zenon_H19a zenon_H2b0 zenon_H4a zenon_H156 zenon_H1ab zenon_H2b4 zenon_H2d zenon_H18c zenon_H48 zenon_H16f zenon_He1 zenon_He2. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.40 apply (zenon_L387_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.40 apply (zenon_L1604_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.40 apply (zenon_L929_); trivial. % 30.27/30.40 apply (zenon_L50_); trivial. % 30.27/30.40 (* end of lemma zenon_L1620_ *) % 30.27/30.40 assert (zenon_L1621_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 30.27/30.40 do 0 intro. intros zenon_H174 zenon_H68 zenon_Had zenon_Hb8 zenon_Hfc zenon_H172 zenon_H56 zenon_H135 zenon_Hde zenon_Hf6 zenon_H100 zenon_H208 zenon_H2bd zenon_H218 zenon_Ha4 zenon_Hd9 zenon_H8d zenon_H1f zenon_Hcd zenon_Hbd zenon_H2a9 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_Hee zenon_H6f zenon_H20 zenon_H23b zenon_H1e zenon_H3f zenon_H1dc zenon_H3c zenon_H69 zenon_H200 zenon_H19e zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H35 zenon_Hd1 zenon_H42 zenon_H16a zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H2b1 zenon_H19a zenon_H2b0 zenon_H4a zenon_H156 zenon_H1ab zenon_H2b4 zenon_H2d zenon_H18c zenon_H48 zenon_H16f zenon_He1 zenon_He2. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.40 apply (zenon_L387_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.40 apply (zenon_L4_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.40 apply (zenon_L149_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.40 apply (zenon_L18_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.40 apply (zenon_L1612_); trivial. % 30.27/30.40 apply (zenon_L50_); trivial. % 30.27/30.40 apply (zenon_L1620_); trivial. % 30.27/30.40 (* end of lemma zenon_L1621_ *) % 30.27/30.40 assert (zenon_L1622_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H16f zenon_H6c zenon_He9 zenon_Hd1 zenon_H4c zenon_H42 zenon_H2d zenon_H156 zenon_H2b0 zenon_H19e zenon_H2b1 zenon_H14e zenon_H2a9 zenon_H23b zenon_Had zenon_H6f zenon_H19a zenon_Hee zenon_H1f zenon_H3f zenon_Hb8 zenon_H1ab zenon_H200 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_H76 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H18c zenon_H100 zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16a. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.40 apply (zenon_L1451_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.40 apply (zenon_L842_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.40 apply (zenon_L752_); trivial. % 30.27/30.40 apply (zenon_L1611_); trivial. % 30.27/30.40 (* end of lemma zenon_L1622_ *) % 30.27/30.40 assert (zenon_L1623_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.27/30.40 do 0 intro. intros zenon_H101 zenon_H16a zenon_H4e zenon_Hf4 zenon_Ha4 zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H4a zenon_H218 zenon_H2bd zenon_H208 zenon_H18c zenon_Hf6 zenon_Hde zenon_Hcd zenon_H76 zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_H48 zenon_Hfc zenon_H200 zenon_H1ab zenon_Hb8 zenon_H3f zenon_H1f zenon_Hee zenon_H6f zenon_Had zenon_H23b zenon_H2a9 zenon_H14e zenon_H2b1 zenon_H2b0 zenon_H156 zenon_H2d zenon_H42 zenon_Hd1 zenon_H6c zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.27/30.40 apply (zenon_L1622_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.27/30.40 exact (zenon_H13b zenon_Hfd). % 30.27/30.40 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.27/30.40 apply (zenon_L824_); trivial. % 30.27/30.40 apply (zenon_L1184_); trivial. % 30.27/30.40 (* end of lemma zenon_L1623_ *) % 30.27/30.40 assert (zenon_L1624_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H8d zenon_H117 zenon_Hd9 zenon_H4c zenon_H100 zenon_H19e zenon_H13b zenon_H16f zenon_H6c zenon_Hd1 zenon_H42 zenon_H2d zenon_H156 zenon_H2b0 zenon_H2b1 zenon_H14e zenon_H2a9 zenon_Had zenon_Hb8 zenon_H200 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H18c zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16a zenon_H101 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.40 apply (zenon_L149_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.40 apply (zenon_L1452_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.40 apply (zenon_L1623_); trivial. % 30.27/30.40 apply (zenon_L1187_); trivial. % 30.27/30.40 (* end of lemma zenon_L1624_ *) % 30.27/30.40 assert (zenon_L1625_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.40 do 0 intro. intros zenon_H42 zenon_H1ab zenon_H2b0 zenon_H2b1 zenon_He9 zenon_H6c zenon_H92 zenon_H1dc zenon_H20 zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H4e zenon_H16a zenon_H159 zenon_H23b zenon_Hcd zenon_H1f zenon_H3f zenon_Hee zenon_H8d zenon_Hf4 zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H4c zenon_H172 zenon_He1 zenon_H200 zenon_H2a9 zenon_H108 zenon_H1a5 zenon_H1fd zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H174 zenon_H1b1 zenon_H173 zenon_He4 zenon_H19e zenon_Hf9 zenon_H69 zenon_Hbd zenon_Hd9 zenon_H15a zenon_Hfc zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H100. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.40 apply (zenon_L4_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.40 apply (zenon_L842_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.40 apply (zenon_L922_); trivial. % 30.27/30.40 apply (zenon_L1600_); trivial. % 30.27/30.40 (* end of lemma zenon_L1625_ *) % 30.27/30.40 assert (zenon_L1626_ : ((op (e1) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.27/30.40 do 0 intro. intros zenon_Hdc zenon_H92 zenon_H1dc zenon_H20 zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H97 zenon_H2b4 zenon_H159 zenon_H1d8 zenon_H108 zenon_H1a5 zenon_H1fd zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H174 zenon_H1b1 zenon_H173 zenon_He4 zenon_Hf9 zenon_H69 zenon_Hbd zenon_H15a zenon_Hee zenon_H3f zenon_H1f zenon_H23b zenon_Hf4 zenon_Ha4 zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_H48 zenon_Hfc zenon_H200 zenon_Hb8 zenon_Had zenon_H2a9 zenon_H14e zenon_Hd9 zenon_H8d zenon_H101 zenon_H16a zenon_H4e zenon_H6f zenon_H2b1 zenon_H2b0 zenon_H4a zenon_H156 zenon_H1ab zenon_H42 zenon_H2d zenon_Hd1 zenon_H1e zenon_H35 zenon_H102 zenon_H6c zenon_H18c zenon_H18f zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.40 apply (zenon_L4_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.40 apply (zenon_L949_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.40 apply (zenon_L922_); trivial. % 30.27/30.40 apply (zenon_L1600_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.27/30.40 exact (zenon_H13b zenon_Hfd). % 30.27/30.40 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.27/30.40 apply (zenon_L824_); trivial. % 30.27/30.40 apply (zenon_L1184_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.40 apply (zenon_L4_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.40 apply (zenon_L1624_); trivial. % 30.27/30.40 apply (zenon_L1454_); trivial. % 30.27/30.40 (* end of lemma zenon_L1626_ *) % 30.27/30.40 assert (zenon_L1627_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.27/30.40 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_Hda zenon_H10d zenon_H90 zenon_H89. % 30.27/30.40 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.27/30.40 apply (zenon_L386_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.27/30.40 apply (zenon_L53_); trivial. % 30.27/30.40 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.27/30.40 apply (zenon_L64_); trivial. % 30.27/30.40 apply (zenon_L538_); trivial. % 30.27/30.40 (* end of lemma zenon_L1627_ *) % 30.27/30.40 assert (zenon_L1628_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.27/30.41 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H222 zenon_H2a9 zenon_H10d zenon_Hda zenon_H110 zenon_H2b7 zenon_Hee zenon_H19a zenon_H6f zenon_H40 zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_H89 zenon_H23b zenon_H156 zenon_H4e zenon_H16c. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.27/30.41 apply (zenon_L273_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.27/30.41 apply (zenon_L775_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.27/30.41 apply (zenon_L1627_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.27/30.41 apply (zenon_L80_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.27/30.41 apply (zenon_L337_); trivial. % 30.27/30.41 apply (zenon_L1553_); trivial. % 30.27/30.41 apply (zenon_L779_); trivial. % 30.27/30.41 (* end of lemma zenon_L1628_ *) % 30.27/30.41 assert (zenon_L1629_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.27/30.41 do 0 intro. intros zenon_H101 zenon_H4e zenon_H156 zenon_H23b zenon_H89 zenon_H3f zenon_Hcd zenon_Hf9 zenon_H6f zenon_Hee zenon_H2b7 zenon_H110 zenon_Hda zenon_H10d zenon_H2a9 zenon_H222 zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H35 zenon_H2b1 zenon_H16a zenon_H2b0 zenon_H1ab zenon_H1e zenon_H2d zenon_H42 zenon_H14e zenon_Hf4 zenon_Hd1 zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.41 apply (zenon_L1451_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.41 apply (zenon_L842_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.41 apply (zenon_L752_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.41 apply (zenon_L4_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.41 apply (zenon_L842_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.41 apply (zenon_L922_); trivial. % 30.27/30.41 apply (zenon_L1628_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.27/30.41 exact (zenon_H13b zenon_Hfd). % 30.27/30.41 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.27/30.41 apply (zenon_L824_); trivial. % 30.27/30.41 apply (zenon_L1184_); trivial. % 30.27/30.41 (* end of lemma zenon_L1629_ *) % 30.27/30.41 assert (zenon_L1630_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.27/30.41 do 0 intro. intros zenon_H101 zenon_H16a zenon_H16b zenon_H4e zenon_H6f zenon_H2b1 zenon_H2b0 zenon_H4a zenon_H156 zenon_H1ab zenon_H42 zenon_H2d zenon_Hd1 zenon_H1e zenon_H19e zenon_H35 zenon_H102 zenon_H6c zenon_H18c zenon_H18f zenon_H16f zenon_H13b zenon_H1bd zenon_Hc9 zenon_H100 zenon_H4c zenon_H19a. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.27/30.41 apply (zenon_L1453_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.27/30.41 exact (zenon_H13b zenon_Hfd). % 30.27/30.41 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.27/30.41 apply (zenon_L282_); trivial. % 30.27/30.41 apply (zenon_L1184_); trivial. % 30.27/30.41 (* end of lemma zenon_L1630_ *) % 30.27/30.41 assert (zenon_L1631_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.27/30.41 do 0 intro. intros zenon_H174 zenon_H1d5 zenon_H222 zenon_H10d zenon_Hda zenon_H110 zenon_H2b7 zenon_Hf9 zenon_Hee zenon_H3f zenon_H1f zenon_H23b zenon_Hf4 zenon_Ha4 zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_H48 zenon_Hfc zenon_H200 zenon_Hb8 zenon_Had zenon_H2a9 zenon_H14e zenon_Hd9 zenon_H8d zenon_H101 zenon_H16a zenon_H4e zenon_H6f zenon_H2b1 zenon_H2b0 zenon_H4a zenon_H156 zenon_H1ab zenon_H42 zenon_H2d zenon_Hd1 zenon_H1e zenon_H19e zenon_H35 zenon_H102 zenon_H6c zenon_H18c zenon_H18f zenon_H16f zenon_H13b zenon_H1bd zenon_Hc9 zenon_H100 zenon_H4c zenon_H19a. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.41 apply (zenon_L1629_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.41 apply (zenon_L4_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.41 apply (zenon_L1624_); trivial. % 30.27/30.41 apply (zenon_L1630_); trivial. % 30.27/30.41 (* end of lemma zenon_L1631_ *) % 30.27/30.41 assert (zenon_L1632_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.41 do 0 intro. intros zenon_H8d zenon_He2 zenon_H4c zenon_H100 zenon_H19e zenon_H13b zenon_H16f zenon_H6c zenon_Hd1 zenon_H42 zenon_H2d zenon_H156 zenon_H2b0 zenon_H2b1 zenon_H14e zenon_H2a9 zenon_Had zenon_Hb8 zenon_H200 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H18c zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16a zenon_H101 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.41 apply (zenon_L387_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.41 apply (zenon_L1452_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.41 apply (zenon_L1623_); trivial. % 30.27/30.41 apply (zenon_L1187_); trivial. % 30.27/30.41 (* end of lemma zenon_L1632_ *) % 30.27/30.41 assert (zenon_L1633_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.27/30.41 do 0 intro. intros zenon_H174 zenon_H64 zenon_H3f zenon_Hc9 zenon_He1 zenon_H68 zenon_Hd9 zenon_H8d zenon_H15a zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.41 apply (zenon_L148_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.41 apply (zenon_L746_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.41 apply (zenon_L958_); trivial. % 30.27/30.41 apply (zenon_L1472_); trivial. % 30.27/30.41 (* end of lemma zenon_L1633_ *) % 30.27/30.41 assert (zenon_L1634_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.41 do 0 intro. intros zenon_H92 zenon_H20 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H4e zenon_H16a zenon_H159 zenon_H23b zenon_Hcd zenon_H1f zenon_H3f zenon_Hee zenon_H8d zenon_Hf4 zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H4c zenon_H172 zenon_He1 zenon_H200 zenon_H174 zenon_H64 zenon_Hd9 zenon_H15a zenon_Hfc zenon_He4 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.27/30.41 apply (zenon_L912_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.27/30.41 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.27/30.41 apply (zenon_L1588_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.27/30.41 apply (zenon_L48_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.27/30.41 apply (zenon_L1633_); trivial. % 30.27/30.41 apply (zenon_L1599_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.27/30.41 apply (zenon_L1450_); trivial. % 30.27/30.41 apply (zenon_L1473_); trivial. % 30.27/30.41 (* end of lemma zenon_L1634_ *) % 30.27/30.41 assert (zenon_L1635_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.41 do 0 intro. intros zenon_Haa zenon_H90 zenon_H92 zenon_H20 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H4e zenon_H16a zenon_H159 zenon_H23b zenon_Hcd zenon_H1f zenon_H3f zenon_Hee zenon_H8d zenon_Hf4 zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H4c zenon_H172 zenon_He1 zenon_H200 zenon_H174 zenon_H64 zenon_Hd9 zenon_H15a zenon_Hfc zenon_He4 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H100. % 30.27/30.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H95 | zenon_intro zenon_Hab ]. % 30.27/30.41 apply (zenon_L29_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H98 | zenon_intro zenon_Hac ]. % 30.27/30.41 apply (zenon_L30_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9d | zenon_intro zenon_H40 ]. % 30.27/30.41 apply (zenon_L1184_); trivial. % 30.27/30.41 apply (zenon_L1634_); trivial. % 30.27/30.41 (* end of lemma zenon_L1635_ *) % 30.27/30.41 assert (zenon_L1636_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e3)) -> False). % 30.27/30.41 do 0 intro. intros zenon_H83 zenon_H100 zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H18c zenon_He4 zenon_Hfc zenon_Hd9 zenon_H174 zenon_H200 zenon_He1 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_Hf6 zenon_H208 zenon_H2bd zenon_H218 zenon_H1e zenon_H35 zenon_Ha4 zenon_Hf4 zenon_H8d zenon_Hee zenon_H3f zenon_H1f zenon_Hcd zenon_H23b zenon_H159 zenon_H16a zenon_H19a zenon_H6f zenon_H2b4 zenon_H2d zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H97 zenon_H20 zenon_H92 zenon_Haa zenon_H90 zenon_He7 zenon_H1a5 zenon_H117 zenon_H4e zenon_H1b1 zenon_H4c zenon_Hfe zenon_H13b zenon_H15a zenon_H173 zenon_Hc8 zenon_H76. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 30.27/30.41 apply (zenon_L1635_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 30.27/30.41 apply (zenon_L1053_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 30.27/30.41 apply (zenon_L1457_); trivial. % 30.27/30.41 apply (zenon_L332_); trivial. % 30.27/30.41 (* end of lemma zenon_L1636_ *) % 30.27/30.41 assert (zenon_L1637_ : ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.27/30.41 do 0 intro. intros zenon_Hdf zenon_Hc8 zenon_H173 zenon_H15a zenon_H13b zenon_H4c zenon_H1b1 zenon_H117 zenon_H1a5 zenon_He7 zenon_H90 zenon_Haa zenon_H92 zenon_H20 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H16a zenon_H159 zenon_H23b zenon_Hcd zenon_H1f zenon_H3f zenon_Hee zenon_H8d zenon_Hf4 zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_He1 zenon_H200 zenon_H174 zenon_Hd9 zenon_Hfc zenon_He4 zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H100 zenon_H83 zenon_H18c zenon_H4e zenon_H76. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.41 apply (zenon_L740_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.41 apply (zenon_L42_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.41 apply (zenon_L1636_); trivial. % 30.27/30.41 apply (zenon_L864_); trivial. % 30.27/30.41 (* end of lemma zenon_L1637_ *) % 30.27/30.41 assert (zenon_L1638_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.41 do 0 intro. intros zenon_H83 zenon_He4 zenon_Hd9 zenon_H174 zenon_H1d8 zenon_H97 zenon_H92 zenon_Haa zenon_He7 zenon_H1a5 zenon_H1b1 zenon_H15a zenon_H173 zenon_Hc8 zenon_Had zenon_Hb8 zenon_Hfc zenon_H172 zenon_H56 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H100 zenon_H208 zenon_H2bd zenon_H218 zenon_Ha4 zenon_H73 zenon_H8d zenon_H90 zenon_Hbd zenon_H2a9 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H20 zenon_H1e zenon_H1dc zenon_H3c zenon_H69 zenon_H200 zenon_H19e zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H35 zenon_Hd1 zenon_H42 zenon_H16a zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H2b1 zenon_H2b0 zenon_H4a zenon_H156 zenon_H2b4 zenon_H2d zenon_H18c zenon_H48 zenon_H16f zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.41 apply (zenon_L538_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.41 apply (zenon_L4_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.41 apply (zenon_L232_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.41 apply (zenon_L4_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.41 apply (zenon_L1449_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.41 apply (zenon_L1467_); trivial. % 30.27/30.41 apply (zenon_L1473_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.41 apply (zenon_L4_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.41 apply (zenon_L842_); trivial. % 30.27/30.41 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.42 apply (zenon_L1637_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.42 apply (zenon_L207_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.42 apply (zenon_L1466_); trivial. % 30.27/30.42 apply (zenon_L737_); trivial. % 30.27/30.42 apply (zenon_L969_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.42 apply (zenon_L842_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.42 apply (zenon_L235_); trivial. % 30.27/30.42 apply (zenon_L1611_); trivial. % 30.27/30.42 apply (zenon_L39_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.42 apply (zenon_L538_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.42 apply (zenon_L1604_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.42 apply (zenon_L929_); trivial. % 30.27/30.42 apply (zenon_L1187_); trivial. % 30.27/30.42 (* end of lemma zenon_L1638_ *) % 30.27/30.42 assert (zenon_L1639_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e3)) -> False). % 30.27/30.42 do 0 intro. intros zenon_H83 zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H18c zenon_He4 zenon_Hfc zenon_Hd9 zenon_H174 zenon_H200 zenon_He1 zenon_H172 zenon_H4c zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_H208 zenon_H2bd zenon_H218 zenon_H1e zenon_H35 zenon_Ha4 zenon_Hf4 zenon_H8d zenon_Hcd zenon_H159 zenon_H16a zenon_H4e zenon_H6f zenon_H2b4 zenon_H2d zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H97 zenon_H20 zenon_H92 zenon_H90 zenon_Haa zenon_H1e5 zenon_Hf6 zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_He7 zenon_H23b zenon_Hdc zenon_H15a zenon_H6e. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 30.27/30.42 apply (zenon_L1635_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 30.27/30.42 apply (zenon_L1058_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 30.27/30.42 apply (zenon_L94_); trivial. % 30.27/30.42 apply (zenon_L241_); trivial. % 30.27/30.42 (* end of lemma zenon_L1639_ *) % 30.27/30.42 assert (zenon_L1640_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.42 do 0 intro. intros zenon_H2b1 zenon_H3d zenon_H19e zenon_H6e zenon_H15a zenon_Hdc zenon_H23b zenon_He7 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hf6 zenon_Haa zenon_H90 zenon_H92 zenon_H20 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H4e zenon_H16a zenon_H159 zenon_Hcd zenon_H8d zenon_Hf4 zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H4c zenon_H172 zenon_He1 zenon_H200 zenon_H174 zenon_Hd9 zenon_Hfc zenon_He4 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H100 zenon_H83 zenon_H1ab. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.27/30.42 apply (zenon_L1460_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.27/30.42 apply (zenon_L731_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.27/30.42 apply (zenon_L1639_); trivial. % 30.27/30.42 exact (zenon_H1ab zenon_H112). % 30.27/30.42 (* end of lemma zenon_L1640_ *) % 30.27/30.42 assert (zenon_L1641_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.27/30.42 do 0 intro. intros zenon_H42 zenon_H2b0 zenon_H1ab zenon_H83 zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_He4 zenon_Hfc zenon_Hd9 zenon_H174 zenon_He1 zenon_H172 zenon_H4c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_H208 zenon_H2bd zenon_H218 zenon_H35 zenon_Ha4 zenon_H8d zenon_Hcd zenon_H159 zenon_H16a zenon_H4e zenon_H2b4 zenon_H2d zenon_H16f zenon_H97 zenon_H92 zenon_H90 zenon_Haa zenon_Hf6 zenon_H1f zenon_He7 zenon_Hdc zenon_H15a zenon_H19e zenon_H2b1 zenon_H200 zenon_H69 zenon_H18c zenon_H3c zenon_H14e zenon_H1dc zenon_H3f zenon_H1e zenon_H23b zenon_H20 zenon_H6f zenon_H19a zenon_Hee zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hf4 zenon_H2a9 zenon_Hbd zenon_H156 zenon_H48 zenon_H6e. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.42 apply (zenon_L4_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.42 apply (zenon_L842_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.42 apply (zenon_L1640_); trivial. % 30.27/30.42 apply (zenon_L969_); trivial. % 30.27/30.42 (* end of lemma zenon_L1641_ *) % 30.27/30.42 assert (zenon_L1642_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.42 do 0 intro. intros zenon_H42 zenon_Hd1 zenon_H1ab zenon_H83 zenon_Had zenon_H4a zenon_H18c zenon_He4 zenon_Hd9 zenon_H174 zenon_H200 zenon_He1 zenon_H172 zenon_H4c zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_H208 zenon_H2bd zenon_H218 zenon_H1e zenon_H35 zenon_Ha4 zenon_Hf4 zenon_H8d zenon_Hcd zenon_H159 zenon_H16a zenon_H4e zenon_H6f zenon_H2b4 zenon_H2d zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H97 zenon_H20 zenon_H92 zenon_H90 zenon_Haa zenon_Hf6 zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_He7 zenon_H23b zenon_Hdc zenon_H15a zenon_H6e zenon_H19e zenon_H2b1 zenon_H102 zenon_Hfe zenon_Hfc zenon_H18f zenon_H13b zenon_H100. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.42 apply (zenon_L4_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.42 apply (zenon_L1449_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.42 apply (zenon_L1640_); trivial. % 30.27/30.42 apply (zenon_L1575_); trivial. % 30.27/30.42 (* end of lemma zenon_L1642_ *) % 30.27/30.42 assert (zenon_L1643_ : ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.42 do 0 intro. intros zenon_Hdf zenon_Hfc zenon_H15a zenon_Hdc zenon_H23b zenon_He7 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hf6 zenon_Haa zenon_H90 zenon_H92 zenon_H97 zenon_H16f zenon_H6f zenon_Hcd zenon_H8d zenon_Hf4 zenon_Ha4 zenon_H218 zenon_H2bd zenon_H208 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H4c zenon_H172 zenon_He1 zenon_H200 zenon_H174 zenon_Hd9 zenon_He4 zenon_H18c zenon_Had zenon_H83 zenon_H42 zenon_H2d zenon_Hd1 zenon_H35 zenon_H1e zenon_H1ab zenon_H156 zenon_H4a zenon_H19e zenon_H4e zenon_H2b4 zenon_H20 zenon_H16a zenon_H14e zenon_H48 zenon_H6e zenon_H2b1 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H100. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.42 apply (zenon_L740_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.42 apply (zenon_L42_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.42 apply (zenon_L1642_); trivial. % 30.27/30.42 apply (zenon_L1464_); trivial. % 30.27/30.42 (* end of lemma zenon_L1643_ *) % 30.27/30.42 assert (zenon_L1644_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.42 do 0 intro. intros zenon_H2b1 zenon_H19e zenon_Hd1 zenon_H42 zenon_Hdc zenon_H4e zenon_H18c zenon_H83 zenon_H100 zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_He4 zenon_Hfc zenon_Hd9 zenon_H174 zenon_H200 zenon_He1 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_Hf6 zenon_H208 zenon_H2bd zenon_H218 zenon_H1e zenon_H35 zenon_Ha4 zenon_Hf4 zenon_H8d zenon_Hcd zenon_H159 zenon_H16a zenon_H2b4 zenon_H2d zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H97 zenon_H20 zenon_H92 zenon_Haa zenon_H90 zenon_He7 zenon_H1a5 zenon_H117 zenon_H1b1 zenon_H4c zenon_H13b zenon_H15a zenon_H173 zenon_Hc8 zenon_Hdf zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.42 apply (zenon_L538_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.42 apply (zenon_L1643_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.42 apply (zenon_L1637_); trivial. % 30.27/30.42 apply (zenon_L1187_); trivial. % 30.27/30.42 (* end of lemma zenon_L1644_ *) % 30.27/30.42 assert (zenon_L1645_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.42 do 0 intro. intros zenon_Hbd zenon_H2a9 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1dc zenon_H69 zenon_H2b0 zenon_H19e zenon_H2b1 zenon_Hd1 zenon_H42 zenon_Hdc zenon_H83 zenon_Had zenon_He4 zenon_Hd9 zenon_H174 zenon_H1d8 zenon_H8d zenon_H159 zenon_H2b4 zenon_H2d zenon_H156 zenon_H14e zenon_H16f zenon_H97 zenon_H20 zenon_H92 zenon_Haa zenon_H90 zenon_He7 zenon_H1a5 zenon_H117 zenon_H1b1 zenon_H4c zenon_H15a zenon_H173 zenon_Hc8 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab zenon_H200 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_H76 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H18c zenon_H100 zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16a. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.42 apply (zenon_L1641_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.42 apply (zenon_L842_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.42 apply (zenon_L752_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.42 apply (zenon_L4_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.42 apply (zenon_L842_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.42 apply (zenon_L1644_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.42 apply (zenon_L207_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.42 apply (zenon_L1466_); trivial. % 30.27/30.42 apply (zenon_L1579_); trivial. % 30.27/30.42 apply (zenon_L1580_); trivial. % 30.27/30.42 (* end of lemma zenon_L1645_ *) % 30.27/30.42 assert (zenon_L1646_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.42 do 0 intro. intros zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H100 zenon_H19e zenon_H15a zenon_Hdc zenon_He7 zenon_Hf6 zenon_Haa zenon_H90 zenon_H92 zenon_H20 zenon_H97 zenon_Hcd zenon_H8d zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_He1 zenon_H200 zenon_H174 zenon_Hd9 zenon_Hfc zenon_He4 zenon_Had zenon_H83 zenon_H42 zenon_H16a zenon_H16b zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H2b1 zenon_H2b0 zenon_H4a zenon_H156 zenon_H2b4 zenon_H2d zenon_H18c zenon_H48 zenon_H16f zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.42 apply (zenon_L538_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.42 apply (zenon_L4_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.42 apply (zenon_L842_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.42 apply (zenon_L1640_); trivial. % 30.27/30.42 apply (zenon_L1470_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.42 apply (zenon_L929_); trivial. % 30.27/30.42 apply (zenon_L1187_); trivial. % 30.27/30.42 (* end of lemma zenon_L1646_ *) % 30.27/30.42 assert (zenon_L1647_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.42 do 0 intro. intros zenon_Hbd zenon_H2a9 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1dc zenon_H69 zenon_Hd1 zenon_H1a5 zenon_H1b1 zenon_H173 zenon_Hc8 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H100 zenon_H19e zenon_H15a zenon_Hdc zenon_He7 zenon_Hf6 zenon_Haa zenon_H90 zenon_H92 zenon_H20 zenon_H97 zenon_Hcd zenon_H8d zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_He1 zenon_H200 zenon_H174 zenon_Hd9 zenon_Hfc zenon_He4 zenon_Had zenon_H83 zenon_H42 zenon_H16a zenon_H4e zenon_H14e zenon_H4c zenon_Hf4 zenon_H2b1 zenon_H2b0 zenon_H4a zenon_H156 zenon_H2b4 zenon_H2d zenon_H18c zenon_H48 zenon_H16f zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.42 apply (zenon_L538_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.42 apply (zenon_L4_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.42 apply (zenon_L538_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.42 apply (zenon_L1641_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.42 apply (zenon_L1645_); trivial. % 30.27/30.42 apply (zenon_L39_); trivial. % 30.27/30.42 apply (zenon_L1646_); trivial. % 30.27/30.42 (* end of lemma zenon_L1647_ *) % 30.27/30.42 assert (zenon_L1648_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.27/30.42 do 0 intro. intros zenon_H8d zenon_Hf4 zenon_H48 zenon_H156 zenon_H23b zenon_H14e zenon_H1dc zenon_H1e zenon_H20 zenon_Hbd zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab zenon_H3c zenon_Hde zenon_H200 zenon_He1 zenon_Hc9 zenon_H6f zenon_H90. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.27/30.42 apply (zenon_L538_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.27/30.42 apply (zenon_L1618_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.27/30.42 apply (zenon_L273_); trivial. % 30.27/30.42 apply (zenon_L39_); trivial. % 30.27/30.42 (* end of lemma zenon_L1648_ *) % 30.27/30.42 assert (zenon_L1649_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.42 do 0 intro. intros zenon_Hc0 zenon_Hcd zenon_H8d zenon_Hf4 zenon_H48 zenon_H156 zenon_H23b zenon_H14e zenon_H1dc zenon_H20 zenon_Hbd zenon_H3f zenon_Hee zenon_H1ab zenon_H3c zenon_Hde zenon_H200 zenon_He1 zenon_H6f zenon_H2a9 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H69 zenon_Hd1 zenon_H1b1 zenon_H173 zenon_Hc8 zenon_H159 zenon_H100 zenon_H19e zenon_H15a zenon_He7 zenon_Hf6 zenon_Haa zenon_H92 zenon_H97 zenon_Ha4 zenon_H218 zenon_H2bd zenon_H208 zenon_H1d8 zenon_H135 zenon_H56 zenon_H172 zenon_H174 zenon_Hd9 zenon_Hfc zenon_He4 zenon_Had zenon_H83 zenon_H42 zenon_H4e zenon_H4c zenon_H2b1 zenon_H2b0 zenon_H2b4 zenon_H2d zenon_H18c zenon_H16f zenon_Hb8 zenon_H225 zenon_H101 zenon_H1d5 zenon_H222 zenon_H10d zenon_Hf9 zenon_H1bd zenon_H108 zenon_H1fd zenon_H20e zenon_H1a5 zenon_H19a zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H13b zenon_H4a zenon_H16a. % 30.27/30.42 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.42 apply (zenon_L734_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.42 apply (zenon_L4_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.42 apply (zenon_L1602_); trivial. % 30.27/30.42 apply (zenon_L1605_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.27/30.42 apply (zenon_L1446_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.27/30.42 apply (zenon_L1615_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.27/30.42 apply (zenon_L48_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.42 apply (zenon_L1617_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.42 apply (zenon_L4_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.42 apply (zenon_L1619_); trivial. % 30.27/30.42 apply (zenon_L1614_); trivial. % 30.27/30.42 apply (zenon_L1621_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.27/30.42 apply (zenon_L232_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.27/30.42 apply (zenon_L4_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.27/30.42 apply (zenon_L1624_); trivial. % 30.27/30.42 apply (zenon_L1454_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.27/30.42 apply (zenon_L1625_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.27/30.42 apply (zenon_L47_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.27/30.42 apply (zenon_L1626_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.27/30.42 apply (zenon_L1631_); trivial. % 30.27/30.42 apply (zenon_L1632_); trivial. % 30.27/30.42 apply (zenon_L819_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.27/30.42 apply (zenon_L1638_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.27/30.42 apply (zenon_L1647_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.27/30.42 apply (zenon_L1648_); trivial. % 30.27/30.42 apply (zenon_L386_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.27/30.42 apply (zenon_L136_); trivial. % 30.27/30.42 apply (zenon_L1448_); trivial. % 30.27/30.42 (* end of lemma zenon_L1649_ *) % 30.27/30.42 assert (zenon_L1650_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.42 do 0 intro. intros zenon_H92 zenon_H84 zenon_H17d zenon_Hf4 zenon_H174 zenon_H64 zenon_H3f zenon_He1 zenon_Hd9 zenon_H8d zenon_H15a zenon_H159 zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H2b4 zenon_H2d zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H97 zenon_Hcd zenon_Hde zenon_He4 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.27/30.42 exact (zenon_H84 zenon_H88). % 30.27/30.42 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.27/30.42 apply (zenon_L1209_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.27/30.42 apply (zenon_L48_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.27/30.42 apply (zenon_L1633_); trivial. % 30.27/30.42 apply (zenon_L847_); trivial. % 30.27/30.42 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.27/30.42 apply (zenon_L1450_); trivial. % 30.27/30.42 apply (zenon_L1473_); trivial. % 30.27/30.42 (* end of lemma zenon_L1650_ *) % 30.27/30.42 assert (zenon_L1651_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.27/30.43 do 0 intro. intros zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H18c zenon_He4 zenon_Hde zenon_Hcd zenon_H97 zenon_H16f zenon_H48 zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_He1 zenon_H3f zenon_H64 zenon_H174 zenon_Hf4 zenon_H17d zenon_H84 zenon_H92 zenon_H2a9 zenon_H14e zenon_H4e zenon_H16c. % 30.27/30.43 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.27/30.43 apply (zenon_L174_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.27/30.43 apply (zenon_L1650_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.27/30.43 exact (zenon_H2a9 zenon_Hb6). % 30.27/30.43 apply (zenon_L875_); trivial. % 30.27/30.43 (* end of lemma zenon_L1651_ *) % 30.27/30.43 assert (zenon_L1652_ : ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.27/30.43 do 0 intro. intros zenon_H1ba zenon_Hd1 zenon_H20 zenon_H1ab zenon_H2b0 zenon_H2b1 zenon_H135 zenon_Hdc zenon_H3c zenon_H4e zenon_H156 zenon_He1 zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H35 zenon_He9 zenon_H19e zenon_Hb8 zenon_H1d8 zenon_H100 zenon_H13b zenon_Had zenon_He4 zenon_Hde zenon_Hcd zenon_H97 zenon_H16f zenon_H48 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_H3f zenon_H64 zenon_H174 zenon_H17d zenon_H84 zenon_H92 zenon_H2a9 zenon_H14e zenon_H1d5 zenon_Hf4 zenon_Hf6. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.43 apply (zenon_L1481_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.43 apply (zenon_L842_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.43 apply (zenon_L235_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.27/30.43 apply (zenon_L142_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.27/30.43 apply (zenon_L88_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.27/30.43 apply (zenon_L1651_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.27/30.43 apply (zenon_L922_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.27/30.43 apply (zenon_L544_); trivial. % 30.27/30.43 apply (zenon_L779_); trivial. % 30.27/30.43 apply (zenon_L56_); trivial. % 30.27/30.43 (* end of lemma zenon_L1652_ *) % 30.27/30.43 assert (zenon_L1653_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H101 zenon_Hf6 zenon_Hf4 zenon_H1d5 zenon_H14e zenon_H2a9 zenon_H92 zenon_H84 zenon_H17d zenon_H174 zenon_H64 zenon_H3f zenon_Hd9 zenon_H8d zenon_H15a zenon_H159 zenon_H16a zenon_H6f zenon_H2b4 zenon_H2d zenon_H48 zenon_H16f zenon_H97 zenon_Hcd zenon_Hde zenon_He4 zenon_Had zenon_H1d8 zenon_Hb8 zenon_H35 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_He1 zenon_H156 zenon_H4e zenon_H3c zenon_Hdc zenon_H135 zenon_H2b1 zenon_H2b0 zenon_H1ab zenon_H20 zenon_Hd1 zenon_H1ba zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.27/30.43 apply (zenon_L1652_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.27/30.43 exact (zenon_H13b zenon_Hfd). % 30.27/30.43 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.27/30.43 apply (zenon_L824_); trivial. % 30.27/30.43 apply (zenon_L1184_); trivial. % 30.27/30.43 (* end of lemma zenon_L1653_ *) % 30.27/30.43 assert (zenon_L1654_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H13b zenon_Hf4 zenon_H95. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.27/30.43 apply (zenon_L763_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.27/30.43 exact (zenon_H18f zenon_Hd2). % 30.27/30.43 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.27/30.43 exact (zenon_H13b zenon_Hfd). % 30.27/30.43 apply (zenon_L513_); trivial. % 30.27/30.43 (* end of lemma zenon_L1654_ *) % 30.27/30.43 assert (zenon_L1655_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H296 zenon_H1a5 zenon_H20e zenon_H1fd zenon_H108 zenon_H1bd zenon_Hf9 zenon_H10d zenon_H222 zenon_H225 zenon_H42 zenon_H83 zenon_Hfc zenon_H172 zenon_H56 zenon_H208 zenon_H2bd zenon_H218 zenon_Ha4 zenon_Haa zenon_He7 zenon_Hc8 zenon_H173 zenon_H1b1 zenon_H69 zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H200 zenon_Hee zenon_Hbd zenon_H1dc zenon_H23b zenon_Hc0 zenon_H19a zenon_H4c zenon_H100 zenon_H19e zenon_Hd1 zenon_H20 zenon_H1ab zenon_H2b0 zenon_H2b1 zenon_H135 zenon_Hdc zenon_H3c zenon_H4e zenon_H156 zenon_He1 zenon_H35 zenon_Hb8 zenon_H1d8 zenon_Had zenon_He4 zenon_Hde zenon_Hcd zenon_H97 zenon_H16f zenon_H48 zenon_H2d zenon_H2b4 zenon_H6f zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_H3f zenon_H64 zenon_H174 zenon_H17d zenon_H84 zenon_H92 zenon_H2a9 zenon_H14e zenon_H1d5 zenon_Hf6 zenon_H101 zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H13b zenon_Hf4. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.27/30.43 apply (zenon_L1649_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.27/30.43 apply (zenon_L763_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.27/30.43 apply (zenon_L1653_); trivial. % 30.27/30.43 apply (zenon_L1654_); trivial. % 30.27/30.43 (* end of lemma zenon_L1655_ *) % 30.27/30.43 assert (zenon_L1656_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.43 do 0 intro. intros zenon_Hc0 zenon_H23b zenon_H1dc zenon_Hbd zenon_Hee zenon_H200 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1b1 zenon_H173 zenon_Hc8 zenon_He7 zenon_Haa zenon_Ha4 zenon_H218 zenon_H2bd zenon_H208 zenon_H56 zenon_H172 zenon_H83 zenon_H225 zenon_H222 zenon_H10d zenon_Hf9 zenon_H1bd zenon_H108 zenon_H1fd zenon_H20e zenon_H1a5 zenon_Hf4 zenon_H18c zenon_H6c zenon_H101 zenon_Hf6 zenon_H1d5 zenon_H2a9 zenon_H92 zenon_H84 zenon_H17d zenon_H174 zenon_H64 zenon_H3f zenon_Hd9 zenon_H8d zenon_H15a zenon_H6f zenon_H2d zenon_H16f zenon_H97 zenon_Hcd zenon_Hde zenon_He4 zenon_Had zenon_H1d8 zenon_Hb8 zenon_H35 zenon_He1 zenon_H4e zenon_H3c zenon_Hdc zenon_H135 zenon_H2b0 zenon_Hd1 zenon_H19e zenon_H100 zenon_H4c zenon_H19a zenon_Hfc zenon_H42 zenon_H296 zenon_H2b1 zenon_H6e zenon_H48 zenon_H14e zenon_H16a zenon_H2b4 zenon_H20 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H1ab. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.43 apply (zenon_L1655_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.43 apply (zenon_L763_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.27/30.43 apply (zenon_L1452_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.27/30.43 apply (zenon_L59_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.27/30.43 apply (zenon_L1653_); trivial. % 30.27/30.43 apply (zenon_L1654_); trivial. % 30.27/30.43 apply (zenon_L1478_); trivial. % 30.27/30.43 (* end of lemma zenon_L1656_ *) % 30.27/30.43 assert (zenon_L1657_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H101 zenon_Hc0 zenon_H1dc zenon_Hbd zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1b1 zenon_H173 zenon_Hc8 zenon_He7 zenon_Haa zenon_H83 zenon_H225 zenon_H222 zenon_H10d zenon_Hf9 zenon_H1bd zenon_H108 zenon_H1fd zenon_H20e zenon_H1a5 zenon_Hf4 zenon_H13b zenon_H18f zenon_H4a zenon_H6c zenon_H102 zenon_Hd1 zenon_H20 zenon_H1ab zenon_H2b0 zenon_H2b1 zenon_H135 zenon_Hdc zenon_H3c zenon_H156 zenon_He1 zenon_H35 zenon_He9 zenon_H19e zenon_Hb8 zenon_H1d8 zenon_H100 zenon_Had zenon_He4 zenon_Hde zenon_Hcd zenon_H97 zenon_H16f zenon_H48 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_H3f zenon_H64 zenon_H174 zenon_H17d zenon_H84 zenon_H92 zenon_H2a9 zenon_H14e zenon_H1d5 zenon_Hf6 zenon_Hfc zenon_H4c zenon_H42 zenon_H23b zenon_Hee zenon_H1f zenon_H200 zenon_H172 zenon_H56 zenon_H208 zenon_H2bd zenon_H218 zenon_Ha4 zenon_H296 zenon_H18c zenon_H4e zenon_H76. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.43 apply (zenon_L1655_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.43 apply (zenon_L763_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.27/30.43 apply (zenon_L1622_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.27/30.43 apply (zenon_L59_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.27/30.43 apply (zenon_L1652_); trivial. % 30.27/30.43 apply (zenon_L1654_); trivial. % 30.27/30.43 apply (zenon_L864_); trivial. % 30.27/30.43 (* end of lemma zenon_L1657_ *) % 30.27/30.43 assert (zenon_L1658_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.27/30.43 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hc9 zenon_H13b zenon_Hcd zenon_H19a zenon_H1fd zenon_H1a5 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H20e zenon_H2a9. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.27/30.43 apply (zenon_L142_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.27/30.43 exact (zenon_H13b zenon_Hfd). % 30.27/30.43 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.27/30.43 apply (zenon_L159_); trivial. % 30.27/30.43 apply (zenon_L830_); trivial. % 30.27/30.43 (* end of lemma zenon_L1658_ *) % 30.27/30.43 assert (zenon_L1659_ : (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H1ab zenon_H1ba zenon_H19e zenon_Hd1 zenon_H20 zenon_H2b1 zenon_H35 zenon_H2c zenon_H4c zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H18c zenon_He4 zenon_Hde zenon_Hcd zenon_H97 zenon_H16f zenon_H48 zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_He1 zenon_H3f zenon_H64 zenon_H174 zenon_Hf4 zenon_H17d zenon_H84 zenon_H92 zenon_H2a9 zenon_H14e zenon_H4e. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.43 apply (zenon_L1481_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.43 apply (zenon_L1002_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.43 apply (zenon_L752_); trivial. % 30.27/30.43 apply (zenon_L1651_); trivial. % 30.27/30.43 (* end of lemma zenon_L1659_ *) % 30.27/30.43 assert (zenon_L1660_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.27/30.43 do 0 intro. intros zenon_H2b7 zenon_H110 zenon_Hb1 zenon_H19a zenon_Hee zenon_Hda zenon_H10d zenon_H2a9. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.27/30.43 apply (zenon_L65_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.27/30.43 apply (zenon_L337_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.27/30.43 apply (zenon_L64_); trivial. % 30.27/30.43 exact (zenon_H2a9 zenon_Hb6). % 30.27/30.43 (* end of lemma zenon_L1660_ *) % 30.27/30.43 assert (zenon_L1661_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.27/30.43 do 0 intro. intros zenon_H2b4 zenon_H1ab zenon_H102 zenon_Hfe zenon_Hfc zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H2b0 zenon_H20 zenon_H2b1 zenon_H76 zenon_H4e zenon_H18c zenon_Hdf zenon_H20d zenon_H2b7 zenon_H110 zenon_H19a zenon_Hee zenon_Hda zenon_H10d zenon_H2a9. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.27/30.43 apply (zenon_L1477_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.27/30.43 apply (zenon_L864_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.27/30.43 apply (zenon_L548_); trivial. % 30.27/30.43 apply (zenon_L1660_); trivial. % 30.27/30.43 (* end of lemma zenon_L1661_ *) % 30.27/30.43 assert (zenon_L1662_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e3)) -> False). % 30.27/30.43 do 0 intro. intros zenon_Hf9 zenon_Hfe zenon_Had zenon_He9 zenon_H3f zenon_Hda zenon_H10d zenon_H14e zenon_H4c zenon_H15e. % 30.27/30.43 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.27/30.43 apply (zenon_L742_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.27/30.43 apply (zenon_L53_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.27/30.43 apply (zenon_L64_); trivial. % 30.27/30.43 apply (zenon_L752_); trivial. % 30.27/30.43 (* end of lemma zenon_L1662_ *) % 30.27/30.43 assert (zenon_L1663_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H101 zenon_H4e zenon_H14e zenon_H2a9 zenon_H92 zenon_H84 zenon_H17d zenon_Hf4 zenon_H174 zenon_H64 zenon_H3f zenon_He1 zenon_Hd9 zenon_H8d zenon_H15a zenon_H159 zenon_H16a zenon_H6f zenon_H2b4 zenon_H2d zenon_H156 zenon_H48 zenon_H16f zenon_H97 zenon_Hcd zenon_Hde zenon_He4 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H76 zenon_H1d8 zenon_Hb8 zenon_Hf9 zenon_Hfe zenon_Hda zenon_H10d zenon_H95 zenon_H200 zenon_Hee zenon_H110 zenon_H2b7 zenon_H20d zenon_H2b0 zenon_Hfc zenon_H1ab zenon_Hd1 zenon_H20 zenon_H2b1 zenon_H20e zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.43 apply (zenon_L1661_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.43 apply (zenon_L1481_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.43 apply (zenon_L350_); trivial. % 30.27/30.43 apply (zenon_L737_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.43 apply (zenon_L513_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.43 apply (zenon_L1662_); trivial. % 30.27/30.43 apply (zenon_L1651_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.27/30.43 exact (zenon_H13b zenon_Hfd). % 30.27/30.43 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.27/30.43 apply (zenon_L824_); trivial. % 30.27/30.43 apply (zenon_L1184_); trivial. % 30.27/30.43 (* end of lemma zenon_L1663_ *) % 30.27/30.43 assert (zenon_L1664_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H296 zenon_H2c zenon_H35 zenon_H101 zenon_H4e zenon_H14e zenon_H2a9 zenon_H92 zenon_H84 zenon_H17d zenon_Hf4 zenon_H174 zenon_H64 zenon_H3f zenon_He1 zenon_Hd9 zenon_H8d zenon_H15a zenon_H159 zenon_H16a zenon_H6f zenon_H2b4 zenon_H2d zenon_H156 zenon_H48 zenon_H16f zenon_H97 zenon_Hcd zenon_Hde zenon_He4 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H76 zenon_H1d8 zenon_Hb8 zenon_Hf9 zenon_Hfe zenon_Hda zenon_H10d zenon_H200 zenon_Hee zenon_H110 zenon_H2b7 zenon_H20d zenon_H2b0 zenon_Hfc zenon_H1ab zenon_Hd1 zenon_H20 zenon_H2b1 zenon_H20e zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.27/30.43 apply (zenon_L4_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.27/30.43 apply (zenon_L59_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.27/30.43 apply (zenon_L1659_); trivial. % 30.27/30.43 apply (zenon_L1663_); trivial. % 30.27/30.43 (* end of lemma zenon_L1664_ *) % 30.27/30.43 assert (zenon_L1665_ : ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.43 do 0 intro. intros zenon_H76 zenon_Hc8 zenon_H173 zenon_H15a zenon_H13b zenon_Hfe zenon_H4c zenon_H1b1 zenon_H4e zenon_H117 zenon_H1a5 zenon_He7 zenon_Haa zenon_H92 zenon_H20 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H16a zenon_H159 zenon_H23b zenon_Hcd zenon_H8d zenon_Hf4 zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_He1 zenon_H200 zenon_H174 zenon_Hd9 zenon_Hfc zenon_He4 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H100 zenon_H83 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.27/30.43 apply (zenon_L1636_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.27/30.43 apply (zenon_L336_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.27/30.43 apply (zenon_L337_); trivial. % 30.27/30.43 exact (zenon_H1ab zenon_H112). % 30.27/30.43 (* end of lemma zenon_L1665_ *) % 30.27/30.43 assert (zenon_L1666_ : ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H1ba zenon_H19e zenon_Hd1 zenon_H20 zenon_H1ab zenon_H2b0 zenon_H2b1 zenon_H4c zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H18c zenon_He4 zenon_Hde zenon_Hcd zenon_H97 zenon_H16f zenon_H48 zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_He1 zenon_H3f zenon_H64 zenon_H174 zenon_Hf4 zenon_H17d zenon_H84 zenon_H92 zenon_H2a9 zenon_H14e zenon_H4e. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.43 apply (zenon_L1481_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.43 apply (zenon_L842_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.43 apply (zenon_L752_); trivial. % 30.27/30.43 apply (zenon_L1651_); trivial. % 30.27/30.43 (* end of lemma zenon_L1666_ *) % 30.27/30.43 assert (zenon_L1667_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.43 do 0 intro. intros zenon_H16f zenon_H102 zenon_H1ba zenon_H19e zenon_H18f zenon_H13b zenon_Hd1 zenon_H2b4 zenon_H20 zenon_H159 zenon_H14e zenon_H48 zenon_H1ab zenon_H156 zenon_H4a zenon_H2b0 zenon_H2b1 zenon_H6f zenon_H19a zenon_H4e zenon_H16b zenon_H16a. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.43 apply (zenon_L1481_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.43 apply (zenon_L842_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.43 apply (zenon_L235_); trivial. % 30.27/30.43 apply (zenon_L859_); trivial. % 30.27/30.43 (* end of lemma zenon_L1667_ *) % 30.27/30.43 assert (zenon_L1668_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H296 zenon_H42 zenon_H2d zenon_He9 zenon_H35 zenon_H100 zenon_H16a zenon_H16b zenon_H4e zenon_H19a zenon_H6f zenon_H2b1 zenon_H2b0 zenon_H156 zenon_H1ab zenon_H48 zenon_H14e zenon_H159 zenon_H20 zenon_H2b4 zenon_Hd1 zenon_H19e zenon_H16f zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H13b zenon_Hf4. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.27/30.43 apply (zenon_L1453_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.27/30.43 apply (zenon_L763_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.27/30.43 apply (zenon_L1667_); trivial. % 30.27/30.43 apply (zenon_L1654_); trivial. % 30.27/30.43 (* end of lemma zenon_L1668_ *) % 30.27/30.43 assert (zenon_L1669_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.27/30.43 do 0 intro. intros zenon_H135 zenon_H2a9 zenon_H20e zenon_H4e zenon_H14e zenon_H4c zenon_H1a5 zenon_H1fd zenon_H19a zenon_H13b zenon_H18c zenon_H173 zenon_Hd5 zenon_Hcd zenon_Hde zenon_H142 zenon_Hf4 zenon_Hf6. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.27/30.43 apply (zenon_L1658_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.27/30.43 apply (zenon_L212_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.27/30.43 apply (zenon_L89_); trivial. % 30.27/30.43 apply (zenon_L56_); trivial. % 30.27/30.43 (* end of lemma zenon_L1669_ *) % 30.27/30.43 assert (zenon_L1670_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H208 zenon_H18f zenon_H4a zenon_H102 zenon_H16f zenon_H19e zenon_Hd1 zenon_H2b4 zenon_H20 zenon_H159 zenon_H48 zenon_H1ab zenon_H156 zenon_H2b0 zenon_H2b1 zenon_H6f zenon_H16b zenon_H16a zenon_H100 zenon_H35 zenon_He9 zenon_H2d zenon_H42 zenon_H296 zenon_Hf6 zenon_Hde zenon_Hcd zenon_H173 zenon_H18c zenon_H13b zenon_H19a zenon_H1fd zenon_H1a5 zenon_H4c zenon_H14e zenon_H4e zenon_H20e zenon_H2a9 zenon_H135 zenon_H56 zenon_H142 zenon_Hf4. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.27/30.43 apply (zenon_L1668_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.27/30.43 apply (zenon_L1669_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.27/30.43 exact (zenon_H56 zenon_H25). % 30.27/30.43 apply (zenon_L944_); trivial. % 30.27/30.43 (* end of lemma zenon_L1670_ *) % 30.27/30.43 assert (zenon_L1671_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.27/30.43 do 0 intro. intros zenon_H101 zenon_H6e zenon_H48 zenon_H156 zenon_H208 zenon_H18f zenon_H4a zenon_H102 zenon_H16f zenon_Hd1 zenon_H2b4 zenon_H20 zenon_H159 zenon_H1ab zenon_H2b0 zenon_H2b1 zenon_H6f zenon_H16b zenon_H16a zenon_H35 zenon_H2d zenon_H42 zenon_H296 zenon_Hf6 zenon_Hde zenon_Hcd zenon_H173 zenon_H18c zenon_H1fd zenon_H1a5 zenon_H14e zenon_H4e zenon_H20e zenon_H2a9 zenon_H135 zenon_H56 zenon_Hf4 zenon_H69 zenon_H200 zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.43 apply (zenon_L740_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.43 apply (zenon_L1481_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.43 apply (zenon_L1670_); trivial. % 30.27/30.43 apply (zenon_L737_); trivial. % 30.27/30.43 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.27/30.43 exact (zenon_H13b zenon_Hfd). % 30.27/30.43 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.27/30.43 apply (zenon_L824_); trivial. % 30.27/30.43 apply (zenon_L1184_); trivial. % 30.27/30.43 (* end of lemma zenon_L1671_ *) % 30.27/30.43 assert (zenon_L1672_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.44 do 0 intro. intros zenon_H42 zenon_Hd1 zenon_H35 zenon_H6e zenon_H48 zenon_H14e zenon_H2d zenon_H16b zenon_H1ab zenon_H159 zenon_H4a zenon_H19e zenon_H4e zenon_H2b4 zenon_H20 zenon_H16a zenon_H2b1 zenon_H156 zenon_H110 zenon_H3f zenon_H1e zenon_H2b7 zenon_Hb5 zenon_H19a zenon_Hee zenon_Hf4 zenon_H2a9 zenon_Hbd zenon_H102 zenon_Hfe zenon_Hfc zenon_H18f zenon_H13b zenon_H100. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.44 apply (zenon_L4_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.44 apply (zenon_L1449_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.44 apply (zenon_L1603_); trivial. % 30.27/30.44 apply (zenon_L1575_); trivial. % 30.27/30.44 (* end of lemma zenon_L1672_ *) % 30.27/30.44 assert (zenon_L1673_ : ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.27/30.44 do 0 intro. intros zenon_Hf4 zenon_H56 zenon_H135 zenon_H2a9 zenon_H20e zenon_H4e zenon_H14e zenon_H4c zenon_H1a5 zenon_H1fd zenon_H19a zenon_H13b zenon_H18c zenon_H173 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H296 zenon_H108 zenon_H1bd zenon_Hf9 zenon_H10d zenon_H222 zenon_H225 zenon_H42 zenon_H83 zenon_Hfc zenon_H172 zenon_H208 zenon_H2bd zenon_H218 zenon_Ha4 zenon_Haa zenon_He7 zenon_Hc8 zenon_H1b1 zenon_H69 zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H200 zenon_Hee zenon_Hbd zenon_H1dc zenon_H23b zenon_Hc0 zenon_H100 zenon_H19e zenon_Hd1 zenon_H20 zenon_H1ab zenon_H2b0 zenon_H2b1 zenon_Hdc zenon_H3c zenon_He1 zenon_H35 zenon_Hb8 zenon_H1d8 zenon_Had zenon_He4 zenon_H97 zenon_H16f zenon_H2d zenon_H2b4 zenon_H6f zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_H3f zenon_H64 zenon_H174 zenon_H17d zenon_H84 zenon_H92 zenon_H1d5 zenon_H101 zenon_H102 zenon_H4a zenon_H18f zenon_H156 zenon_H48 zenon_H6e. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.27/30.44 apply (zenon_L740_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.27/30.44 apply (zenon_L1481_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.27/30.44 apply (zenon_L1655_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.27/30.44 apply (zenon_L1669_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.27/30.44 exact (zenon_H56 zenon_H25). % 30.27/30.44 apply (zenon_L944_); trivial. % 30.27/30.44 apply (zenon_L737_); trivial. % 30.27/30.44 (* end of lemma zenon_L1673_ *) % 30.27/30.44 assert (zenon_L1674_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.44 do 0 intro. intros zenon_H2b1 zenon_H88 zenon_H2c1 zenon_H3d zenon_H4e zenon_H19e zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_Hfc zenon_Hfe zenon_H102 zenon_H1ab. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.27/30.44 apply (zenon_L940_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.27/30.44 apply (zenon_L731_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.27/30.44 apply (zenon_L1476_); trivial. % 30.27/30.44 exact (zenon_H1ab zenon_H112). % 30.27/30.44 (* end of lemma zenon_L1674_ *) % 30.27/30.44 assert (zenon_L1675_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.44 do 0 intro. intros zenon_H23b zenon_H88 zenon_He7 zenon_H40 zenon_H6f zenon_H19a zenon_Hee zenon_H1ab. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.27/30.44 apply (zenon_L1053_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.27/30.44 apply (zenon_L80_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.27/30.44 apply (zenon_L337_); trivial. % 30.27/30.44 exact (zenon_H1ab zenon_H112). % 30.27/30.44 (* end of lemma zenon_L1675_ *) % 30.27/30.44 assert (zenon_L1676_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.44 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H18c zenon_Hee zenon_H19a zenon_H6f zenon_He7 zenon_H88 zenon_H23b zenon_H2c1 zenon_Hfc zenon_H42 zenon_H2d zenon_Hd1 zenon_H35 zenon_H1e zenon_H1ab zenon_H156 zenon_H4a zenon_H19e zenon_H4e zenon_H2b4 zenon_H20 zenon_H16a zenon_H14e zenon_H48 zenon_H6e zenon_H2b1 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H100. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.44 apply (zenon_L740_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.44 apply (zenon_L42_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.44 apply (zenon_L4_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.44 apply (zenon_L1449_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.44 apply (zenon_L1674_); trivial. % 30.27/30.44 apply (zenon_L1675_); trivial. % 30.27/30.44 apply (zenon_L1464_); trivial. % 30.27/30.44 (* end of lemma zenon_L1676_ *) % 30.27/30.44 assert (zenon_L1677_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.27/30.44 do 0 intro. intros zenon_H2b1 zenon_H16a zenon_H37 zenon_H19a zenon_H2b0 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_Hfc zenon_Hfe zenon_H102 zenon_H1ab. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.27/30.44 apply (zenon_L839_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.27/30.44 apply (zenon_L840_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.27/30.44 apply (zenon_L1476_); trivial. % 30.27/30.44 exact (zenon_H1ab zenon_H112). % 30.27/30.44 (* end of lemma zenon_L1677_ *) % 30.27/30.44 assert (zenon_L1678_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.27/30.44 do 0 intro. intros zenon_H42 zenon_H2d zenon_H2b0 zenon_H19a zenon_H1ab zenon_Hfe zenon_H156 zenon_H19e zenon_H2c1 zenon_H88 zenon_H2b1 zenon_H200 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_H76 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H18c zenon_H100 zenon_H208 zenon_H2bd zenon_H218 zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Ha4 zenon_Hf4 zenon_H4e zenon_H16c zenon_H16a. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.44 apply (zenon_L4_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.44 apply (zenon_L1677_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.44 apply (zenon_L1674_); trivial. % 30.27/30.44 apply (zenon_L1580_); trivial. % 30.27/30.44 (* end of lemma zenon_L1678_ *) % 30.27/30.44 assert (zenon_L1679_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.27/30.44 do 0 intro. intros zenon_H16a zenon_Hf4 zenon_Ha4 zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H13b zenon_H4a zenon_H218 zenon_H2bd zenon_H208 zenon_H100 zenon_Hf6 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_H48 zenon_Hfc zenon_H200 zenon_H2b1 zenon_H88 zenon_H2c1 zenon_H19e zenon_H156 zenon_H1ab zenon_H19a zenon_H2b0 zenon_H2d zenon_H42 zenon_H6f zenon_Hdf zenon_Hee zenon_He7 zenon_H23b zenon_Hd1 zenon_H2b4 zenon_H20 zenon_H14e zenon_H159 zenon_H16f zenon_H18c zenon_H4e zenon_H76. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.44 apply (zenon_L740_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.44 apply (zenon_L42_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.44 apply (zenon_L1676_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.44 apply (zenon_L1677_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.44 apply (zenon_L235_); trivial. % 30.27/30.44 apply (zenon_L1678_); trivial. % 30.27/30.44 apply (zenon_L864_); trivial. % 30.27/30.44 (* end of lemma zenon_L1679_ *) % 30.27/30.44 assert (zenon_L1680_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.27/30.44 do 0 intro. intros zenon_H135 zenon_H4c zenon_H18c zenon_Hd5 zenon_Hcd zenon_H16c zenon_H4e zenon_H156 zenon_He1 zenon_H2b1 zenon_H88 zenon_H2c1 zenon_H19e zenon_H4a zenon_H13b zenon_H18f zenon_Hfc zenon_Hfe zenon_H102 zenon_H1ab zenon_H8a zenon_H1d8 zenon_H1d5 zenon_Hf4 zenon_Hf6. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.27/30.44 apply (zenon_L784_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.27/30.44 apply (zenon_L212_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.27/30.44 apply (zenon_L174_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.27/30.44 apply (zenon_L1674_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.27/30.44 apply (zenon_L544_); trivial. % 30.27/30.44 apply (zenon_L779_); trivial. % 30.27/30.44 apply (zenon_L56_); trivial. % 30.27/30.44 (* end of lemma zenon_L1680_ *) % 30.27/30.44 assert (zenon_L1681_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 30.27/30.44 do 0 intro. intros zenon_H42 zenon_H2d zenon_H6e zenon_Hd1 zenon_H35 zenon_H1e zenon_H16a zenon_H1ab zenon_H102 zenon_Hfe zenon_Hfc zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H19e zenon_H4e zenon_H2c1 zenon_H88 zenon_H2b1 zenon_H6f zenon_H98. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.27/30.44 apply (zenon_L4_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.27/30.44 apply (zenon_L1449_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.27/30.44 apply (zenon_L1674_); trivial. % 30.27/30.44 apply (zenon_L80_); trivial. % 30.27/30.44 (* end of lemma zenon_L1681_ *) % 30.27/30.44 assert (zenon_L1682_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> False). % 30.27/30.44 do 0 intro. intros zenon_H208 zenon_Hc8 zenon_Hf6 zenon_Hf4 zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H1ab zenon_H19e zenon_H2c1 zenon_H88 zenon_H2b1 zenon_He1 zenon_H4e zenon_H16c zenon_Hcd zenon_H18c zenon_H4c zenon_H135 zenon_H56 zenon_H102 zenon_Hfe zenon_Hfc zenon_H18f zenon_H13b zenon_H156 zenon_H4a. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.27/30.44 apply (zenon_L809_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.27/30.44 apply (zenon_L1680_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.27/30.44 exact (zenon_H56 zenon_H25). % 30.27/30.44 apply (zenon_L1476_); trivial. % 30.27/30.44 (* end of lemma zenon_L1682_ *) % 30.27/30.44 assert (zenon_L1683_ : ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.27/30.44 do 0 intro. intros zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_Hfc zenon_H102 zenon_H56 zenon_H135 zenon_H4c zenon_H18c zenon_Hcd zenon_He1 zenon_H2b1 zenon_H88 zenon_H2c1 zenon_H19e zenon_H1ab zenon_H1d8 zenon_H1d5 zenon_Hf4 zenon_Hf6 zenon_Hc8 zenon_H208 zenon_H19a zenon_H6f zenon_H16a zenon_H2b0 zenon_H42 zenon_H2d zenon_Hd1 zenon_H35 zenon_H1e zenon_H16f zenon_H100 zenon_H159 zenon_H48 zenon_H14e zenon_H20 zenon_H2b4 zenon_H23b zenon_He7 zenon_Hee zenon_Hdf zenon_H172 zenon_H3f zenon_H124 zenon_Had zenon_H4e zenon_H8a. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.44 apply (zenon_L740_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.44 apply (zenon_L42_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.27/30.44 apply (zenon_L1187_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.27/30.44 exact (zenon_H18f zenon_Hd2). % 30.27/30.44 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.44 apply (zenon_L1676_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.44 apply (zenon_L1677_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.44 apply (zenon_L235_); trivial. % 30.27/30.44 apply (zenon_L1680_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.44 apply (zenon_L1681_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.44 apply (zenon_L1677_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.27/30.44 apply (zenon_L235_); trivial. % 30.27/30.44 apply (zenon_L1682_); trivial. % 30.27/30.44 apply (zenon_L913_); trivial. % 30.27/30.44 (* end of lemma zenon_L1683_ *) % 30.27/30.44 assert (zenon_L1684_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.27/30.44 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H18c zenon_Hfc zenon_Hbd zenon_H2a9 zenon_Hf4 zenon_Hee zenon_H19a zenon_Hb5 zenon_H2b7 zenon_H3f zenon_H110 zenon_H16b zenon_H42 zenon_H2d zenon_Hd1 zenon_H35 zenon_H1e zenon_H1ab zenon_H156 zenon_H4a zenon_H19e zenon_H4e zenon_H2b4 zenon_H20 zenon_H16a zenon_H14e zenon_H48 zenon_H6e zenon_H2b1 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H100. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.44 apply (zenon_L740_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.44 apply (zenon_L42_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.44 apply (zenon_L1672_); trivial. % 30.27/30.44 apply (zenon_L1464_); trivial. % 30.27/30.44 (* end of lemma zenon_L1684_ *) % 30.27/30.44 assert (zenon_L1685_ : ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.27/30.44 do 0 intro. intros zenon_Hdf zenon_H1ab zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_H83 zenon_H100 zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_He4 zenon_Hfc zenon_Hd9 zenon_H174 zenon_H200 zenon_He1 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_Hf6 zenon_H208 zenon_H2bd zenon_H218 zenon_H1e zenon_H35 zenon_Ha4 zenon_Hf4 zenon_H8d zenon_Hcd zenon_H23b zenon_H159 zenon_H16a zenon_H6f zenon_H2b4 zenon_H2d zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H97 zenon_H20 zenon_H92 zenon_Haa zenon_He7 zenon_H1a5 zenon_H117 zenon_H1b1 zenon_H4c zenon_H13b zenon_H15a zenon_H173 zenon_Hc8 zenon_H18c zenon_H4e zenon_H76. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.44 apply (zenon_L740_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.44 apply (zenon_L42_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.44 apply (zenon_L1665_); trivial. % 30.27/30.44 apply (zenon_L864_); trivial. % 30.27/30.44 (* end of lemma zenon_L1685_ *) % 30.27/30.44 assert (zenon_L1686_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.27/30.44 do 0 intro. intros zenon_H16a zenon_H16b zenon_H19a zenon_H6f zenon_H19e zenon_H2a9 zenon_He1 zenon_Hfc zenon_Hdf zenon_H1ab zenon_Hee zenon_H3f zenon_H1f zenon_H83 zenon_H100 zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_He4 zenon_Hd9 zenon_H174 zenon_H200 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_H208 zenon_H2bd zenon_H218 zenon_H1e zenon_H35 zenon_Ha4 zenon_H8d zenon_Hcd zenon_H23b zenon_H159 zenon_H2b4 zenon_H2d zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H97 zenon_H20 zenon_H92 zenon_Haa zenon_He7 zenon_H1a5 zenon_H1b1 zenon_H4c zenon_H13b zenon_H15a zenon_H173 zenon_Hc8 zenon_H1fd zenon_Hf4 zenon_Hf6 zenon_Hbd zenon_Hb5 zenon_H2b7 zenon_H110 zenon_H42 zenon_Hd1 zenon_H2b1 zenon_H18c zenon_H4e zenon_H76. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.27/30.44 apply (zenon_L740_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.27/30.44 apply (zenon_L42_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.27/30.44 apply (zenon_L1684_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.27/30.44 apply (zenon_L784_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.27/30.44 apply (zenon_L824_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.27/30.44 apply (zenon_L1685_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.27/30.44 apply (zenon_L203_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.27/30.44 apply (zenon_L544_); trivial. % 30.27/30.44 exact (zenon_H2a9 zenon_Hb6). % 30.27/30.44 apply (zenon_L56_); trivial. % 30.27/30.44 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.44 apply (zenon_L235_); trivial. % 30.34/30.44 apply (zenon_L859_); trivial. % 30.34/30.44 apply (zenon_L864_); trivial. % 30.34/30.44 (* end of lemma zenon_L1686_ *) % 30.34/30.44 assert (zenon_L1687_ : ((op (e0) (e0)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.34/30.44 do 0 intro. intros zenon_H73 zenon_H4e zenon_H18c zenon_H2b1 zenon_Hd1 zenon_H42 zenon_H110 zenon_H2b7 zenon_Hb5 zenon_Hbd zenon_Hf6 zenon_Hf4 zenon_H1fd zenon_Hc8 zenon_H173 zenon_H15a zenon_H13b zenon_H4c zenon_H1b1 zenon_H1a5 zenon_He7 zenon_Haa zenon_H92 zenon_H20 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H159 zenon_Hcd zenon_H8d zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_H200 zenon_H174 zenon_Hd9 zenon_He4 zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H100 zenon_H83 zenon_Hdf zenon_Hfc zenon_He1 zenon_H2a9 zenon_H19e zenon_H16b zenon_H16a zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.44 apply (zenon_L232_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.44 apply (zenon_L1684_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.44 apply (zenon_L1686_); trivial. % 30.34/30.44 apply (zenon_L1187_); trivial. % 30.34/30.44 (* end of lemma zenon_L1687_ *) % 30.34/30.44 assert (zenon_L1688_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.34/30.44 do 0 intro. intros zenon_H19e zenon_H42 zenon_Hd1 zenon_H2b1 zenon_H6c zenon_H101 zenon_H4e zenon_H18c zenon_Hc8 zenon_H173 zenon_H15a zenon_H13b zenon_H4c zenon_H1b1 zenon_H117 zenon_H1a5 zenon_He7 zenon_Haa zenon_H92 zenon_H20 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H16a zenon_H159 zenon_Hcd zenon_H8d zenon_Hf4 zenon_Ha4 zenon_H35 zenon_H1e zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_He1 zenon_H200 zenon_H174 zenon_Hd9 zenon_Hfc zenon_He4 zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H100 zenon_H83 zenon_Hdf zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.44 apply (zenon_L149_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.44 apply (zenon_L1452_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.44 apply (zenon_L1685_); trivial. % 30.34/30.44 apply (zenon_L1187_); trivial. % 30.34/30.44 (* end of lemma zenon_L1688_ *) % 30.34/30.44 assert (zenon_L1689_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.34/30.44 do 0 intro. intros zenon_H19a zenon_H4c zenon_H100 zenon_H19e zenon_H13b zenon_H16f zenon_Hd1 zenon_Hc8 zenon_H1fd zenon_Hd9 zenon_H108 zenon_H3c zenon_Hdc zenon_H42 zenon_H2d zenon_Hf6 zenon_Hf4 zenon_H1d5 zenon_H1ab zenon_Hb8 zenon_H3f zenon_H1f zenon_Hee zenon_H6f zenon_Had zenon_H23b zenon_H2a9 zenon_H14e zenon_H172 zenon_Hdf zenon_H48 zenon_H1e zenon_H16a zenon_H2b1 zenon_He1 zenon_H156 zenon_H135 zenon_H35 zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_Hfc zenon_H18f zenon_H101 zenon_H4e zenon_H89 zenon_H15a. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.44 apply (zenon_L740_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.44 apply (zenon_L763_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.34/30.44 apply (zenon_L1451_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.34/30.44 apply (zenon_L949_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.44 apply (zenon_L752_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.34/30.44 apply (zenon_L4_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.34/30.44 apply (zenon_L784_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.34/30.44 apply (zenon_L824_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.34/30.44 apply (zenon_L1610_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.34/30.44 apply (zenon_L131_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.34/30.44 apply (zenon_L544_); trivial. % 30.34/30.44 apply (zenon_L779_); trivial. % 30.34/30.44 apply (zenon_L56_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.34/30.44 apply (zenon_L922_); trivial. % 30.34/30.44 apply (zenon_L1575_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.34/30.44 exact (zenon_H13b zenon_Hfd). % 30.34/30.44 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.34/30.44 apply (zenon_L824_); trivial. % 30.34/30.44 apply (zenon_L1184_); trivial. % 30.34/30.44 apply (zenon_L744_); trivial. % 30.34/30.44 (* end of lemma zenon_L1689_ *) % 30.34/30.44 assert (zenon_L1690_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.34/30.44 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H6c zenon_H4a zenon_He2 zenon_H4c zenon_Had zenon_H18c zenon_H4e zenon_H76. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.44 apply (zenon_L740_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.44 apply (zenon_L763_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.44 apply (zenon_L742_); trivial. % 30.34/30.44 apply (zenon_L864_); trivial. % 30.34/30.44 (* end of lemma zenon_L1690_ *) % 30.34/30.44 assert (zenon_L1691_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.34/30.44 do 0 intro. intros zenon_H8d zenon_H15a zenon_H100 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H2b1 zenon_H14e zenon_H16a zenon_H20 zenon_H2b4 zenon_H19e zenon_H156 zenon_H1e zenon_H35 zenon_Hd1 zenon_H2d zenon_H42 zenon_H4e zenon_H18c zenon_Had zenon_H4c zenon_He2 zenon_H4a zenon_H6c zenon_H48 zenon_Hdf zenon_H172 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.44 apply (zenon_L745_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.44 apply (zenon_L740_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.44 apply (zenon_L763_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.44 apply (zenon_L742_); trivial. % 30.34/30.44 apply (zenon_L1464_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.44 apply (zenon_L1690_); trivial. % 30.34/30.44 apply (zenon_L1187_); trivial. % 30.34/30.44 (* end of lemma zenon_L1691_ *) % 30.34/30.44 assert (zenon_L1692_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.34/30.44 do 0 intro. intros zenon_H8d zenon_He1 zenon_H100 zenon_H18f zenon_H159 zenon_H102 zenon_H2b1 zenon_H14e zenon_H16a zenon_H20 zenon_H2b4 zenon_H19e zenon_H4a zenon_H156 zenon_Hd1 zenon_H2d zenon_H42 zenon_Had zenon_H90 zenon_H4e zenon_H18c zenon_H173 zenon_H73 zenon_H15a zenon_H13b zenon_H4c zenon_H1b1 zenon_H117 zenon_H1a5 zenon_H1e zenon_H35 zenon_H48 zenon_Hdf zenon_H172 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.44 apply (zenon_L232_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.44 apply (zenon_L1465_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.44 apply (zenon_L1589_); trivial. % 30.34/30.44 apply (zenon_L1187_); trivial. % 30.34/30.44 (* end of lemma zenon_L1692_ *) % 30.34/30.44 assert (zenon_L1693_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.34/30.44 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H18c zenon_H90 zenon_Had zenon_Hfc zenon_Hbd zenon_H2a9 zenon_Hf4 zenon_Hee zenon_H19a zenon_Hb5 zenon_H2b7 zenon_H3f zenon_H110 zenon_H16b zenon_H42 zenon_H2d zenon_Hd1 zenon_H35 zenon_H1e zenon_H1ab zenon_H156 zenon_H4a zenon_H19e zenon_H4e zenon_H2b4 zenon_H20 zenon_H16a zenon_H14e zenon_H48 zenon_H6e zenon_H2b1 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H100. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.44 apply (zenon_L740_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.44 apply (zenon_L769_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.44 apply (zenon_L1672_); trivial. % 30.34/30.44 apply (zenon_L1464_); trivial. % 30.34/30.44 (* end of lemma zenon_L1693_ *) % 30.34/30.44 assert (zenon_L1694_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.34/30.44 do 0 intro. intros zenon_H2b4 zenon_H2d zenon_H16b zenon_H76 zenon_H4e zenon_H18c zenon_Hdf zenon_H20d zenon_H9c zenon_H110. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.34/30.44 apply (zenon_L848_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.34/30.44 apply (zenon_L864_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.34/30.44 apply (zenon_L548_); trivial. % 30.34/30.44 apply (zenon_L65_); trivial. % 30.34/30.44 (* end of lemma zenon_L1694_ *) % 30.34/30.44 assert (zenon_L1695_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.34/30.44 do 0 intro. intros zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H90 zenon_H102 zenon_H2a9 zenon_Hb1 zenon_H2d. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.34/30.44 apply (zenon_L174_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.34/30.44 apply (zenon_L1473_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.34/30.44 exact (zenon_H2a9 zenon_Hb6). % 30.34/30.44 apply (zenon_L107_); trivial. % 30.34/30.44 (* end of lemma zenon_L1695_ *) % 30.34/30.44 assert (zenon_L1696_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 30.34/30.44 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H37 zenon_Hf4 zenon_H110 zenon_H20d zenon_Hdf zenon_H18c zenon_H4e zenon_H16b zenon_H2b4 zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H90 zenon_H102 zenon_H2a9 zenon_H2d. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.34/30.44 apply (zenon_L27_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.34/30.44 apply (zenon_L513_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.34/30.44 apply (zenon_L1694_); trivial. % 30.34/30.44 apply (zenon_L1695_); trivial. % 30.34/30.44 (* end of lemma zenon_L1696_ *) % 30.34/30.44 assert (zenon_L1697_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.34/30.44 do 0 intro. intros zenon_H246 zenon_H20e zenon_H1bd zenon_Hf9 zenon_H10d zenon_H222 zenon_H225 zenon_H1dc zenon_H16a zenon_H4a zenon_H13b zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_H1a5 zenon_H101 zenon_H1d5 zenon_H108 zenon_H1fd zenon_H6f zenon_Hbd zenon_H20 zenon_H20d zenon_H2b4 zenon_Hb8 zenon_H1d8 zenon_H100 zenon_Had zenon_H2d zenon_H42 zenon_Hd1 zenon_H1ab zenon_H83 zenon_He4 zenon_Hd9 zenon_H174 zenon_H200 zenon_He1 zenon_H172 zenon_H4c zenon_H3c zenon_H56 zenon_H135 zenon_H208 zenon_H2bd zenon_H218 zenon_Ha4 zenon_H8d zenon_H159 zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H97 zenon_H92 zenon_Haa zenon_Hf6 zenon_H3f zenon_He7 zenon_H23b zenon_H15a zenon_H19e zenon_H2b1 zenon_Hfc zenon_H18c zenon_H4e zenon_H1b1 zenon_H173 zenon_Hc8 zenon_Hde zenon_Hcd zenon_H2c1 zenon_H2b0 zenon_H124 zenon_Hc0 zenon_H2b7 zenon_Hb5 zenon_H19a zenon_Hee zenon_H110 zenon_Hf4 zenon_H2a9. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.34/30.44 apply (zenon_L912_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.34/30.44 apply (zenon_L1446_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.44 apply (zenon_L148_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.44 apply (zenon_L4_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.44 apply (zenon_L1613_); trivial. % 30.34/30.44 apply (zenon_L1614_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.44 apply (zenon_L148_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.44 apply (zenon_L4_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.44 apply (zenon_L1624_); trivial. % 30.34/30.44 apply (zenon_L1454_); trivial. % 30.34/30.44 apply (zenon_L1635_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.34/30.44 apply (zenon_L136_); trivial. % 30.34/30.44 apply (zenon_L1448_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.34/30.44 apply (zenon_L1649_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.44 apply (zenon_L734_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.44 apply (zenon_L1676_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.44 apply (zenon_L1679_); trivial. % 30.34/30.44 apply (zenon_L1683_); trivial. % 30.34/30.44 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.34/30.45 apply (zenon_L1446_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_L232_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L4_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.45 apply (zenon_L149_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.45 apply (zenon_L18_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.45 apply (zenon_L1589_); trivial. % 30.34/30.45 apply (zenon_L1187_); trivial. % 30.34/30.45 apply (zenon_L1687_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.34/30.45 apply (zenon_L48_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.34/30.45 apply (zenon_L49_); trivial. % 30.34/30.45 apply (zenon_L1590_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_L232_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L4_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_L1688_); trivial. % 30.34/30.45 apply (zenon_L1687_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_L1689_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L4_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_L1688_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.45 apply (zenon_L1689_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.45 apply (zenon_L1684_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.45 apply (zenon_L1686_); trivial. % 30.34/30.45 apply (zenon_L1187_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.34/30.45 apply (zenon_L49_); trivial. % 30.34/30.45 apply (zenon_L1691_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_L232_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L4_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_L1692_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.45 apply (zenon_L538_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.45 apply (zenon_L1693_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.34/30.45 apply (zenon_L1693_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.34/30.45 apply (zenon_L1696_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.45 apply (zenon_L752_); trivial. % 30.34/30.45 apply (zenon_L859_); trivial. % 30.34/30.45 apply (zenon_L39_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_L538_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L4_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_L1644_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.45 apply (zenon_L538_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.45 apply (zenon_L1693_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.45 apply (zenon_L740_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.45 apply (zenon_L769_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.34/30.45 apply (zenon_L1642_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.34/30.45 apply (zenon_L1696_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.45 apply (zenon_L235_); trivial. % 30.34/30.45 apply (zenon_L859_); trivial. % 30.34/30.45 apply (zenon_L864_); trivial. % 30.34/30.45 apply (zenon_L39_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.34/30.45 apply (zenon_L49_); trivial. % 30.34/30.45 apply (zenon_L386_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.34/30.45 apply (zenon_L136_); trivial. % 30.34/30.45 apply (zenon_L1448_); trivial. % 30.34/30.45 apply (zenon_L853_); trivial. % 30.34/30.45 (* end of lemma zenon_L1697_ *) % 30.34/30.45 assert (zenon_L1698_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H90 zenon_Had zenon_H1ab zenon_H102 zenon_Hfc zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H2b0 zenon_H19a zenon_H185 zenon_H20 zenon_H2b1 zenon_H18c zenon_H4e zenon_H76. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.45 apply (zenon_L740_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.45 apply (zenon_L769_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.45 apply (zenon_L1477_); trivial. % 30.34/30.45 apply (zenon_L864_); trivial. % 30.34/30.45 (* end of lemma zenon_L1698_ *) % 30.34/30.45 assert (zenon_L1699_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H8d zenon_H117 zenon_Hd9 zenon_H159 zenon_H2b4 zenon_H16a zenon_H14e zenon_H4e zenon_H18c zenon_H2b1 zenon_H20 zenon_H185 zenon_H19a zenon_H2b0 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_Hfc zenon_H102 zenon_H1ab zenon_Had zenon_H48 zenon_Hdf zenon_H172 zenon_H6f zenon_H90. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.45 apply (zenon_L149_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.45 apply (zenon_L1482_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.45 apply (zenon_L1698_); trivial. % 30.34/30.45 apply (zenon_L39_); trivial. % 30.34/30.45 (* end of lemma zenon_L1699_ *) % 30.34/30.45 assert (zenon_L1700_ : ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H90 zenon_H6f zenon_H172 zenon_Had zenon_Hfc zenon_H2b0 zenon_H19a zenon_H18c zenon_H4e zenon_Hd9 zenon_H117 zenon_H8d zenon_H1ab zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H20 zenon_H2b4 zenon_H16a zenon_H14e zenon_H48 zenon_H6e zenon_H2b1 zenon_Hdf zenon_H20d zenon_H95 zenon_H113. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.34/30.45 apply (zenon_L1699_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.34/30.45 apply (zenon_L1478_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.34/30.45 apply (zenon_L548_); trivial. % 30.34/30.45 apply (zenon_L798_); trivial. % 30.34/30.45 (* end of lemma zenon_L1700_ *) % 30.34/30.45 assert (zenon_L1701_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H208 zenon_Hf6 zenon_Hf4 zenon_H1fd zenon_H113 zenon_H95 zenon_H20d zenon_Hdf zenon_H2b1 zenon_H6e zenon_H48 zenon_H16a zenon_H2b4 zenon_H20 zenon_H159 zenon_H1ab zenon_H8d zenon_Hd9 zenon_H4e zenon_H18c zenon_H19a zenon_H2b0 zenon_Had zenon_H172 zenon_H6f zenon_H90 zenon_H4c zenon_H14e zenon_He1 zenon_H2a9 zenon_Hcd zenon_Hde zenon_H135 zenon_H56 zenon_H102 zenon_Hfe zenon_Hfc zenon_H18f zenon_H13b zenon_H156 zenon_H4a. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.34/30.45 apply (zenon_L1654_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.34/30.45 apply (zenon_L49_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.34/30.45 apply (zenon_L212_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.34/30.45 apply (zenon_L1700_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.34/30.45 apply (zenon_L752_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.34/30.45 apply (zenon_L544_); trivial. % 30.34/30.45 exact (zenon_H2a9 zenon_Hb6). % 30.34/30.45 apply (zenon_L56_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.34/30.45 exact (zenon_H56 zenon_H25). % 30.34/30.45 apply (zenon_L1476_); trivial. % 30.34/30.45 (* end of lemma zenon_L1701_ *) % 30.34/30.45 assert (zenon_L1702_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H200 zenon_Hfc zenon_H56 zenon_H135 zenon_Hde zenon_Hcd zenon_H2a9 zenon_He1 zenon_H4c zenon_H90 zenon_H6f zenon_H172 zenon_Had zenon_H2b0 zenon_H19a zenon_H18c zenon_Hd9 zenon_H8d zenon_H20d zenon_H95 zenon_H113 zenon_H1fd zenon_Hf4 zenon_Hf6 zenon_H208 zenon_H1ab zenon_H102 zenon_H19e zenon_H18f zenon_H13b zenon_H4a zenon_H4e zenon_Hd1 zenon_H2b4 zenon_H20 zenon_H16a zenon_H159 zenon_H14e zenon_H2b1 zenon_H20e zenon_Hfe zenon_H156 zenon_H48 zenon_H6e. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.34/30.45 apply (zenon_L1701_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.34/30.45 apply (zenon_L1481_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.34/30.45 apply (zenon_L350_); trivial. % 30.34/30.45 apply (zenon_L737_); trivial. % 30.34/30.45 (* end of lemma zenon_L1702_ *) % 30.34/30.45 assert (zenon_L1703_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H84 zenon_H17d zenon_H64 zenon_Hdc zenon_H20e zenon_Hd1 zenon_H4e zenon_H19e zenon_H208 zenon_Hf6 zenon_Hf4 zenon_H1fd zenon_H113 zenon_H20d zenon_H8d zenon_Hd9 zenon_H18c zenon_H19a zenon_H2b0 zenon_Had zenon_H172 zenon_H6f zenon_H90 zenon_H4c zenon_He1 zenon_H2a9 zenon_Hcd zenon_Hde zenon_H135 zenon_H56 zenon_Hfc zenon_H200 zenon_H246 zenon_H1bd zenon_Hf9 zenon_H10d zenon_H222 zenon_H225 zenon_H1dc zenon_H35 zenon_H1a5 zenon_H101 zenon_H1d5 zenon_H108 zenon_Hbd zenon_Hb8 zenon_H1d8 zenon_H100 zenon_H2d zenon_H42 zenon_H83 zenon_He4 zenon_H174 zenon_H3c zenon_H2bd zenon_H218 zenon_Ha4 zenon_H16f zenon_H97 zenon_H92 zenon_Haa zenon_H3f zenon_He7 zenon_H23b zenon_H15a zenon_H1b1 zenon_H173 zenon_Hc8 zenon_H2c1 zenon_H124 zenon_Hc0 zenon_H2b7 zenon_Hb5 zenon_Hee zenon_H110 zenon_H296 zenon_H2b1 zenon_H6e zenon_H48 zenon_H14e zenon_H16a zenon_H2b4 zenon_H20 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H1ab. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.45 apply (zenon_L1673_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.45 apply (zenon_L769_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.34/30.45 apply (zenon_L1697_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.34/30.45 apply (zenon_L59_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.34/30.45 apply (zenon_L1481_); trivial. % 30.34/30.45 apply (zenon_L1702_); trivial. % 30.34/30.45 apply (zenon_L1478_); trivial. % 30.34/30.45 (* end of lemma zenon_L1703_ *) % 30.34/30.45 assert (zenon_L1704_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H101 zenon_H1d5 zenon_H35 zenon_H3c zenon_Hdc zenon_H2b1 zenon_H2b0 zenon_H1ab zenon_H20 zenon_Hd1 zenon_H19e zenon_Hc0 zenon_H23b zenon_H1dc zenon_Hbd zenon_Hee zenon_H200 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H69 zenon_H1b1 zenon_Hc8 zenon_He7 zenon_Haa zenon_Ha4 zenon_H218 zenon_H2bd zenon_H208 zenon_H172 zenon_Hfc zenon_H83 zenon_H42 zenon_H225 zenon_H222 zenon_H10d zenon_Hf9 zenon_H1bd zenon_H108 zenon_H296 zenon_Hf6 zenon_H173 zenon_H1fd zenon_H1a5 zenon_H4c zenon_H20e zenon_H135 zenon_H56 zenon_H95 zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H18c zenon_He4 zenon_Hde zenon_Hcd zenon_H97 zenon_H16f zenon_H48 zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_He1 zenon_H3f zenon_H64 zenon_H174 zenon_Hf4 zenon_H17d zenon_H84 zenon_H92 zenon_H2a9 zenon_H14e zenon_H4e. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.34/30.45 apply (zenon_L1673_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.34/30.45 apply (zenon_L513_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.45 apply (zenon_L235_); trivial. % 30.34/30.45 apply (zenon_L1651_); trivial. % 30.34/30.45 (* end of lemma zenon_L1704_ *) % 30.34/30.45 assert (zenon_L1705_ : ((op (e3) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H90 zenon_H2c zenon_H101 zenon_H1d5 zenon_H35 zenon_H3c zenon_Hdc zenon_H2b1 zenon_H2b0 zenon_H1ab zenon_H20 zenon_Hd1 zenon_H19e zenon_Hc0 zenon_H23b zenon_H1dc zenon_Hbd zenon_Hee zenon_H200 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H69 zenon_H1b1 zenon_Hc8 zenon_He7 zenon_Haa zenon_Ha4 zenon_H218 zenon_H2bd zenon_H208 zenon_H172 zenon_Hfc zenon_H83 zenon_H42 zenon_H225 zenon_H222 zenon_H10d zenon_Hf9 zenon_H1bd zenon_H108 zenon_H296 zenon_Hf6 zenon_H173 zenon_H1fd zenon_H1a5 zenon_H4c zenon_H20e zenon_H135 zenon_H56 zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H18c zenon_He4 zenon_Hde zenon_Hcd zenon_H97 zenon_H16f zenon_H48 zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_He1 zenon_H3f zenon_H64 zenon_H174 zenon_Hf4 zenon_H17d zenon_H84 zenon_H92 zenon_H2a9 zenon_H14e zenon_H4e. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.34/30.45 apply (zenon_L1649_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.34/30.45 apply (zenon_L769_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.34/30.45 apply (zenon_L1659_); trivial. % 30.34/30.45 apply (zenon_L1704_); trivial. % 30.34/30.45 (* end of lemma zenon_L1705_ *) % 30.34/30.45 assert (zenon_L1706_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H2b1 zenon_H20 zenon_H185 zenon_H35 zenon_H2c zenon_H4e zenon_Hf4 zenon_H142 zenon_H1ab. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.34/30.45 apply (zenon_L117_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.34/30.45 apply (zenon_L730_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.34/30.45 apply (zenon_L944_); trivial. % 30.34/30.45 exact (zenon_H1ab zenon_H112). % 30.34/30.45 (* end of lemma zenon_L1706_ *) % 30.34/30.45 assert (zenon_L1707_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((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). % 30.34/30.45 do 0 intro. intros zenon_H200 zenon_H69 zenon_H18c zenon_H102 zenon_H19e zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H6e zenon_Hd1 zenon_H2b4 zenon_H16a zenon_H159 zenon_H14e zenon_H48 zenon_H1ab zenon_Hf4 zenon_H4e zenon_H2c zenon_H35 zenon_H20 zenon_H2b1 zenon_H218 zenon_H185. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.34/30.45 apply (zenon_L740_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.34/30.45 apply (zenon_L1481_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.34/30.45 apply (zenon_L1706_); trivial. % 30.34/30.45 apply (zenon_L1088_); trivial. % 30.34/30.45 (* end of lemma zenon_L1707_ *) % 30.34/30.45 assert (zenon_L1708_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H102 zenon_H95 zenon_H100 zenon_H18f zenon_H142 zenon_H19e zenon_H3d. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.34/30.45 apply (zenon_L1497_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.34/30.45 exact (zenon_H18f zenon_Hd2). % 30.34/30.45 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.34/30.45 apply (zenon_L79_); trivial. % 30.34/30.45 apply (zenon_L131_); trivial. % 30.34/30.45 (* end of lemma zenon_L1708_ *) % 30.34/30.45 assert (zenon_L1709_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H18c zenon_H35 zenon_H1e zenon_Hfc zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.45 apply (zenon_L740_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.45 apply (zenon_L42_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.45 apply (zenon_L1575_); trivial. % 30.34/30.45 apply (zenon_L1463_); trivial. % 30.34/30.45 (* end of lemma zenon_L1709_ *) % 30.34/30.45 assert (zenon_L1710_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H246 zenon_H16a zenon_H4a zenon_H1a5 zenon_H92 zenon_H1dc zenon_H97 zenon_H16f zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H4e zenon_Hcd zenon_H3f zenon_H8d zenon_Ha4 zenon_H218 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H4c zenon_He1 zenon_H200 zenon_H108 zenon_H1fd zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H174 zenon_H1b1 zenon_H173 zenon_He4 zenon_H19e zenon_Hf9 zenon_Hbd zenon_Hd9 zenon_H15a zenon_Had zenon_Hc0 zenon_H100 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_Hfc zenon_H1e zenon_H35 zenon_H18c zenon_H48 zenon_H172 zenon_H23b zenon_H20 zenon_H40 zenon_H6f zenon_H19a zenon_Hee zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hf4 zenon_H2a9. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.34/30.45 apply (zenon_L912_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.34/30.45 apply (zenon_L1634_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.34/30.45 apply (zenon_L136_); trivial. % 30.34/30.45 apply (zenon_L1448_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.34/30.45 apply (zenon_L1601_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.34/30.45 apply (zenon_L1709_); trivial. % 30.34/30.45 apply (zenon_L968_); trivial. % 30.34/30.45 (* end of lemma zenon_L1710_ *) % 30.34/30.45 assert (zenon_L1711_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H174 zenon_H3f zenon_H10e zenon_H8d zenon_He1 zenon_H73 zenon_H68 zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_L232_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L746_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_L87_); trivial. % 30.34/30.45 apply (zenon_L1587_); trivial. % 30.34/30.45 (* end of lemma zenon_L1711_ *) % 30.34/30.45 assert (zenon_L1712_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H174 zenon_H10e zenon_H8d zenon_He2 zenon_Hee zenon_H3f zenon_H1f zenon_Hcd zenon_H23b zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_L387_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L746_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_L87_); trivial. % 30.34/30.45 apply (zenon_L1597_); trivial. % 30.34/30.45 (* end of lemma zenon_L1712_ *) % 30.34/30.45 assert (zenon_L1713_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H1e6 zenon_Hdf zenon_H20d zenon_H112 zenon_Hf6 zenon_H108 zenon_Hcc zenon_H156 zenon_H4e zenon_H16c. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.34/30.45 apply (zenon_L548_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.34/30.45 apply (zenon_L187_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.34/30.45 apply (zenon_L62_); trivial. % 30.34/30.45 apply (zenon_L779_); trivial. % 30.34/30.45 (* end of lemma zenon_L1713_ *) % 30.34/30.45 assert (zenon_L1714_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H23b zenon_Hc3 zenon_H4a zenon_Had zenon_H40 zenon_H6f zenon_H19a zenon_Hee zenon_H1e6 zenon_Hdf zenon_H20d zenon_Hf6 zenon_H108 zenon_Hcc zenon_H156 zenon_H4e zenon_H16c. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.34/30.45 apply (zenon_L769_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.34/30.45 apply (zenon_L80_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.34/30.45 apply (zenon_L337_); trivial. % 30.34/30.45 apply (zenon_L1713_); trivial. % 30.34/30.45 (* end of lemma zenon_L1714_ *) % 30.34/30.45 assert (zenon_L1715_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H135 zenon_He2 zenon_H1d8 zenon_Hd5 zenon_Hcd zenon_H16c zenon_H4e zenon_H156 zenon_H108 zenon_H20d zenon_Hdf zenon_H1e6 zenon_Hee zenon_H19a zenon_H6f zenon_H40 zenon_Had zenon_H4a zenon_Hc3 zenon_H23b zenon_Hf4 zenon_Hf6. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.34/30.45 apply (zenon_L307_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.34/30.45 apply (zenon_L212_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.34/30.45 apply (zenon_L1714_); trivial. % 30.34/30.45 apply (zenon_L56_); trivial. % 30.34/30.45 (* end of lemma zenon_L1715_ *) % 30.34/30.45 assert (zenon_L1716_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H102 zenon_H1ba zenon_H19e zenon_H18f zenon_Hed zenon_Hfc zenon_H4a zenon_H33 zenon_H16a. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.34/30.45 apply (zenon_L347_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.34/30.45 exact (zenon_H18f zenon_Hd2). % 30.34/30.45 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.34/30.45 apply (zenon_L58_); trivial. % 30.34/30.45 apply (zenon_L839_); trivial. % 30.34/30.45 (* end of lemma zenon_L1716_ *) % 30.34/30.45 assert (zenon_L1717_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H1d5 zenon_Hf6 zenon_Hf4 zenon_Hde zenon_Hcd zenon_Hd5 zenon_He1 zenon_H135 zenon_H222 zenon_H40 zenon_H2d zenon_H142 zenon_H156 zenon_H4e zenon_H16c. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.34/30.45 apply (zenon_L1577_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.34/30.45 apply (zenon_L775_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.34/30.45 apply (zenon_L175_); trivial. % 30.34/30.45 apply (zenon_L779_); trivial. % 30.34/30.45 (* end of lemma zenon_L1717_ *) % 30.34/30.45 assert (zenon_L1718_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H102 zenon_H1ba zenon_H19e zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.34/30.45 apply (zenon_L347_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.34/30.45 exact (zenon_H18f zenon_Hd2). % 30.34/30.45 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.34/30.45 exact (zenon_H13b zenon_Hfd). % 30.34/30.45 apply (zenon_L150_); trivial. % 30.34/30.45 (* end of lemma zenon_L1718_ *) % 30.34/30.45 assert (zenon_L1719_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H174 zenon_H19e zenon_H124 zenon_H2a9 zenon_H108 zenon_H4c zenon_Hf4 zenon_H1a5 zenon_H1fd zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H200 zenon_H23b zenon_Had zenon_Hee zenon_H1e6 zenon_H20d zenon_H33 zenon_H4a zenon_Hfc zenon_Hf6 zenon_H135 zenon_He2 zenon_H1d8 zenon_Hcd zenon_He1 zenon_Hde zenon_H68 zenon_H173 zenon_H35 zenon_H296 zenon_H3f zenon_H10e zenon_H8d zenon_H15a zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.34/30.45 apply (zenon_L1448_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.34/30.45 apply (zenon_L387_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.34/30.45 exact (zenon_H18f zenon_Hd2). % 30.34/30.45 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.34/30.45 apply (zenon_L48_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.34/30.45 exact (zenon_H13b zenon_Hfd). % 30.34/30.45 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.34/30.45 apply (zenon_L241_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.34/30.45 apply (zenon_L364_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.45 apply (zenon_L235_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.34/30.45 apply (zenon_L1715_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.34/30.45 apply (zenon_L1716_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.34/30.45 apply (zenon_L1717_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.34/30.45 apply (zenon_L307_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.34/30.45 apply (zenon_L212_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.34/30.45 apply (zenon_L961_); trivial. % 30.34/30.45 apply (zenon_L294_); trivial. % 30.34/30.45 apply (zenon_L857_); trivial. % 30.34/30.45 apply (zenon_L80_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.34/30.45 apply (zenon_L1718_); trivial. % 30.34/30.45 apply (zenon_L766_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L746_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_L87_); trivial. % 30.34/30.45 apply (zenon_L1472_); trivial. % 30.34/30.45 (* end of lemma zenon_L1719_ *) % 30.34/30.45 assert (zenon_L1720_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 30.34/30.45 do 0 intro. intros zenon_H208 zenon_Hc3 zenon_H4a zenon_H18c zenon_H16c zenon_H4e zenon_H156 zenon_H2d zenon_H40 zenon_H222 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H1d5 zenon_H56 zenon_H142 zenon_Hf4. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.34/30.45 apply (zenon_L763_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.34/30.45 apply (zenon_L1717_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.34/30.45 exact (zenon_H56 zenon_H25). % 30.34/30.45 apply (zenon_L944_); trivial. % 30.34/30.45 (* end of lemma zenon_L1720_ *) % 30.34/30.45 assert (zenon_L1721_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H208 zenon_H18c zenon_Hf4 zenon_Hc3 zenon_H1e6 zenon_Hdf zenon_H20d zenon_H108 zenon_H156 zenon_H4e zenon_H16c zenon_Hcd zenon_H76 zenon_He1 zenon_H135 zenon_H56 zenon_H23b zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H40 zenon_H6f zenon_H19a zenon_Hee zenon_Hf6. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.34/30.45 apply (zenon_L763_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.34/30.45 apply (zenon_L273_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.34/30.45 apply (zenon_L212_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.34/30.45 apply (zenon_L1714_); trivial. % 30.34/30.45 apply (zenon_L56_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.34/30.45 exact (zenon_H56 zenon_H25). % 30.34/30.45 apply (zenon_L1608_); trivial. % 30.34/30.45 (* end of lemma zenon_L1721_ *) % 30.34/30.45 assert (zenon_L1722_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H174 zenon_H3f zenon_H172 zenon_Hf6 zenon_Hee zenon_H4a zenon_Had zenon_H23b zenon_H56 zenon_H135 zenon_Hcd zenon_H108 zenon_H20d zenon_Hdf zenon_H1e6 zenon_Hf4 zenon_H208 zenon_H1a5 zenon_H1b1 zenon_H4c zenon_H15a zenon_H173 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_Hd9 zenon_H8d zenon_He1 zenon_H73 zenon_H68 zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_L232_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L746_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.45 apply (zenon_L149_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.45 apply (zenon_L18_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.45 apply (zenon_L740_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.34/30.45 apply (zenon_L18_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.34/30.45 apply (zenon_L364_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.45 apply (zenon_L752_); trivial. % 30.34/30.45 apply (zenon_L1721_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.45 apply (zenon_L1457_); trivial. % 30.34/30.45 apply (zenon_L1463_); trivial. % 30.34/30.45 apply (zenon_L862_); trivial. % 30.34/30.45 apply (zenon_L1587_); trivial. % 30.34/30.45 (* end of lemma zenon_L1722_ *) % 30.34/30.45 assert (zenon_L1723_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.34/30.45 do 0 intro. intros zenon_Hb8 zenon_He2 zenon_He1 zenon_H98 zenon_H6f zenon_H9c zenon_H2d zenon_H14e zenon_H4e zenon_H16c. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.34/30.45 apply (zenon_L50_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.34/30.45 apply (zenon_L80_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.34/30.45 apply (zenon_L304_); trivial. % 30.34/30.45 apply (zenon_L875_); trivial. % 30.34/30.45 (* end of lemma zenon_L1723_ *) % 30.34/30.45 assert (zenon_L1724_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H208 zenon_H18c zenon_Hf4 zenon_Hc3 zenon_H4a zenon_Had zenon_H14e zenon_H2d zenon_H9c zenon_H6f zenon_He1 zenon_Hb8 zenon_H1e6 zenon_Hdf zenon_H20d zenon_H108 zenon_H156 zenon_H4e zenon_H16c zenon_H76 zenon_H135 zenon_H56 zenon_H23b zenon_Hcd zenon_He2 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_Hf6. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.34/30.45 apply (zenon_L763_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.34/30.45 apply (zenon_L273_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.34/30.45 apply (zenon_L212_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.34/30.45 apply (zenon_L769_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.34/30.45 apply (zenon_L1723_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.34/30.45 apply (zenon_L337_); trivial. % 30.34/30.45 apply (zenon_L1713_); trivial. % 30.34/30.45 apply (zenon_L56_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.34/30.45 exact (zenon_H56 zenon_H25). % 30.34/30.45 apply (zenon_L1273_); trivial. % 30.34/30.45 (* end of lemma zenon_L1724_ *) % 30.34/30.45 assert (zenon_L1725_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H174 zenon_H172 zenon_H1a5 zenon_H68 zenon_H14b zenon_H1b1 zenon_Hde zenon_H208 zenon_Hf4 zenon_H4a zenon_He1 zenon_Hb8 zenon_H1e6 zenon_Hdf zenon_H20d zenon_H108 zenon_H135 zenon_H56 zenon_H23b zenon_Hcd zenon_H1f zenon_H3f zenon_Hee zenon_Hf6 zenon_H173 zenon_He2 zenon_H4c zenon_Had zenon_Hd9 zenon_H8d zenon_H15a zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_L387_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L746_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.34/30.45 apply (zenon_L149_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.34/30.45 apply (zenon_L18_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.45 apply (zenon_L740_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.34/30.45 apply (zenon_L48_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.34/30.45 exact (zenon_H13b zenon_Hfd). % 30.34/30.45 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.34/30.45 apply (zenon_L18_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.34/30.45 apply (zenon_L364_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.45 apply (zenon_L235_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.34/30.45 apply (zenon_L87_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.34/30.45 apply (zenon_L1177_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.34/30.45 apply (zenon_L1578_); trivial. % 30.34/30.45 apply (zenon_L1724_); trivial. % 30.34/30.45 apply (zenon_L828_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.45 apply (zenon_L742_); trivial. % 30.34/30.45 apply (zenon_L864_); trivial. % 30.34/30.45 apply (zenon_L862_); trivial. % 30.34/30.45 apply (zenon_L1472_); trivial. % 30.34/30.45 (* end of lemma zenon_L1725_ *) % 30.34/30.45 assert (zenon_L1726_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H4a zenon_H33 zenon_H20 zenon_H2b4 zenon_H100 zenon_H40 zenon_H6f zenon_H19a zenon_H4e zenon_H16b zenon_H16a. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.34/30.45 apply (zenon_L1460_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.34/30.45 apply (zenon_L150_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.45 apply (zenon_L235_); trivial. % 30.34/30.45 apply (zenon_L859_); trivial. % 30.34/30.45 (* end of lemma zenon_L1726_ *) % 30.34/30.45 assert (zenon_L1727_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_He4 zenon_H15a zenon_Had zenon_H4c zenon_H124 zenon_H97 zenon_H18c zenon_H8d zenon_Hd9 zenon_H173 zenon_H56 zenon_Hb8 zenon_He1 zenon_H208 zenon_Hde zenon_H1b1 zenon_H14b zenon_H68 zenon_H1a5 zenon_H172 zenon_H174 zenon_Hf6 zenon_Hf4 zenon_H23b zenon_Hee zenon_H1e6 zenon_Hdf zenon_H20d zenon_H108 zenon_Hcd zenon_H1d8 zenon_H135 zenon_H3f zenon_H2d zenon_H10e zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H4a zenon_H33 zenon_H20 zenon_H2b4 zenon_H100 zenon_H40 zenon_H6f zenon_H19a zenon_H4e zenon_H16a. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.34/30.45 apply (zenon_L1722_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.34/30.45 apply (zenon_L48_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.34/30.45 apply (zenon_L49_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.34/30.45 apply (zenon_L740_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.34/30.45 apply (zenon_L1725_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.34/30.45 exact (zenon_H18f zenon_Hd2). % 30.34/30.45 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.34/30.45 apply (zenon_L241_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.34/30.45 apply (zenon_L364_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.45 apply (zenon_L752_); trivial. % 30.34/30.45 apply (zenon_L1715_); trivial. % 30.34/30.45 apply (zenon_L80_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.34/30.45 apply (zenon_L742_); trivial. % 30.34/30.45 apply (zenon_L744_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L746_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_L87_); trivial. % 30.34/30.45 apply (zenon_L1726_); trivial. % 30.34/30.45 (* end of lemma zenon_L1727_ *) % 30.34/30.45 assert (zenon_L1728_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.34/30.45 do 0 intro. intros zenon_Hbd zenon_H69 zenon_H48 zenon_Had zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H1e1. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.34/30.45 apply (zenon_L749_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.34/30.45 apply (zenon_L1497_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.34/30.45 apply (zenon_L63_); trivial. % 30.34/30.45 apply (zenon_L690_); trivial. % 30.34/30.45 (* end of lemma zenon_L1728_ *) % 30.34/30.45 assert (zenon_L1729_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.34/30.45 do 0 intro. intros zenon_H84 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H4e zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_H10e zenon_H3f zenon_H296 zenon_H35 zenon_H173 zenon_Hde zenon_He1 zenon_Hcd zenon_H1d8 zenon_H135 zenon_Hf6 zenon_Hfc zenon_H20d zenon_H1e6 zenon_Hee zenon_H23b zenon_H200 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_H20e zenon_H1fd zenon_H1a5 zenon_Hf4 zenon_H4c zenon_H108 zenon_H2a9 zenon_H124 zenon_H19e zenon_H174 zenon_H172 zenon_H14b zenon_H1b1 zenon_Hb8 zenon_He4 zenon_H56 zenon_H208 zenon_Hf9 zenon_Hbd zenon_H69 zenon_H10d zenon_Hc0 zenon_H3c zenon_H2bd zenon_H218 zenon_Ha4 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1dc zenon_H92 zenon_Hd9 zenon_H20 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.34/30.45 exact (zenon_H84 zenon_H88). % 30.34/30.45 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.34/30.45 exact (zenon_H84 zenon_H88). % 30.34/30.45 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.34/30.45 apply (zenon_L1711_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.34/30.45 apply (zenon_L48_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.34/30.45 apply (zenon_L1595_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.34/30.45 apply (zenon_L142_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.34/30.45 exact (zenon_H13b zenon_Hfd). % 30.34/30.45 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.34/30.45 apply (zenon_L241_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.34/30.45 apply (zenon_L364_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.34/30.45 apply (zenon_L752_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.34/30.45 apply (zenon_L49_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.34/30.45 apply (zenon_L1718_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.34/30.45 apply (zenon_L1720_); trivial. % 30.34/30.45 apply (zenon_L1594_); trivial. % 30.34/30.45 apply (zenon_L857_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.34/30.45 apply (zenon_L1718_); trivial. % 30.34/30.45 apply (zenon_L766_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.34/30.45 apply (zenon_L746_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.34/30.45 apply (zenon_L87_); trivial. % 30.34/30.45 apply (zenon_L1472_); trivial. % 30.34/30.45 apply (zenon_L1712_); trivial. % 30.34/30.45 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.34/30.45 apply (zenon_L1450_); trivial. % 30.36/30.46 apply (zenon_L1473_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.36/30.46 apply (zenon_L136_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.46 apply (zenon_L1711_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.46 apply (zenon_L48_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.46 apply (zenon_L1601_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.36/30.46 apply (zenon_L48_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.36/30.46 exact (zenon_H13b zenon_Hfd). % 30.36/30.46 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.46 apply (zenon_L1460_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.46 apply (zenon_L150_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.46 apply (zenon_L235_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.46 apply (zenon_L1727_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.46 apply (zenon_L1716_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.46 apply (zenon_L1720_); trivial. % 30.36/30.46 apply (zenon_L1594_); trivial. % 30.36/30.46 apply (zenon_L857_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.36/30.46 exact (zenon_H18f zenon_Hd2). % 30.36/30.46 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.36/30.46 apply (zenon_L142_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.36/30.46 exact (zenon_H13b zenon_Hfd). % 30.36/30.46 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.46 apply (zenon_L241_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.46 apply (zenon_L364_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.46 apply (zenon_L752_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.46 apply (zenon_L740_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.46 apply (zenon_L1716_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.46 apply (zenon_L1717_); trivial. % 30.36/30.46 apply (zenon_L1728_); trivial. % 30.36/30.46 apply (zenon_L857_); trivial. % 30.36/30.46 apply (zenon_L80_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.46 apply (zenon_L1718_); trivial. % 30.36/30.46 apply (zenon_L766_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.36/30.46 apply (zenon_L746_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.36/30.46 apply (zenon_L958_); trivial. % 30.36/30.46 apply (zenon_L1726_); trivial. % 30.36/30.46 apply (zenon_L1719_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.36/30.46 apply (zenon_L1450_); trivial. % 30.36/30.46 apply (zenon_L1473_); trivial. % 30.36/30.46 (* end of lemma zenon_L1729_ *) % 30.36/30.46 assert (zenon_L1730_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.36/30.46 do 0 intro. intros zenon_He4 zenon_H174 zenon_H172 zenon_H1a5 zenon_H68 zenon_H14b zenon_H1b1 zenon_Hde zenon_H208 zenon_Hf4 zenon_H4a zenon_He1 zenon_Hb8 zenon_H1e6 zenon_Hdf zenon_H20d zenon_H108 zenon_H135 zenon_H56 zenon_H23b zenon_Hcd zenon_H1f zenon_H3f zenon_Hee zenon_Hf6 zenon_H173 zenon_H4c zenon_Had zenon_Hd9 zenon_H8d zenon_H15a zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H16a zenon_H4e zenon_H19a zenon_H6f zenon_H100 zenon_H2b4 zenon_H2d zenon_H18c zenon_H156 zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_H97. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.46 apply (zenon_L1722_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.46 apply (zenon_L48_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.46 apply (zenon_L49_); trivial. % 30.36/30.46 apply (zenon_L1725_); trivial. % 30.36/30.46 (* end of lemma zenon_L1730_ *) % 30.36/30.46 assert (zenon_L1731_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.36/30.46 do 0 intro. intros zenon_H92 zenon_H84 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H4e zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_H4c zenon_H173 zenon_Hf6 zenon_Hee zenon_H3f zenon_H1f zenon_Hcd zenon_H23b zenon_H56 zenon_H135 zenon_H108 zenon_H20d zenon_Hdf zenon_H1e6 zenon_Hb8 zenon_He1 zenon_Hf4 zenon_H208 zenon_Hde zenon_H1b1 zenon_H14b zenon_H1a5 zenon_H172 zenon_H174 zenon_He4 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H40 zenon_H100. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.36/30.46 apply (zenon_L1730_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.36/30.46 apply (zenon_L1450_); trivial. % 30.36/30.46 apply (zenon_L1473_); trivial. % 30.36/30.46 (* end of lemma zenon_L1731_ *) % 30.36/30.46 assert (zenon_L1732_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.36/30.46 do 0 intro. intros zenon_H16f zenon_H68 zenon_H2d zenon_H4c zenon_H14e zenon_H200 zenon_Hee zenon_H19a zenon_H6f zenon_Had zenon_H23b zenon_H4e zenon_H156 zenon_H108 zenon_H20d zenon_H1e6 zenon_Hc3 zenon_H19e zenon_Hf4 zenon_H56 zenon_H135 zenon_He1 zenon_H76 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H102 zenon_H4a zenon_H18c zenon_H18f zenon_H13b zenon_H40 zenon_H100 zenon_H208 zenon_H218 zenon_H185. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.46 apply (zenon_L18_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.46 apply (zenon_L364_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.46 apply (zenon_L752_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.46 apply (zenon_L1721_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.46 apply (zenon_L1718_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.46 apply (zenon_L1578_); trivial. % 30.36/30.46 apply (zenon_L1088_); trivial. % 30.36/30.46 (* end of lemma zenon_L1732_ *) % 30.36/30.46 assert (zenon_L1733_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.36/30.46 do 0 intro. intros zenon_H296 zenon_H16a zenon_Ha4 zenon_H35 zenon_H2bd zenon_H3c zenon_H172 zenon_H48 zenon_Hfc zenon_H69 zenon_H1dc zenon_H3f zenon_H20 zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H2a9 zenon_Hbd zenon_H185 zenon_H218 zenon_H208 zenon_H18c zenon_H4a zenon_Hf6 zenon_Hde zenon_Hcd zenon_H76 zenon_He1 zenon_H135 zenon_H56 zenon_Hf4 zenon_H1e6 zenon_H20d zenon_H108 zenon_H156 zenon_H4e zenon_H23b zenon_Had zenon_H6f zenon_H19a zenon_Hee zenon_H200 zenon_H14e zenon_H4c zenon_H68 zenon_H16f zenon_H100 zenon_H13b zenon_H18f zenon_H19e zenon_H102 zenon_H2d zenon_H40. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.46 apply (zenon_L1581_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.46 apply (zenon_L1732_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.46 apply (zenon_L1718_); trivial. % 30.36/30.46 apply (zenon_L766_); trivial. % 30.36/30.46 (* end of lemma zenon_L1733_ *) % 30.36/30.46 assert (zenon_L1734_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.36/30.46 do 0 intro. intros zenon_H8d zenon_H117 zenon_Hd9 zenon_H2d zenon_H102 zenon_H19e zenon_H18f zenon_H13b zenon_H100 zenon_H16f zenon_H68 zenon_H4c zenon_H14e zenon_H200 zenon_Hee zenon_H19a zenon_H6f zenon_Had zenon_H23b zenon_H4e zenon_H156 zenon_H108 zenon_H20d zenon_H1e6 zenon_Hf4 zenon_H56 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_Hf6 zenon_H4a zenon_H18c zenon_H208 zenon_H218 zenon_H185 zenon_Hbd zenon_H2a9 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H20 zenon_H3f zenon_H1dc zenon_H69 zenon_Hfc zenon_H48 zenon_H172 zenon_H3c zenon_H2bd zenon_H35 zenon_Ha4 zenon_H16a zenon_H296 zenon_H40 zenon_H97. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.46 apply (zenon_L149_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.46 apply (zenon_L18_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.46 apply (zenon_L1733_); trivial. % 30.36/30.46 apply (zenon_L862_); trivial. % 30.36/30.46 (* end of lemma zenon_L1734_ *) % 30.36/30.46 assert (zenon_L1735_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.36/30.46 do 0 intro. intros zenon_H301 zenon_H17d zenon_H1d8 zenon_H124 zenon_H10d zenon_H246 zenon_H19e zenon_H200 zenon_H218 zenon_Hbd zenon_H1dc zenon_Hfc zenon_H3c zenon_H2bd zenon_H35 zenon_Ha4 zenon_H296 zenon_H1d5 zenon_H222 zenon_Hf9 zenon_Hc8 zenon_H20e zenon_H1fd zenon_H1a5 zenon_H92 zenon_H84 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H4e zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_H4c zenon_H173 zenon_Hf6 zenon_H3f zenon_Hcd zenon_H56 zenon_H135 zenon_H108 zenon_H20d zenon_H1e6 zenon_Hb8 zenon_He1 zenon_H208 zenon_Hde zenon_H1b1 zenon_H14b zenon_H172 zenon_H174 zenon_He4 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H100 zenon_Hc0 zenon_H23b zenon_H20 zenon_H40 zenon_H6f zenon_H19a zenon_Hee zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hf4 zenon_H2a9. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.36/30.46 apply (zenon_L1650_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.36/30.46 apply (zenon_L1710_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.46 apply (zenon_L1711_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.46 apply (zenon_L48_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.46 apply (zenon_L1633_); trivial. % 30.36/30.46 apply (zenon_L1712_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.36/30.46 apply (zenon_L1450_); trivial. % 30.36/30.46 apply (zenon_L1473_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.36/30.46 apply (zenon_L136_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.46 apply (zenon_L1711_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.46 apply (zenon_L48_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.46 apply (zenon_L1633_); trivial. % 30.36/30.46 apply (zenon_L1719_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.36/30.46 apply (zenon_L1450_); trivial. % 30.36/30.46 apply (zenon_L1473_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.36/30.46 apply (zenon_L1729_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.36/30.46 apply (zenon_L1731_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.36/30.46 apply (zenon_L136_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.36/30.46 apply (zenon_L1727_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.36/30.46 apply (zenon_L1450_); trivial. % 30.36/30.46 apply (zenon_L1473_); trivial. % 30.36/30.46 apply (zenon_L853_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.46 apply (zenon_L1209_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.46 apply (zenon_L48_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.46 apply (zenon_L1633_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.36/30.46 apply (zenon_L387_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.36/30.46 apply (zenon_L746_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.46 apply (zenon_L149_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.46 apply (zenon_L18_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.46 apply (zenon_L1733_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.46 apply (zenon_L1732_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.46 apply (zenon_L742_); trivial. % 30.36/30.46 apply (zenon_L864_); trivial. % 30.36/30.46 apply (zenon_L862_); trivial. % 30.36/30.46 apply (zenon_L848_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.36/30.46 apply (zenon_L1450_); trivial. % 30.36/30.46 apply (zenon_L1473_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.36/30.46 apply (zenon_L136_); trivial. % 30.36/30.46 apply (zenon_L117_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.36/30.46 apply (zenon_L232_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.36/30.46 apply (zenon_L746_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.36/30.46 apply (zenon_L1734_); trivial. % 30.36/30.46 apply (zenon_L1587_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.46 apply (zenon_L48_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.46 apply (zenon_L1595_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.46 apply (zenon_L241_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.46 apply (zenon_L364_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.46 apply (zenon_L235_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.46 apply (zenon_L1730_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.46 apply (zenon_L1718_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.46 apply (zenon_L1720_); trivial. % 30.36/30.46 apply (zenon_L1088_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.46 apply (zenon_L1718_); trivial. % 30.36/30.46 apply (zenon_L766_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.36/30.46 apply (zenon_L746_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.36/30.46 apply (zenon_L958_); trivial. % 30.36/30.46 apply (zenon_L1472_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.36/30.46 apply (zenon_L387_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.36/30.46 apply (zenon_L746_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.36/30.46 apply (zenon_L1734_); trivial. % 30.36/30.46 apply (zenon_L848_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.36/30.46 apply (zenon_L1450_); trivial. % 30.36/30.46 apply (zenon_L1473_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.36/30.46 apply (zenon_L136_); trivial. % 30.36/30.46 apply (zenon_L117_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.36/30.46 exact (zenon_H84 zenon_H88). % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.36/30.46 apply (zenon_L1731_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.36/30.46 apply (zenon_L136_); trivial. % 30.36/30.46 apply (zenon_L117_); trivial. % 30.36/30.46 apply (zenon_L968_); trivial. % 30.36/30.46 (* end of lemma zenon_L1735_ *) % 30.36/30.46 assert (zenon_L1736_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.36/30.46 do 0 intro. intros zenon_H1bd zenon_H101 zenon_H225 zenon_H83 zenon_Haa zenon_He7 zenon_H42 zenon_H69 zenon_H6e zenon_H2b1 zenon_Hd1 zenon_H1ab zenon_H90 zenon_H2b0 zenon_H185 zenon_H301 zenon_H17d zenon_H1d8 zenon_H124 zenon_H10d zenon_H246 zenon_H19e zenon_H200 zenon_H218 zenon_Hbd zenon_H1dc zenon_Hfc zenon_H3c zenon_H2bd zenon_H35 zenon_Ha4 zenon_H296 zenon_H1d5 zenon_H222 zenon_Hf9 zenon_Hc8 zenon_H20e zenon_H1fd zenon_H1a5 zenon_H92 zenon_H84 zenon_H97 zenon_H16f zenon_H48 zenon_H14e zenon_H156 zenon_H2d zenon_H2b4 zenon_H4e zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_H4c zenon_H173 zenon_Hf6 zenon_H3f zenon_Hcd zenon_H56 zenon_H135 zenon_H108 zenon_H20d zenon_H1e6 zenon_Hb8 zenon_He1 zenon_H208 zenon_Hde zenon_H1b1 zenon_H14b zenon_H172 zenon_H174 zenon_He4 zenon_H18c zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H100 zenon_Hc0 zenon_H23b zenon_H20 zenon_H6f zenon_H19a zenon_Hee zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hf4 zenon_H2a9. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.46 apply (zenon_L1649_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.46 apply (zenon_L769_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.46 apply (zenon_L1481_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.36/30.46 apply (zenon_L1707_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.36/30.46 apply (zenon_L513_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.46 apply (zenon_L1482_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.46 apply (zenon_L1481_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.46 apply (zenon_L1708_); trivial. % 30.36/30.46 apply (zenon_L737_); trivial. % 30.36/30.46 apply (zenon_L1735_); trivial. % 30.36/30.46 (* end of lemma zenon_L1736_ *) % 30.36/30.46 assert (zenon_L1737_ : (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.46 do 0 intro. intros zenon_H2a9 zenon_Hf4 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_Hee zenon_H6f zenon_H23b zenon_Hc0 zenon_H100 zenon_H18c zenon_He4 zenon_H174 zenon_H172 zenon_H14b zenon_H1b1 zenon_Hde zenon_H208 zenon_He1 zenon_Hb8 zenon_H1e6 zenon_H20d zenon_H108 zenon_H135 zenon_H56 zenon_Hcd zenon_H3f zenon_Hf6 zenon_H173 zenon_H4c zenon_Hd9 zenon_H8d zenon_H15a zenon_H4e zenon_H2d zenon_H16f zenon_H97 zenon_H84 zenon_H92 zenon_H1a5 zenon_H1fd zenon_H20e zenon_Hc8 zenon_Hf9 zenon_H222 zenon_H1d5 zenon_H296 zenon_Ha4 zenon_H35 zenon_H2bd zenon_H3c zenon_H1dc zenon_Hbd zenon_H218 zenon_H200 zenon_H19e zenon_H246 zenon_H10d zenon_H124 zenon_H1d8 zenon_H17d zenon_H301 zenon_Hd1 zenon_H42 zenon_He7 zenon_Haa zenon_H83 zenon_H225 zenon_H101 zenon_H1bd zenon_H90 zenon_Had zenon_Hfc zenon_H2b0 zenon_H19a zenon_H185 zenon_H2b1 zenon_H6e zenon_H48 zenon_H14e zenon_H16a zenon_H2b4 zenon_H20 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H1ab. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.46 apply (zenon_L1736_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.46 apply (zenon_L769_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.46 apply (zenon_L1477_); trivial. % 30.36/30.46 apply (zenon_L1478_); trivial. % 30.36/30.46 (* end of lemma zenon_L1737_ *) % 30.36/30.46 assert (zenon_L1738_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.46 do 0 intro. intros zenon_H2b1 zenon_H20 zenon_H185 zenon_H2b0 zenon_H16c zenon_H4e zenon_H14e zenon_H2a9 zenon_H23b zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H6f zenon_H19a zenon_Hee zenon_Hf6 zenon_H1f zenon_H3f zenon_Hb8 zenon_H1ab. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.36/30.46 apply (zenon_L117_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.36/30.46 apply (zenon_L840_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.36/30.46 apply (zenon_L1609_); trivial. % 30.36/30.46 exact (zenon_H1ab zenon_H112). % 30.36/30.46 (* end of lemma zenon_L1738_ *) % 30.36/30.46 assert (zenon_L1739_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.46 do 0 intro. intros zenon_H16f zenon_H1ba zenon_H19e zenon_Hd1 zenon_H2b4 zenon_H159 zenon_H48 zenon_H156 zenon_H16a zenon_Hf4 zenon_H4c zenon_H2b1 zenon_H20 zenon_H185 zenon_H2b0 zenon_H4e zenon_H14e zenon_H2a9 zenon_H23b zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H6f zenon_H19a zenon_Hee zenon_Hf6 zenon_H1f zenon_H3f zenon_Hb8 zenon_H1ab. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.46 apply (zenon_L1481_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.46 apply (zenon_L842_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.46 apply (zenon_L752_); trivial. % 30.36/30.46 apply (zenon_L1738_); trivial. % 30.36/30.46 (* end of lemma zenon_L1739_ *) % 30.36/30.46 assert (zenon_L1740_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.46 do 0 intro. intros zenon_H16f zenon_H2d zenon_H200 zenon_H76 zenon_H18c zenon_Hfc zenon_H90 zenon_H172 zenon_Hd1 zenon_H2b4 zenon_H16a zenon_H159 zenon_H19e zenon_H156 zenon_H48 zenon_H69 zenon_H35 zenon_H218 zenon_H42 zenon_H95 zenon_Hf4 zenon_H2b1 zenon_H20 zenon_H185 zenon_H2b0 zenon_H4e zenon_H14e zenon_H2a9 zenon_H23b zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H6f zenon_H19a zenon_Hee zenon_Hf6 zenon_H1f zenon_H3f zenon_Hb8 zenon_H1ab. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.36/30.46 apply (zenon_L1707_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.36/30.46 apply (zenon_L842_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.46 apply (zenon_L1698_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.46 apply (zenon_L1481_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.46 apply (zenon_L1708_); trivial. % 30.36/30.46 apply (zenon_L737_); trivial. % 30.36/30.46 apply (zenon_L766_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.46 apply (zenon_L513_); trivial. % 30.36/30.46 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.46 apply (zenon_L235_); trivial. % 30.36/30.46 apply (zenon_L1738_); trivial. % 30.36/30.46 (* end of lemma zenon_L1740_ *) % 30.36/30.46 assert (zenon_L1741_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.47 do 0 intro. intros zenon_H296 zenon_H83 zenon_He4 zenon_Hd9 zenon_H174 zenon_He1 zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_H208 zenon_H2bd zenon_Ha4 zenon_H8d zenon_Hcd zenon_H97 zenon_H92 zenon_Haa zenon_He7 zenon_Hdc zenon_H15a zenon_Hc8 zenon_H173 zenon_H1b1 zenon_H1a5 zenon_H1dc zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hbd zenon_H4c zenon_H16f zenon_H2d zenon_H200 zenon_H76 zenon_H18c zenon_Hfc zenon_H90 zenon_H172 zenon_Hd1 zenon_H2b4 zenon_H16a zenon_H159 zenon_H19e zenon_H156 zenon_H48 zenon_H69 zenon_H35 zenon_H218 zenon_H42 zenon_Hf4 zenon_H2b1 zenon_H20 zenon_H185 zenon_H2b0 zenon_H4e zenon_H14e zenon_H2a9 zenon_H23b zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H6f zenon_H19a zenon_Hee zenon_Hf6 zenon_H1f zenon_H3f zenon_Hb8 zenon_H1ab. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.47 apply (zenon_L1647_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.47 apply (zenon_L769_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.47 apply (zenon_L1739_); trivial. % 30.36/30.47 apply (zenon_L1740_); trivial. % 30.36/30.47 (* end of lemma zenon_L1741_ *) % 30.36/30.47 assert (zenon_L1742_ : ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.47 do 0 intro. intros zenon_H64 zenon_H1bd zenon_H101 zenon_H225 zenon_H301 zenon_H17d zenon_H124 zenon_H10d zenon_H246 zenon_H1d5 zenon_H222 zenon_Hf9 zenon_H20e zenon_H1fd zenon_H84 zenon_H108 zenon_H20d zenon_H1e6 zenon_H14b zenon_Hc0 zenon_H4e zenon_H18c zenon_H2b1 zenon_H20 zenon_H185 zenon_H2b0 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_Hfc zenon_H102 zenon_Had zenon_H90 zenon_H296 zenon_H83 zenon_He4 zenon_Hd9 zenon_H174 zenon_He1 zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_H208 zenon_H2bd zenon_Ha4 zenon_H8d zenon_Hcd zenon_H97 zenon_H92 zenon_Haa zenon_He7 zenon_Hdc zenon_H15a zenon_Hc8 zenon_H173 zenon_H1b1 zenon_H1a5 zenon_H1dc zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hbd zenon_H4c zenon_H16f zenon_H2d zenon_H200 zenon_H172 zenon_Hd1 zenon_H2b4 zenon_H16a zenon_H159 zenon_H19e zenon_H48 zenon_H35 zenon_H218 zenon_H42 zenon_Hf4 zenon_H14e zenon_H2a9 zenon_H100 zenon_Hf6 zenon_Hb8 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.47 apply (zenon_L148_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.47 apply (zenon_L1737_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.47 apply (zenon_L1741_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.47 apply (zenon_L769_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.47 apply (zenon_L1477_); trivial. % 30.36/30.47 apply (zenon_L864_); trivial. % 30.36/30.47 apply (zenon_L1187_); trivial. % 30.36/30.47 (* end of lemma zenon_L1742_ *) % 30.36/30.47 assert (zenon_L1743_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.36/30.47 do 0 intro. intros zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_H6f zenon_H23b zenon_Hb8 zenon_Hf6 zenon_H100 zenon_H2a9 zenon_Hf4 zenon_H42 zenon_H218 zenon_H35 zenon_Hd1 zenon_H172 zenon_H200 zenon_H2d zenon_H16f zenon_H4c zenon_Hbd zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1dc zenon_H1a5 zenon_H1b1 zenon_H173 zenon_Hc8 zenon_H15a zenon_Hdc zenon_He7 zenon_Haa zenon_H92 zenon_H97 zenon_Hcd zenon_H8d zenon_Ha4 zenon_H2bd zenon_H208 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_He1 zenon_H174 zenon_Hd9 zenon_He4 zenon_H83 zenon_H296 zenon_H90 zenon_Had zenon_Hfc zenon_H2b0 zenon_H18c zenon_Hc0 zenon_H14b zenon_H1e6 zenon_H20d zenon_H108 zenon_H84 zenon_H1fd zenon_H20e zenon_Hf9 zenon_H222 zenon_H1d5 zenon_H246 zenon_H10d zenon_H124 zenon_H17d zenon_H301 zenon_H225 zenon_H101 zenon_H1bd zenon_H64 zenon_H1ab zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H4a zenon_H19e zenon_H4e zenon_H3d zenon_H2b4 zenon_H20 zenon_H16a zenon_H14e zenon_H2b1 zenon_H6e zenon_H48 zenon_H156 zenon_H95 zenon_H113. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.36/30.47 apply (zenon_L1742_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.36/30.47 apply (zenon_L1462_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.36/30.47 apply (zenon_L737_); trivial. % 30.36/30.47 apply (zenon_L798_); trivial. % 30.36/30.47 (* end of lemma zenon_L1743_ *) % 30.36/30.47 assert (zenon_L1744_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.36/30.47 do 0 intro. intros zenon_H172 zenon_H48 zenon_H90 zenon_Had zenon_H2a9 zenon_H10d zenon_Hda zenon_Hee zenon_H19a zenon_H110 zenon_H2b7 zenon_H20d zenon_Hdf zenon_H2b1 zenon_H20 zenon_H2b0 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_Hfc zenon_H102 zenon_H1ab zenon_H2b4 zenon_H18c zenon_H4e zenon_H76. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.47 apply (zenon_L740_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.47 apply (zenon_L769_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.47 apply (zenon_L1661_); trivial. % 30.36/30.47 apply (zenon_L864_); trivial. % 30.36/30.47 (* end of lemma zenon_L1744_ *) % 30.36/30.47 assert (zenon_L1745_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.47 do 0 intro. intros zenon_H296 zenon_Ha4 zenon_H2bd zenon_H208 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_Hc8 zenon_H173 zenon_H15a zenon_H1b1 zenon_H117 zenon_H1a5 zenon_He7 zenon_Haa zenon_H92 zenon_H97 zenon_H8d zenon_H1d8 zenon_H174 zenon_Hd9 zenon_He4 zenon_H83 zenon_Hdc zenon_H1dc zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hbd zenon_H4c zenon_H16f zenon_H2d zenon_H200 zenon_H76 zenon_H18c zenon_Hfc zenon_H90 zenon_H172 zenon_Hd1 zenon_H2b4 zenon_H16a zenon_H159 zenon_H19e zenon_H156 zenon_H48 zenon_H69 zenon_H35 zenon_H218 zenon_H42 zenon_Hf4 zenon_H2b1 zenon_H20 zenon_H185 zenon_H2b0 zenon_H4e zenon_H14e zenon_H2a9 zenon_H23b zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H6f zenon_H19a zenon_Hee zenon_Hf6 zenon_H1f zenon_H3f zenon_Hb8 zenon_H1ab. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.47 apply (zenon_L1645_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.47 apply (zenon_L769_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.47 apply (zenon_L1739_); trivial. % 30.36/30.47 apply (zenon_L1740_); trivial. % 30.36/30.47 (* end of lemma zenon_L1745_ *) % 30.36/30.47 assert (zenon_L1746_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.36/30.47 do 0 intro. intros zenon_H1bd zenon_H101 zenon_H225 zenon_H301 zenon_H17d zenon_H124 zenon_H10d zenon_H246 zenon_H1d5 zenon_H222 zenon_Hf9 zenon_H20e zenon_H1fd zenon_H84 zenon_H108 zenon_H20d zenon_H1e6 zenon_H14b zenon_Hc0 zenon_H4e zenon_H18c zenon_H2b1 zenon_H20 zenon_H185 zenon_H19a zenon_H2b0 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_Hfc zenon_H102 zenon_H1ab zenon_Had zenon_H296 zenon_Ha4 zenon_H2bd zenon_H208 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_Hc8 zenon_H173 zenon_H15a zenon_H1b1 zenon_H117 zenon_H1a5 zenon_He7 zenon_Haa zenon_H92 zenon_H97 zenon_H8d zenon_H1d8 zenon_H174 zenon_Hd9 zenon_He4 zenon_H83 zenon_Hdc zenon_H1dc zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hbd zenon_H4c zenon_H16f zenon_H2d zenon_H200 zenon_H172 zenon_Hd1 zenon_H2b4 zenon_H16a zenon_H159 zenon_H19e zenon_H48 zenon_H35 zenon_H218 zenon_H42 zenon_Hf4 zenon_H14e zenon_H2a9 zenon_H23b zenon_H100 zenon_Hee zenon_Hf6 zenon_H1f zenon_H3f zenon_Hb8 zenon_H6f zenon_H90. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.47 apply (zenon_L149_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.47 apply (zenon_L1737_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.47 apply (zenon_L1745_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.47 apply (zenon_L769_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.47 apply (zenon_L1477_); trivial. % 30.36/30.47 apply (zenon_L864_); trivial. % 30.36/30.47 apply (zenon_L39_); trivial. % 30.36/30.47 (* end of lemma zenon_L1746_ *) % 30.36/30.47 assert (zenon_L1747_ : ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.36/30.47 do 0 intro. intros zenon_H90 zenon_H6f zenon_Hb8 zenon_H3f zenon_H1f zenon_Hf6 zenon_H100 zenon_H23b zenon_Hf4 zenon_H42 zenon_H218 zenon_H35 zenon_H19e zenon_Hd1 zenon_H172 zenon_H200 zenon_H2d zenon_H16f zenon_H4c zenon_Hbd zenon_Hb5 zenon_H1dc zenon_Hdc zenon_H83 zenon_He4 zenon_Hd9 zenon_H174 zenon_H1d8 zenon_H8d zenon_H97 zenon_H92 zenon_Haa zenon_He7 zenon_H1a5 zenon_H117 zenon_H1b1 zenon_H15a zenon_H173 zenon_Hc8 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_H208 zenon_H2bd zenon_Ha4 zenon_H296 zenon_Had zenon_Hfc zenon_H2b0 zenon_H18c zenon_H4e zenon_Hc0 zenon_H14b zenon_H1e6 zenon_H20d zenon_H108 zenon_H84 zenon_H1fd zenon_H20e zenon_Hf9 zenon_H222 zenon_H1d5 zenon_H246 zenon_H124 zenon_H17d zenon_H301 zenon_H225 zenon_H101 zenon_H1bd zenon_H1ab zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H4a zenon_H20 zenon_H2b4 zenon_H16a zenon_H14e zenon_H2b1 zenon_H6e zenon_H48 zenon_H156 zenon_H2b7 zenon_H110 zenon_H19a zenon_Hee zenon_Hda zenon_H10d zenon_H2a9. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.36/30.47 apply (zenon_L1746_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.36/30.47 apply (zenon_L1478_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.36/30.47 apply (zenon_L737_); trivial. % 30.36/30.47 apply (zenon_L1660_); trivial. % 30.36/30.47 (* end of lemma zenon_L1747_ *) % 30.36/30.47 assert (zenon_L1748_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.36/30.47 do 0 intro. intros zenon_H10d zenon_Hda zenon_Hee zenon_H110 zenon_H2b7 zenon_H156 zenon_H48 zenon_H6e zenon_H2b1 zenon_H14e zenon_H16a zenon_H2b4 zenon_H20 zenon_H4a zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H1ab zenon_H1bd zenon_H101 zenon_H225 zenon_H301 zenon_H17d zenon_H124 zenon_H246 zenon_H1d5 zenon_H222 zenon_Hf9 zenon_H20e zenon_H1fd zenon_H84 zenon_H20d zenon_H1e6 zenon_H14b zenon_Hc0 zenon_H4e zenon_H18c zenon_H2b0 zenon_Hfc zenon_Had zenon_H296 zenon_Ha4 zenon_H2bd zenon_H208 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_Hc8 zenon_H173 zenon_H15a zenon_H1b1 zenon_H1a5 zenon_He7 zenon_Haa zenon_H92 zenon_H97 zenon_H8d zenon_H1d8 zenon_H174 zenon_Hd9 zenon_He4 zenon_H83 zenon_Hdc zenon_H1dc zenon_Hb5 zenon_Hbd zenon_H4c zenon_H16f zenon_H2d zenon_H200 zenon_H172 zenon_Hd1 zenon_H19e zenon_H35 zenon_H218 zenon_H42 zenon_Hf4 zenon_H23b zenon_H100 zenon_Hf6 zenon_H1f zenon_H3f zenon_Hb8 zenon_H90 zenon_H6f zenon_H19a zenon_H1c5 zenon_H108 zenon_H2a9. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.36/30.47 apply (zenon_L1747_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.36/30.47 apply (zenon_L235_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.36/30.47 apply (zenon_L171_); trivial. % 30.36/30.47 exact (zenon_H2a9 zenon_Hb6). % 30.36/30.47 (* end of lemma zenon_L1748_ *) % 30.36/30.47 assert (zenon_L1749_ : (((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) (e2)) = (e3))) -> False). % 30.36/30.47 do 0 intro. intros zenon_H2b7 zenon_H8b zenon_Hb5 zenon_H19a zenon_Hee zenon_Hda zenon_H10d zenon_H2a9. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.36/30.47 apply (zenon_L297_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.36/30.47 apply (zenon_L337_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.36/30.47 apply (zenon_L64_); trivial. % 30.36/30.47 exact (zenon_H2a9 zenon_Hb6). % 30.36/30.47 (* end of lemma zenon_L1749_ *) % 30.36/30.47 assert (zenon_L1750_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.36/30.47 do 0 intro. intros zenon_H16f zenon_H48 zenon_H156 zenon_H2d zenon_H2a9 zenon_H102 zenon_H90 zenon_H4a zenon_H18f zenon_H13b zenon_H100 zenon_H76 zenon_H1d8 zenon_Hb8 zenon_H2b4 zenon_H18c zenon_Hdf zenon_H20d zenon_H110 zenon_Hf4 zenon_H2b7 zenon_Hb5 zenon_H19a zenon_Hee zenon_Hbd zenon_H4c zenon_H14e zenon_H10d zenon_Hda zenon_H3f zenon_He9 zenon_Had zenon_Hfe zenon_Hf9 zenon_H4e zenon_H16b zenon_H16a. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.47 apply (zenon_L865_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.47 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.36/30.47 apply (zenon_L1749_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.36/30.47 apply (zenon_L513_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.36/30.47 apply (zenon_L1694_); trivial. % 30.36/30.47 apply (zenon_L1695_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.47 apply (zenon_L1662_); trivial. % 30.36/30.47 apply (zenon_L859_); trivial. % 30.36/30.47 (* end of lemma zenon_L1750_ *) % 30.36/30.47 assert (zenon_L1751_ : ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.36/30.47 do 0 intro. intros zenon_Hf4 zenon_H101 zenon_Hf6 zenon_H1d5 zenon_H14e zenon_H2a9 zenon_H92 zenon_H84 zenon_H17d zenon_H174 zenon_H64 zenon_H3f zenon_Hd9 zenon_H8d zenon_H15a zenon_H6f zenon_H2b4 zenon_H2d zenon_H48 zenon_H16f zenon_H97 zenon_Hcd zenon_Hde zenon_He4 zenon_Had zenon_H1d8 zenon_Hb8 zenon_H35 zenon_He1 zenon_H156 zenon_H4e zenon_H3c zenon_Hdc zenon_H135 zenon_H2b1 zenon_H2b0 zenon_H1ab zenon_H20 zenon_Hd1 zenon_H19e zenon_H100 zenon_H4c zenon_H19a zenon_Hc0 zenon_H23b zenon_H1dc zenon_Hbd zenon_Hee zenon_H200 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1b1 zenon_H173 zenon_Hc8 zenon_He7 zenon_Haa zenon_Ha4 zenon_H218 zenon_H2bd zenon_H208 zenon_H56 zenon_H172 zenon_H83 zenon_H42 zenon_H225 zenon_H222 zenon_H10d zenon_Hf9 zenon_H1bd zenon_H108 zenon_H1fd zenon_H20e zenon_H1a5 zenon_H296 zenon_H6c zenon_H18c zenon_Hfc zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H4a zenon_H33 zenon_H16a. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.47 apply (zenon_L1655_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.47 apply (zenon_L763_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.47 apply (zenon_L1606_); trivial. % 30.36/30.47 apply (zenon_L1459_); trivial. % 30.36/30.47 (* end of lemma zenon_L1751_ *) % 30.36/30.47 assert (zenon_L1752_ : ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.36/30.47 do 0 intro. intros zenon_H33 zenon_H20 zenon_H1ab zenon_H2b0 zenon_H2b1 zenon_H4c zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H100 zenon_H13b zenon_H18f zenon_Had zenon_H4a zenon_H102 zenon_H18c zenon_He4 zenon_Hde zenon_Hcd zenon_H97 zenon_H16f zenon_H48 zenon_H156 zenon_H2d zenon_H2b4 zenon_H6f zenon_H19a zenon_H16a zenon_H159 zenon_H15a zenon_H8d zenon_Hd9 zenon_He1 zenon_H3f zenon_H64 zenon_H174 zenon_Hf4 zenon_H17d zenon_H84 zenon_H92 zenon_H2a9 zenon_H14e zenon_H4e. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.47 apply (zenon_L1460_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.47 apply (zenon_L842_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.47 apply (zenon_L752_); trivial. % 30.36/30.47 apply (zenon_L1651_); trivial. % 30.36/30.47 (* end of lemma zenon_L1752_ *) % 30.36/30.47 assert (zenon_L1753_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.36/30.47 do 0 intro. intros zenon_H16f zenon_Had zenon_H6f zenon_H42 zenon_H2d zenon_H1ab zenon_H156 zenon_H2b0 zenon_H19a zenon_H2b1 zenon_H16a zenon_H4e zenon_Hf4 zenon_Ha4 zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H13b zenon_H4a zenon_H218 zenon_H2bd zenon_H19e zenon_H3c zenon_Hde zenon_Hc9 zenon_H200 zenon_H8a zenon_H97. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.47 apply (zenon_L34_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.47 apply (zenon_L842_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.47 apply (zenon_L235_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.36/30.47 apply (zenon_L4_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.36/30.47 apply (zenon_L842_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.36/30.47 apply (zenon_L1616_); trivial. % 30.36/30.47 apply (zenon_L862_); trivial. % 30.36/30.47 (* end of lemma zenon_L1753_ *) % 30.36/30.47 assert (zenon_L1754_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.36/30.47 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hc9 zenon_H13b zenon_H16a zenon_H33 zenon_H4a zenon_Hfc zenon_H18f zenon_H19e zenon_H1ba zenon_H102 zenon_H1fd zenon_H1a5 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H20e zenon_H2a9. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.36/30.47 apply (zenon_L142_); trivial. % 30.36/30.47 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.36/30.47 exact (zenon_H13b zenon_Hfd). % 30.36/30.47 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.36/30.47 apply (zenon_L1716_); trivial. % 30.36/30.47 apply (zenon_L830_); trivial. % 30.36/30.47 (* end of lemma zenon_L1754_ *) % 30.36/30.47 assert (zenon_L1755_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H296 zenon_H97 zenon_H8a zenon_H200 zenon_Hde zenon_H3c zenon_H2bd zenon_H218 zenon_H35 zenon_Ha4 zenon_H2b1 zenon_H19a zenon_H2b0 zenon_H156 zenon_H1ab zenon_H2d zenon_H42 zenon_H6f zenon_Had zenon_H16f zenon_H2a9 zenon_H20e zenon_H4e zenon_H14e zenon_H4c zenon_H1a5 zenon_H1fd zenon_H19e zenon_Hfc zenon_H33 zenon_H16a zenon_Hc9 zenon_H173 zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H13b zenon_Hf4. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.48 apply (zenon_L1753_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.48 apply (zenon_L763_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.48 apply (zenon_L1754_); trivial. % 30.36/30.48 apply (zenon_L1654_); trivial. % 30.36/30.48 (* end of lemma zenon_L1755_ *) % 30.36/30.48 assert (zenon_L1756_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H92 zenon_H84 zenon_H17d zenon_H174 zenon_H64 zenon_H3f zenon_He1 zenon_Hd9 zenon_H8d zenon_H15a zenon_H159 zenon_H2b4 zenon_H48 zenon_Hcd zenon_He4 zenon_H100 zenon_H1d8 zenon_Hb8 zenon_H20 zenon_H296 zenon_H97 zenon_H200 zenon_Hde zenon_H3c zenon_H2bd zenon_H218 zenon_H35 zenon_Ha4 zenon_H2b1 zenon_H19a zenon_H2b0 zenon_H156 zenon_H1ab zenon_H2d zenon_H42 zenon_H6f zenon_Had zenon_H16f zenon_H2a9 zenon_H20e zenon_H4e zenon_H14e zenon_H4c zenon_H1a5 zenon_H1fd zenon_H19e zenon_Hfc zenon_H33 zenon_H16a zenon_Hc9 zenon_H173 zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H13b zenon_Hf4. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.48 apply (zenon_L148_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.48 apply (zenon_L1460_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.48 apply (zenon_L1752_); trivial. % 30.36/30.48 apply (zenon_L1755_); trivial. % 30.36/30.48 (* end of lemma zenon_L1756_ *) % 30.36/30.48 assert (zenon_L1757_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.36/30.48 do 0 intro. intros zenon_H135 zenon_H73 zenon_Hc8 zenon_H4c zenon_H19e zenon_H2a9 zenon_He1 zenon_H19a zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.36/30.48 apply (zenon_L43_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.36/30.48 apply (zenon_L824_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.36/30.48 apply (zenon_L825_); trivial. % 30.36/30.48 apply (zenon_L56_); trivial. % 30.36/30.48 (* end of lemma zenon_L1757_ *) % 30.36/30.48 assert (zenon_L1758_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_H1ab zenon_H102 zenon_H19e zenon_H18f zenon_H13b zenon_H4a zenon_H4e zenon_Hd1 zenon_H2b4 zenon_H20 zenon_H16a zenon_H159 zenon_H2b1 zenon_H2a9 zenon_H2d zenon_H14e zenon_H4c zenon_Hf4 zenon_H10e zenon_H1fd zenon_H156 zenon_H48 zenon_H6e. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.48 apply (zenon_L49_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.48 apply (zenon_L1481_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.48 apply (zenon_L939_); trivial. % 30.36/30.48 apply (zenon_L737_); trivial. % 30.36/30.48 (* end of lemma zenon_L1758_ *) % 30.36/30.48 assert (zenon_L1759_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.36/30.48 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_Hd5 zenon_Hcd zenon_H2a9 zenon_He1 zenon_H19a zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_Hf4 zenon_Hf6. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.36/30.48 apply (zenon_L49_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.36/30.48 apply (zenon_L212_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.36/30.48 apply (zenon_L825_); trivial. % 30.36/30.48 apply (zenon_L56_); trivial. % 30.36/30.48 (* end of lemma zenon_L1759_ *) % 30.36/30.48 assert (zenon_L1760_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H208 zenon_Hc3 zenon_H4a zenon_H18c zenon_Hf6 zenon_Hf4 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_He1 zenon_H2a9 zenon_Hcd zenon_Hde zenon_Hdf zenon_H135 zenon_H56 zenon_H218 zenon_H33. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.36/30.48 apply (zenon_L763_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.36/30.48 apply (zenon_L1759_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.36/30.48 exact (zenon_H56 zenon_H25). % 30.36/30.48 apply (zenon_L870_); trivial. % 30.36/30.48 (* end of lemma zenon_L1760_ *) % 30.36/30.48 assert (zenon_L1761_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.36/30.48 do 0 intro. intros zenon_H173 zenon_H68 zenon_H13b zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_Had zenon_H48 zenon_H69 zenon_Hbd zenon_H2d zenon_H102 zenon_H19e zenon_H18f zenon_Hfc zenon_H4a zenon_H33 zenon_H16a zenon_H208 zenon_H18c zenon_H6f zenon_H19a zenon_He1 zenon_Hcd zenon_Hde zenon_H135 zenon_H56 zenon_H218 zenon_H200 zenon_H1fd zenon_H1a5 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H20e zenon_H2a9. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.36/30.48 apply (zenon_L48_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.36/30.48 exact (zenon_H13b zenon_Hfd). % 30.36/30.48 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.48 apply (zenon_L1760_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.48 apply (zenon_L1716_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.48 apply (zenon_L939_); trivial. % 30.36/30.48 apply (zenon_L1728_); trivial. % 30.36/30.48 apply (zenon_L830_); trivial. % 30.36/30.48 (* end of lemma zenon_L1761_ *) % 30.36/30.48 assert (zenon_L1762_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H208 zenon_H8a zenon_H4e zenon_Had zenon_H1a5 zenon_H18c zenon_H4a zenon_H48 zenon_H172 zenon_Hf6 zenon_Hf4 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_He1 zenon_H2a9 zenon_Hcd zenon_Hde zenon_Hdf zenon_H135 zenon_H56 zenon_H218 zenon_H33. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.36/30.48 apply (zenon_L918_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.36/30.48 apply (zenon_L1759_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.36/30.48 exact (zenon_H56 zenon_H25). % 30.36/30.48 apply (zenon_L870_); trivial. % 30.36/30.48 (* end of lemma zenon_L1762_ *) % 30.36/30.48 assert (zenon_L1763_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (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)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.36/30.48 do 0 intro. intros zenon_He4 zenon_H33 zenon_H218 zenon_H56 zenon_H135 zenon_H2a9 zenon_He1 zenon_H19a zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_Hf6 zenon_H172 zenon_H48 zenon_H4a zenon_H18c zenon_H1a5 zenon_Had zenon_H4e zenon_H208 zenon_H16a zenon_H13b zenon_H18f zenon_Hfc zenon_H102 zenon_H8d zenon_Hcd zenon_H68 zenon_Hdf zenon_Hde zenon_Hf4 zenon_H17d. % 30.36/30.48 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.48 apply (zenon_L232_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.48 apply (zenon_L18_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.48 apply (zenon_L740_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.48 apply (zenon_L1760_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.48 apply (zenon_L1606_); trivial. % 30.36/30.48 apply (zenon_L864_); trivial. % 30.36/30.48 apply (zenon_L1762_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.48 apply (zenon_L48_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.48 apply (zenon_L49_); trivial. % 30.36/30.48 apply (zenon_L847_); trivial. % 30.36/30.48 (* end of lemma zenon_L1763_ *) % 30.36/30.48 assert (zenon_L1764_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H102 zenon_H1e1 zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Had zenon_H48 zenon_H69 zenon_Hbd zenon_H18f zenon_H13b zenon_Hf4 zenon_H95. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.36/30.48 apply (zenon_L1728_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.36/30.48 exact (zenon_H18f zenon_Hd2). % 30.36/30.48 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.36/30.48 exact (zenon_H13b zenon_Hfd). % 30.36/30.48 apply (zenon_L513_); trivial. % 30.36/30.48 (* end of lemma zenon_L1764_ *) % 30.36/30.48 assert (zenon_L1765_ : (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 30.36/30.48 do 0 intro. intros zenon_H13b zenon_H18f zenon_Hbd zenon_H69 zenon_H48 zenon_Had zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H102 zenon_H208 zenon_H18c zenon_H4a zenon_H173 zenon_Hc9 zenon_H16a zenon_H33 zenon_Hfc zenon_H16f zenon_H6f zenon_H42 zenon_H1ab zenon_H2b0 zenon_H19a zenon_H2b1 zenon_Ha4 zenon_H35 zenon_H218 zenon_H2bd zenon_H3c zenon_H200 zenon_H8a zenon_H97 zenon_H296 zenon_H156 zenon_H2d zenon_H19e zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_H1d5 zenon_H56 zenon_He4 zenon_H172 zenon_H8d zenon_H68 zenon_H17d zenon_H1fd zenon_H1a5 zenon_Hf4 zenon_H4c zenon_H14e zenon_H4e zenon_H20e zenon_H2a9. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.48 apply (zenon_L1753_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.48 apply (zenon_L1761_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.48 apply (zenon_L1754_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.36/30.48 apply (zenon_L142_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.36/30.48 exact (zenon_H13b zenon_Hfd). % 30.36/30.48 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.48 apply (zenon_L34_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.48 apply (zenon_L842_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.48 apply (zenon_L235_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.48 apply (zenon_L1763_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.48 apply (zenon_L1716_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.36/30.48 apply (zenon_L1755_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.36/30.48 apply (zenon_L1577_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.36/30.48 apply (zenon_L1708_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.36/30.48 apply (zenon_L175_); trivial. % 30.36/30.48 apply (zenon_L779_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.36/30.48 exact (zenon_H56 zenon_H25). % 30.36/30.48 apply (zenon_L944_); trivial. % 30.36/30.48 apply (zenon_L1764_); trivial. % 30.36/30.48 apply (zenon_L830_); trivial. % 30.36/30.48 (* end of lemma zenon_L1765_ *) % 30.36/30.48 assert (zenon_L1766_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H8d zenon_Hf4 zenon_H48 zenon_H14e zenon_H156 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H4a zenon_H33 zenon_H16a zenon_H20 zenon_H2b4 zenon_He1 zenon_Hc9 zenon_H6f zenon_H90. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.48 apply (zenon_L538_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.48 apply (zenon_L1460_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.48 apply (zenon_L273_); trivial. % 30.36/30.48 apply (zenon_L39_); trivial. % 30.36/30.48 (* end of lemma zenon_L1766_ *) % 30.36/30.48 assert (zenon_L1767_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.36/30.48 do 0 intro. intros zenon_He4 zenon_Hc8 zenon_Hf6 zenon_H1fd zenon_H2d zenon_H10e zenon_H19a zenon_H2a9 zenon_H19e zenon_H4c zenon_H18c zenon_H135 zenon_H6f zenon_He1 zenon_H2b4 zenon_H20 zenon_H16a zenon_H33 zenon_H4a zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H156 zenon_H14e zenon_H48 zenon_Hf4 zenon_H8d zenon_H90 zenon_Hcd. % 30.36/30.48 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.48 apply (zenon_L1757_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.48 apply (zenon_L826_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.48 apply (zenon_L1766_); trivial. % 30.36/30.48 apply (zenon_L386_); trivial. % 30.36/30.48 (* end of lemma zenon_L1767_ *) % 30.36/30.48 assert (zenon_L1768_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.48 do 0 intro. intros zenon_H8d zenon_H90 zenon_H48 zenon_H156 zenon_H1fd zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H2d zenon_H2a9 zenon_H2b1 zenon_H159 zenon_H16a zenon_H20 zenon_H2b4 zenon_Hd1 zenon_H4e zenon_H4a zenon_H13b zenon_H18f zenon_H19e zenon_H102 zenon_Hde zenon_H200 zenon_He1 zenon_Hc9 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.48 apply (zenon_L538_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.48 apply (zenon_L1758_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.48 apply (zenon_L273_); trivial. % 30.36/30.48 apply (zenon_L1187_); trivial. % 30.36/30.48 (* end of lemma zenon_L1768_ *) % 30.36/30.48 assert (zenon_L1769_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H1d5 zenon_He9 zenon_H35 zenon_H1ab zenon_H3f zenon_H1f zenon_H8d zenon_H48 zenon_H1fd zenon_H10e zenon_Hf4 zenon_H4c zenon_H14e zenon_H2d zenon_H2a9 zenon_H2b1 zenon_H159 zenon_H16a zenon_H20 zenon_H2b4 zenon_Hd1 zenon_H4a zenon_H13b zenon_H18f zenon_H19e zenon_H102 zenon_Hde zenon_H200 zenon_He1 zenon_Hc9 zenon_H23b zenon_H6f zenon_H19a zenon_Hee zenon_H10d zenon_H6c zenon_H18c zenon_Hbd zenon_H156 zenon_H4e zenon_H16c. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.36/30.48 apply (zenon_L273_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.36/30.48 apply (zenon_L922_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.36/30.48 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.36/30.48 apply (zenon_L1214_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.36/30.48 apply (zenon_L1654_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.36/30.48 apply (zenon_L63_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.36/30.48 apply (zenon_L1768_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.36/30.48 apply (zenon_L336_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.36/30.48 apply (zenon_L751_); trivial. % 30.36/30.48 exact (zenon_H1ab zenon_H112). % 30.36/30.48 apply (zenon_L779_); trivial. % 30.36/30.48 (* end of lemma zenon_L1769_ *) % 30.36/30.48 assert (zenon_L1770_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.36/30.48 do 0 intro. intros zenon_He4 zenon_Hc8 zenon_Hf6 zenon_H18c zenon_H135 zenon_H1ab zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_H6f zenon_H23b zenon_He1 zenon_H200 zenon_Hde zenon_H102 zenon_H19e zenon_H18f zenon_H13b zenon_H4a zenon_H4e zenon_Hd1 zenon_H2b4 zenon_H20 zenon_H16a zenon_H159 zenon_H2b1 zenon_H2a9 zenon_H2d zenon_H14e zenon_H4c zenon_Hf4 zenon_H10e zenon_H1fd zenon_H156 zenon_H48 zenon_H8d zenon_H90 zenon_Hcd. % 30.36/30.48 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.48 apply (zenon_L1757_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.48 apply (zenon_L826_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.48 apply (zenon_L1768_); trivial. % 30.36/30.48 apply (zenon_L386_); trivial. % 30.36/30.48 (* end of lemma zenon_L1770_ *) % 30.36/30.48 assert (zenon_L1771_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.48 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H6c zenon_H18c zenon_H10e zenon_H1a5 zenon_H2b1 zenon_H6e zenon_H48 zenon_H14e zenon_H16a zenon_H2b4 zenon_H20 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H1ab. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.48 apply (zenon_L740_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.48 apply (zenon_L763_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.48 apply (zenon_L764_); trivial. % 30.36/30.48 apply (zenon_L1478_); trivial. % 30.36/30.48 (* end of lemma zenon_L1771_ *) % 30.36/30.48 assert (zenon_L1772_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.48 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H18c zenon_H90 zenon_Had zenon_H10e zenon_H1a5 zenon_H2b1 zenon_H6e zenon_H48 zenon_H14e zenon_H16a zenon_H2b4 zenon_H20 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H1ab. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.48 apply (zenon_L740_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.48 apply (zenon_L769_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.48 apply (zenon_L764_); trivial. % 30.36/30.48 apply (zenon_L1478_); trivial. % 30.36/30.48 (* end of lemma zenon_L1772_ *) % 30.36/30.48 assert (zenon_L1773_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.48 do 0 intro. intros zenon_H2b1 zenon_H20 zenon_H185 zenon_H3d zenon_H4e zenon_H19e zenon_H4a zenon_H156 zenon_He9 zenon_H35 zenon_H18f zenon_H18c zenon_H6c zenon_H102 zenon_H1ab. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.36/30.48 apply (zenon_L117_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.36/30.48 apply (zenon_L731_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.36/30.48 apply (zenon_L763_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.36/30.48 exact (zenon_H18f zenon_Hd2). % 30.36/30.48 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.36/30.48 apply (zenon_L95_); trivial. % 30.36/30.48 apply (zenon_L841_); trivial. % 30.36/30.48 exact (zenon_H1ab zenon_H112). % 30.36/30.48 (* end of lemma zenon_L1773_ *) % 30.36/30.48 assert (zenon_L1774_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.36/30.48 do 0 intro. intros zenon_H42 zenon_H218 zenon_H48 zenon_H14e zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H6e zenon_H69 zenon_H200 zenon_H95 zenon_Hf4 zenon_H1ab zenon_H35 zenon_He9 zenon_H156 zenon_H19e zenon_H4e zenon_H185 zenon_H20 zenon_H2b1 zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H13b zenon_H100. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.36/30.48 apply (zenon_L1707_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.36/30.48 apply (zenon_L513_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.36/30.48 apply (zenon_L1773_); trivial. % 30.36/30.48 apply (zenon_L1450_); trivial. % 30.36/30.48 (* end of lemma zenon_L1774_ *) % 30.36/30.48 assert (zenon_L1775_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H101 zenon_H1ab zenon_Hb8 zenon_H3f zenon_H1f zenon_Hf6 zenon_Hee zenon_H6f zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H23b zenon_H2a9 zenon_H14e zenon_H4e zenon_H2b0 zenon_H185 zenon_H20 zenon_H2b1 zenon_Hf4 zenon_H95 zenon_H42 zenon_H218 zenon_H48 zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H69 zenon_H200 zenon_H35 zenon_H156 zenon_H6c zenon_H18c zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.48 apply (zenon_L1774_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.48 apply (zenon_L513_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.48 apply (zenon_L235_); trivial. % 30.36/30.48 apply (zenon_L1738_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.36/30.48 exact (zenon_H13b zenon_Hfd). % 30.36/30.48 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.36/30.48 apply (zenon_L824_); trivial. % 30.36/30.48 apply (zenon_L1184_); trivial. % 30.36/30.48 (* end of lemma zenon_L1775_ *) % 30.36/30.48 assert (zenon_L1776_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H296 zenon_H2d zenon_H8d zenon_Hd9 zenon_Hfc zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_H208 zenon_H2bd zenon_Ha4 zenon_H15a zenon_Hbd zenon_Hf9 zenon_He4 zenon_H173 zenon_H1b1 zenon_H174 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_H20e zenon_H1fd zenon_H1a5 zenon_H108 zenon_H1d8 zenon_H97 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1dc zenon_H92 zenon_Hdc zenon_H101 zenon_H1ab zenon_Hb8 zenon_H3f zenon_H1f zenon_Hf6 zenon_Hee zenon_H6f zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H23b zenon_H2a9 zenon_H14e zenon_H4e zenon_H2b0 zenon_H185 zenon_H20 zenon_H2b1 zenon_Hf4 zenon_H42 zenon_H218 zenon_H48 zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H69 zenon_H200 zenon_H35 zenon_H156 zenon_H6c zenon_H18c zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.48 apply (zenon_L1626_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.48 apply (zenon_L763_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.48 apply (zenon_L1739_); trivial. % 30.36/30.48 apply (zenon_L1775_); trivial. % 30.36/30.48 (* end of lemma zenon_L1776_ *) % 30.36/30.48 assert (zenon_L1777_ : ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.48 do 0 intro. intros zenon_H4c zenon_H100 zenon_H19e zenon_H16f zenon_H35 zenon_H200 zenon_Hd1 zenon_H218 zenon_H42 zenon_Hf4 zenon_H4e zenon_H2a9 zenon_H23b zenon_Had zenon_H6f zenon_Hee zenon_Hf6 zenon_H1f zenon_H3f zenon_Hb8 zenon_H101 zenon_Hdc zenon_H92 zenon_H1dc zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H97 zenon_H1d8 zenon_H108 zenon_H1a5 zenon_H1fd zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H174 zenon_H1b1 zenon_H173 zenon_He4 zenon_Hf9 zenon_Hbd zenon_H15a zenon_Ha4 zenon_H2bd zenon_H208 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_Hd9 zenon_H8d zenon_H2d zenon_H296 zenon_H6c zenon_H18c zenon_Hfc zenon_H2b0 zenon_H19a zenon_H185 zenon_H2b1 zenon_H6e zenon_H48 zenon_H14e zenon_H16a zenon_H2b4 zenon_H20 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H159 zenon_H102 zenon_H1ab. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.48 apply (zenon_L1776_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.48 apply (zenon_L763_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.48 apply (zenon_L1477_); trivial. % 30.36/30.48 apply (zenon_L1478_); trivial. % 30.36/30.48 (* end of lemma zenon_L1777_ *) % 30.36/30.48 assert (zenon_L1778_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.36/30.48 do 0 intro. intros zenon_H296 zenon_H2d zenon_Hfc zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_H76 zenon_Hcd zenon_Hde zenon_H208 zenon_H2bd zenon_Ha4 zenon_H101 zenon_H1ab zenon_Hb8 zenon_H3f zenon_H1f zenon_Hf6 zenon_Hee zenon_H6f zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H23b zenon_H2a9 zenon_H14e zenon_H4e zenon_H2b0 zenon_H185 zenon_H20 zenon_H2b1 zenon_Hf4 zenon_H42 zenon_H218 zenon_H48 zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H69 zenon_H200 zenon_H35 zenon_H156 zenon_H6c zenon_H18c zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.48 apply (zenon_L1623_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.48 apply (zenon_L763_); trivial. % 30.36/30.48 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.48 apply (zenon_L1739_); trivial. % 30.36/30.48 apply (zenon_L1775_); trivial. % 30.36/30.48 (* end of lemma zenon_L1778_ *) % 30.36/30.48 assert (zenon_L1779_ : ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.36/30.49 do 0 intro. intros zenon_H4c zenon_H100 zenon_H19e zenon_H16f zenon_H35 zenon_H200 zenon_Hd1 zenon_H2b4 zenon_H16a zenon_H159 zenon_H48 zenon_H218 zenon_H42 zenon_Hf4 zenon_H14e zenon_H2a9 zenon_H23b zenon_Had zenon_H6f zenon_Hee zenon_Hf6 zenon_H1f zenon_H3f zenon_Hb8 zenon_H101 zenon_Ha4 zenon_H2bd zenon_H208 zenon_Hde zenon_Hcd zenon_He1 zenon_H135 zenon_H56 zenon_H3c zenon_H172 zenon_H2d zenon_H296 zenon_H6c zenon_H1ab zenon_H102 zenon_Hfc zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H2b0 zenon_H19a zenon_H185 zenon_H20 zenon_H2b1 zenon_H18c zenon_H4e zenon_H76. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.49 apply (zenon_L1778_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.49 apply (zenon_L763_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.49 apply (zenon_L1477_); trivial. % 30.36/30.49 apply (zenon_L864_); trivial. % 30.36/30.49 (* end of lemma zenon_L1779_ *) % 30.36/30.49 assert (zenon_L1780_ : ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.49 do 0 intro. intros zenon_H64 zenon_H8d zenon_Hd9 zenon_H15a zenon_Hbd zenon_Hf9 zenon_He4 zenon_H173 zenon_H1b1 zenon_H174 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_H20e zenon_H1fd zenon_H1a5 zenon_H108 zenon_H1d8 zenon_H97 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1dc zenon_H92 zenon_Hdc zenon_H4e zenon_H18c zenon_H2b1 zenon_H20 zenon_H185 zenon_H2b0 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_Hfc zenon_H102 zenon_H6c zenon_H296 zenon_H2d zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_H208 zenon_H2bd zenon_Ha4 zenon_H101 zenon_Hb8 zenon_Hf6 zenon_Had zenon_H2a9 zenon_H14e zenon_Hf4 zenon_H42 zenon_H218 zenon_H48 zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H200 zenon_H35 zenon_H16f zenon_H19e zenon_H100 zenon_H4c zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.49 apply (zenon_L148_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.49 apply (zenon_L1777_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.49 apply (zenon_L1779_); trivial. % 30.36/30.49 apply (zenon_L1187_); trivial. % 30.36/30.49 (* end of lemma zenon_L1780_ *) % 30.36/30.49 assert (zenon_L1781_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.36/30.49 do 0 intro. intros zenon_H296 zenon_H1dc zenon_Hbd zenon_H3c zenon_Hde zenon_Hb8 zenon_H3f zenon_H1f zenon_Hf6 zenon_Hee zenon_H6f zenon_Had zenon_H23b zenon_H2a9 zenon_H2b0 zenon_H16f zenon_H101 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_H2b1 zenon_H20 zenon_H185 zenon_H4e zenon_H19e zenon_H156 zenon_H35 zenon_H1ab zenon_Hf4 zenon_H200 zenon_H69 zenon_H6e zenon_Hd1 zenon_H2b4 zenon_H16a zenon_H159 zenon_H14e zenon_H48 zenon_H218 zenon_H42 zenon_H13b zenon_H1bd zenon_Hc9 zenon_H100 zenon_H4c zenon_H19a. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.49 apply (zenon_L1618_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.49 apply (zenon_L763_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.49 apply (zenon_L1739_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.36/30.49 apply (zenon_L1774_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.36/30.49 exact (zenon_H13b zenon_Hfd). % 30.36/30.49 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.36/30.49 apply (zenon_L282_); trivial. % 30.36/30.49 apply (zenon_L1184_); trivial. % 30.36/30.49 (* end of lemma zenon_L1781_ *) % 30.36/30.49 assert (zenon_L1782_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.49 do 0 intro. intros zenon_H8d zenon_H64 zenon_H2d zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H20 zenon_H2b4 zenon_H16a zenon_H14e zenon_H48 zenon_H2b1 zenon_H185 zenon_H2b0 zenon_Hfc zenon_H18c zenon_H6c zenon_H296 zenon_H1dc zenon_Hbd zenon_H3c zenon_Hde zenon_Hb8 zenon_Hf6 zenon_Had zenon_H2a9 zenon_H16f zenon_H101 zenon_H4e zenon_H19e zenon_H35 zenon_Hf4 zenon_H200 zenon_Hd1 zenon_H218 zenon_H42 zenon_H1bd zenon_H100 zenon_H4c zenon_H172 zenon_He1 zenon_Hc9 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.49 apply (zenon_L148_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.49 apply (zenon_L1781_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.49 apply (zenon_L763_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.49 apply (zenon_L1477_); trivial. % 30.36/30.49 apply (zenon_L1478_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.49 apply (zenon_L273_); trivial. % 30.36/30.49 apply (zenon_L1187_); trivial. % 30.36/30.49 (* end of lemma zenon_L1782_ *) % 30.36/30.49 assert (zenon_L1783_ : ((op (e0) (e0)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.49 do 0 intro. intros zenon_H64 zenon_H102 zenon_H159 zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H20 zenon_H2b4 zenon_H16a zenon_H14e zenon_H48 zenon_H2b1 zenon_H185 zenon_H2b0 zenon_Hfc zenon_Had zenon_H90 zenon_H1bd zenon_H101 zenon_H225 zenon_H83 zenon_Haa zenon_He7 zenon_H42 zenon_Hd1 zenon_H301 zenon_H17d zenon_H1d8 zenon_H124 zenon_H10d zenon_H246 zenon_H19e zenon_H200 zenon_H218 zenon_Hbd zenon_H1dc zenon_H3c zenon_H2bd zenon_H35 zenon_Ha4 zenon_H296 zenon_H1d5 zenon_H222 zenon_Hf9 zenon_Hc8 zenon_H20e zenon_H1fd zenon_H1a5 zenon_H92 zenon_H84 zenon_H97 zenon_H16f zenon_H2d zenon_H4e zenon_H15a zenon_H8d zenon_Hd9 zenon_H4c zenon_H173 zenon_Hf6 zenon_Hcd zenon_H56 zenon_H135 zenon_H108 zenon_H20d zenon_H1e6 zenon_Hb8 zenon_H208 zenon_Hde zenon_H1b1 zenon_H14b zenon_H172 zenon_H174 zenon_He4 zenon_H18c zenon_H100 zenon_Hc0 zenon_H2b7 zenon_Hb5 zenon_H110 zenon_Hf4 zenon_H2a9 zenon_He1 zenon_Hc9 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.49 apply (zenon_L148_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.49 apply (zenon_L1737_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.49 apply (zenon_L273_); trivial. % 30.36/30.49 apply (zenon_L1187_); trivial. % 30.36/30.49 (* end of lemma zenon_L1783_ *) % 30.36/30.49 assert (zenon_L1784_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.36/30.49 do 0 intro. intros zenon_H296 zenon_H97 zenon_Hbd zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1dc zenon_Hfc zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_He1 zenon_Hcd zenon_Hde zenon_H208 zenon_H2bd zenon_Ha4 zenon_Hd9 zenon_H117 zenon_H8d zenon_H2d zenon_H6e zenon_H101 zenon_H1ab zenon_Hb8 zenon_H3f zenon_H1f zenon_Hf6 zenon_Hee zenon_H6f zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H23b zenon_H2a9 zenon_H14e zenon_H4e zenon_H2b0 zenon_H185 zenon_H20 zenon_H2b1 zenon_Hf4 zenon_H42 zenon_H218 zenon_H48 zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H69 zenon_H200 zenon_H35 zenon_H156 zenon_H6c zenon_H18c zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.49 apply (zenon_L1583_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.49 apply (zenon_L763_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.49 apply (zenon_L1481_); trivial. % 30.36/30.49 apply (zenon_L1775_); trivial. % 30.36/30.49 (* end of lemma zenon_L1784_ *) % 30.36/30.49 assert (zenon_L1785_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 30.36/30.49 do 0 intro. intros zenon_H296 zenon_H2d zenon_H42 zenon_H218 zenon_H48 zenon_H14e zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H6e zenon_H69 zenon_H200 zenon_Hf4 zenon_H1ab zenon_H35 zenon_He9 zenon_H156 zenon_H19e zenon_H4e zenon_H185 zenon_H20 zenon_H2b1 zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H13b zenon_H100. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.49 apply (zenon_L1451_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.49 apply (zenon_L763_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.49 apply (zenon_L1481_); trivial. % 30.36/30.49 apply (zenon_L1774_); trivial. % 30.36/30.49 (* end of lemma zenon_L1785_ *) % 30.36/30.49 assert (zenon_L1786_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.36/30.49 do 0 intro. intros zenon_H296 zenon_Hfc zenon_H15a zenon_Hd9 zenon_Hbd zenon_Hf9 zenon_He4 zenon_H173 zenon_H1b1 zenon_H174 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_H20e zenon_H1fd zenon_H1a5 zenon_H108 zenon_He1 zenon_H172 zenon_H3c zenon_H56 zenon_H135 zenon_H1d8 zenon_Hde zenon_H208 zenon_H2bd zenon_Ha4 zenon_H8d zenon_Hcd zenon_H2d zenon_H97 zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1dc zenon_H92 zenon_Hc9 zenon_H89 zenon_H101 zenon_H1ab zenon_Hb8 zenon_H3f zenon_H1f zenon_Hf6 zenon_Hee zenon_H6f zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H23b zenon_H2a9 zenon_H14e zenon_H4e zenon_H2b0 zenon_H185 zenon_H20 zenon_H2b1 zenon_Hf4 zenon_H42 zenon_H218 zenon_H48 zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H69 zenon_H200 zenon_H35 zenon_H156 zenon_H6c zenon_H18c zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.49 apply (zenon_L1617_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.49 apply (zenon_L763_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.49 apply (zenon_L1739_); trivial. % 30.36/30.49 apply (zenon_L1775_); trivial. % 30.36/30.49 (* end of lemma zenon_L1786_ *) % 30.36/30.49 assert (zenon_L1787_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.49 do 0 intro. intros zenon_H8d zenon_H117 zenon_Hd9 zenon_H4c zenon_H100 zenon_H1bd zenon_H13b zenon_H42 zenon_H218 zenon_H48 zenon_H14e zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H69 zenon_H200 zenon_Hf4 zenon_H35 zenon_H156 zenon_H19e zenon_H4e zenon_H185 zenon_H20 zenon_H2b1 zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H101 zenon_H16f zenon_H2b0 zenon_H2a9 zenon_Had zenon_Hf6 zenon_Hb8 zenon_Hde zenon_H3c zenon_Hbd zenon_H1dc zenon_H296 zenon_He1 zenon_Hc9 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.49 apply (zenon_L149_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.49 apply (zenon_L1781_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.49 apply (zenon_L273_); trivial. % 30.36/30.49 apply (zenon_L1187_); trivial. % 30.36/30.49 (* end of lemma zenon_L1787_ *) % 30.36/30.49 assert (zenon_L1788_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.36/30.49 do 0 intro. intros zenon_H296 zenon_H2d zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H222 zenon_H10d zenon_Hda zenon_H110 zenon_H2b7 zenon_Hf9 zenon_Hcd zenon_H89 zenon_H101 zenon_H1ab zenon_Hb8 zenon_H3f zenon_H1f zenon_Hf6 zenon_Hee zenon_H6f zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H23b zenon_H2a9 zenon_H14e zenon_H4e zenon_H2b0 zenon_H185 zenon_H20 zenon_H2b1 zenon_Hf4 zenon_H42 zenon_H218 zenon_H48 zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H69 zenon_H200 zenon_H35 zenon_H156 zenon_H6c zenon_H18c zenon_H16f zenon_H13b zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.49 apply (zenon_L1629_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.49 apply (zenon_L763_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.49 apply (zenon_L1739_); trivial. % 30.36/30.49 apply (zenon_L1775_); trivial. % 30.36/30.49 (* end of lemma zenon_L1788_ *) % 30.36/30.49 assert (zenon_L1789_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.49 do 0 intro. intros zenon_Hc0 zenon_H14b zenon_H1e6 zenon_H20d zenon_H108 zenon_H84 zenon_H1fd zenon_H20e zenon_Hf9 zenon_H222 zenon_H1d5 zenon_H246 zenon_H10d zenon_H124 zenon_H17d zenon_H301 zenon_H225 zenon_H101 zenon_H1bd zenon_Hb8 zenon_Hf6 zenon_H102 zenon_H4a zenon_Had zenon_H18f zenon_H13b zenon_H100 zenon_H2a9 zenon_H14e zenon_H4e zenon_H2b0 zenon_H185 zenon_H20 zenon_H2b1 zenon_Hf4 zenon_H42 zenon_H218 zenon_H35 zenon_H69 zenon_H48 zenon_H156 zenon_H19e zenon_H159 zenon_H16a zenon_H2b4 zenon_Hd1 zenon_H172 zenon_H90 zenon_Hfc zenon_H18c zenon_H200 zenon_H2d zenon_H16f zenon_H4c zenon_Hbd zenon_H110 zenon_Hb5 zenon_H2b7 zenon_H1dc zenon_H1a5 zenon_H1b1 zenon_H173 zenon_Hc8 zenon_H15a zenon_Hdc zenon_He7 zenon_Haa zenon_H92 zenon_H97 zenon_Hcd zenon_H8d zenon_Ha4 zenon_H2bd zenon_H208 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_He1 zenon_H174 zenon_Hd9 zenon_He4 zenon_H83 zenon_H296 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.49 apply (zenon_L538_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.49 apply (zenon_L1736_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.49 apply (zenon_L1741_); trivial. % 30.36/30.49 apply (zenon_L1187_); trivial. % 30.36/30.49 (* end of lemma zenon_L1789_ *) % 30.36/30.49 assert (zenon_L1790_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.49 do 0 intro. intros zenon_H2b1 zenon_H16a zenon_Hfc zenon_Hed zenon_H3d zenon_H4e zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_H19e zenon_H1ba zenon_H102 zenon_H1ab. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.36/30.49 apply (zenon_L1716_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.36/30.49 apply (zenon_L731_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.36/30.49 apply (zenon_L1480_); trivial. % 30.36/30.49 exact (zenon_H1ab zenon_H112). % 30.36/30.49 (* end of lemma zenon_L1790_ *) % 30.36/30.49 assert (zenon_L1791_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 30.36/30.49 do 0 intro. intros zenon_H296 zenon_H92 zenon_H1dc zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H97 zenon_H16f zenon_H23b zenon_Hcd zenon_H3f zenon_Hee zenon_Ha4 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H4c zenon_He1 zenon_H2a9 zenon_H108 zenon_H1fd zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H174 zenon_H1b1 zenon_He4 zenon_Hf9 zenon_Hbd zenon_H15a zenon_Hc0 zenon_H173 zenon_Hc9 zenon_H2d zenon_H200 zenon_H90 zenon_H6f zenon_H172 zenon_Had zenon_H2b0 zenon_H19a zenon_H185 zenon_H20 zenon_H18c zenon_H14e zenon_H2b4 zenon_H159 zenon_Hd9 zenon_H8d zenon_H1ab zenon_H13b zenon_H4a zenon_Hfc zenon_H16a zenon_H2b1 zenon_H19e zenon_H18f zenon_H100 zenon_H102 zenon_H156 zenon_H48 zenon_H6e zenon_Hf4 zenon_H69 zenon_Hd1 zenon_H35 zenon_H218 zenon_H42 zenon_H4e zenon_H117 zenon_H1a5. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.49 apply (zenon_L1602_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.49 apply (zenon_L769_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.36/30.49 apply (zenon_L1481_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.36/30.49 apply (zenon_L142_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.36/30.49 exact (zenon_H13b zenon_Hfd). % 30.36/30.49 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.36/30.49 apply (zenon_L1707_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.36/30.49 apply (zenon_L513_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.49 apply (zenon_L1699_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.49 apply (zenon_L1790_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.49 apply (zenon_L1708_); trivial. % 30.36/30.49 apply (zenon_L737_); trivial. % 30.36/30.49 apply (zenon_L766_); trivial. % 30.36/30.49 apply (zenon_L828_); trivial. % 30.36/30.49 (* end of lemma zenon_L1791_ *) % 30.36/30.49 assert (zenon_L1792_ : ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.36/30.49 do 0 intro. intros zenon_H1f zenon_H90 zenon_H6f zenon_Hc9 zenon_He1 zenon_H296 zenon_H92 zenon_H1dc zenon_H2b7 zenon_Hb5 zenon_H110 zenon_H97 zenon_H16f zenon_H23b zenon_Hcd zenon_H3f zenon_Hee zenon_Ha4 zenon_H2bd zenon_H208 zenon_Hf6 zenon_Hde zenon_H1d8 zenon_H135 zenon_H56 zenon_H3c zenon_H4c zenon_H2a9 zenon_H108 zenon_H1fd zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H174 zenon_H1b1 zenon_He4 zenon_Hf9 zenon_Hbd zenon_H15a zenon_Hc0 zenon_H173 zenon_H200 zenon_H172 zenon_Had zenon_H2b0 zenon_H19a zenon_H20 zenon_H18c zenon_H14e zenon_H2b4 zenon_H159 zenon_Hd9 zenon_H8d zenon_H1ab zenon_H13b zenon_H4a zenon_Hfc zenon_H16a zenon_H2b1 zenon_H19e zenon_H18f zenon_H100 zenon_H102 zenon_H156 zenon_H48 zenon_Hf4 zenon_H69 zenon_Hd1 zenon_H35 zenon_H218 zenon_H42 zenon_H4e zenon_H1a5 zenon_H185 zenon_H2d. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.36/30.49 apply (zenon_L538_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.49 apply (zenon_L538_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.49 apply (zenon_L1707_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.49 apply (zenon_L273_); trivial. % 30.36/30.49 apply (zenon_L1187_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.49 apply (zenon_L149_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.49 apply (zenon_L1791_); trivial. % 30.36/30.49 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.49 apply (zenon_L273_); trivial. % 30.36/30.49 apply (zenon_L39_); trivial. % 30.36/30.49 apply (zenon_L848_); trivial. % 30.36/30.49 (* end of lemma zenon_L1792_ *) % 30.36/30.49 assert (zenon_L1793_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H6c zenon_H18c zenon_H1ab zenon_H102 zenon_Hfc zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H2b0 zenon_H19a zenon_H185 zenon_H20 zenon_H2b1 zenon_H4e zenon_H89 zenon_H15a. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.50 apply (zenon_L740_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.50 apply (zenon_L763_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.50 apply (zenon_L1477_); trivial. % 30.36/30.50 apply (zenon_L744_); trivial. % 30.36/30.50 (* end of lemma zenon_L1793_ *) % 30.36/30.50 assert (zenon_L1794_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 30.36/30.50 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H6c zenon_H1ab zenon_H102 zenon_Hfc zenon_H18f zenon_H13b zenon_H156 zenon_H4a zenon_H2b0 zenon_H19a zenon_H185 zenon_H20 zenon_H2b1 zenon_H18c zenon_H4e zenon_H76. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.36/30.50 apply (zenon_L740_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.36/30.50 apply (zenon_L763_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.36/30.50 apply (zenon_L1477_); trivial. % 30.36/30.50 apply (zenon_L864_); trivial. % 30.36/30.50 (* end of lemma zenon_L1794_ *) % 30.36/30.50 assert (zenon_L1795_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H8d zenon_H15a zenon_H159 zenon_H2b4 zenon_H16a zenon_H14e zenon_H4e zenon_H18c zenon_H2b1 zenon_H20 zenon_H185 zenon_H2b0 zenon_H4a zenon_H156 zenon_H13b zenon_H18f zenon_Hfc zenon_H102 zenon_H6c zenon_H48 zenon_Hdf zenon_H172 zenon_H23b zenon_H6f zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H1ab. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.36/30.50 apply (zenon_L1793_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.36/30.50 apply (zenon_L1479_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.36/30.50 apply (zenon_L1794_); trivial. % 30.36/30.50 apply (zenon_L1187_); trivial. % 30.36/30.50 (* end of lemma zenon_L1795_ *) % 30.36/30.50 assert (zenon_L1796_ : (((op (e0) (op (e0) (e0))) = (e0))/\(((op (e0) (op (e0) (e1))) = (e1))/\(((op (e0) (op (e0) (e2))) = (e2))/\(((op (e0) (op (e0) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1)))/\(((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2)))/\((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3)))))))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H2ec zenon_He7 zenon_H30a zenon_H16a zenon_H89 zenon_H218 zenon_H2b4. % 30.36/30.50 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.36/30.50 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.36/30.50 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.36/30.50 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.36/30.50 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.36/30.50 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.36/30.50 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.36/30.50 exact (zenon_H30a zenon_H185). % 30.36/30.50 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.36/30.50 apply (zenon_L1562_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.36/30.50 apply (zenon_L1563_); trivial. % 30.36/30.50 exact (zenon_H122 zenon_Hb1). % 30.36/30.50 apply (zenon_L199_); trivial. % 30.36/30.50 (* end of lemma zenon_L1796_ *) % 30.36/30.50 assert (zenon_L1797_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H102 zenon_H35 zenon_H1e zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.36/30.50 apply (zenon_L42_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.36/30.50 apply (zenon_L1131_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.36/30.50 exact (zenon_H13b zenon_Hfd). % 30.36/30.50 exact (zenon_H103 zenon_H37). % 30.36/30.50 (* end of lemma zenon_L1797_ *) % 30.36/30.50 assert (zenon_L1798_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H1d5 zenon_H6b zenon_H103 zenon_Hd1 zenon_Hdc zenon_H182 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H1c7 zenon_H60 zenon_H1af zenon_Hd6 zenon_H102 zenon_Hf5 zenon_He1. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.36/30.50 apply (zenon_L193_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.36/30.50 apply (zenon_L144_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.36/30.50 apply (zenon_L348_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.36/30.50 apply (zenon_L1131_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.36/30.50 apply (zenon_L154_); trivial. % 30.36/30.50 exact (zenon_H103 zenon_H37). % 30.36/30.50 apply (zenon_L221_); trivial. % 30.36/30.50 (* end of lemma zenon_L1798_ *) % 30.36/30.50 assert (zenon_L1799_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H135 zenon_H18c zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_H103 zenon_Hd1 zenon_Hdc zenon_H182 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H1c7 zenon_H60 zenon_H1af zenon_Hd6 zenon_H102 zenon_He1. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.36/30.50 apply (zenon_L142_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.36/30.50 apply (zenon_L88_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.36/30.50 exact (zenon_Hd0 zenon_Hcc). % 30.36/30.50 apply (zenon_L1798_); trivial. % 30.36/30.50 (* end of lemma zenon_L1799_ *) % 30.36/30.50 assert (zenon_L1800_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H16f zenon_H89 zenon_H15a zenon_H103 zenon_H20e zenon_H1af zenon_Hd0 zenon_He9 zenon_H3c zenon_H1d8 zenon_He2 zenon_H135 zenon_H182 zenon_H6f. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.50 apply (zenon_L241_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.50 exact (zenon_H103 zenon_H37). % 30.36/30.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.50 apply (zenon_L591_); trivial. % 30.36/30.50 apply (zenon_L758_); trivial. % 30.36/30.50 (* end of lemma zenon_L1800_ *) % 30.36/30.50 assert (zenon_L1801_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H225 zenon_H6f zenon_H182 zenon_H1d8 zenon_H3c zenon_H1af zenon_H20e zenon_H103 zenon_H15a zenon_H16f zenon_H18c zenon_H6b zenon_Hd1 zenon_H159 zenon_H1ca zenon_H19e zenon_H6c zenon_H5e zenon_H1c7 zenon_Hd6 zenon_H102 zenon_He4 zenon_Hde zenon_H135 zenon_H10e zenon_H5c zenon_H108 zenon_H26 zenon_H27 zenon_H1bd zenon_H60 zenon_H1d2 zenon_He1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hd0 zenon_H218. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.36/30.50 apply (zenon_L232_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.36/30.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.50 apply (zenon_L232_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.50 apply (zenon_L1799_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.50 apply (zenon_L191_); trivial. % 30.36/30.50 apply (zenon_L1800_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.36/30.50 apply (zenon_L192_); trivial. % 30.36/30.50 apply (zenon_L636_); trivial. % 30.36/30.50 (* end of lemma zenon_L1801_ *) % 30.36/30.50 assert (zenon_L1802_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (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) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H267 zenon_H218 zenon_H1b9 zenon_Heb zenon_He1 zenon_H60 zenon_H156 zenon_H19a zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_Hc9 zenon_H20d zenon_H231. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.36/30.50 apply (zenon_L259_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.36/30.50 apply (zenon_L237_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.36/30.50 apply (zenon_L627_); trivial. % 30.36/30.50 exact (zenon_H231 zenon_Hf4). % 30.36/30.50 (* end of lemma zenon_L1802_ *) % 30.36/30.50 assert (zenon_L1803_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.36/30.50 do 0 intro. intros zenon_Hf9 zenon_H1d8 zenon_He9 zenon_H3f zenon_H20d zenon_Hc9 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_H156 zenon_H60 zenon_He1 zenon_H1b9 zenon_H218 zenon_H267 zenon_H231. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.36/30.50 apply (zenon_L307_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.36/30.50 apply (zenon_L53_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.36/30.50 apply (zenon_L1802_); trivial. % 30.36/30.50 exact (zenon_H231 zenon_Hf4). % 30.36/30.50 (* end of lemma zenon_L1803_ *) % 30.36/30.50 assert (zenon_L1804_ : (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H231 zenon_H267 zenon_H218 zenon_H60 zenon_H156 zenon_H19a zenon_H10e zenon_H2d zenon_H1fd zenon_Hc9 zenon_H20d zenon_H1d8 zenon_H23b zenon_H89 zenon_He1 zenon_He9 zenon_Hcd zenon_Hf9 zenon_H1f zenon_H3f zenon_H6f zenon_H182 zenon_H14e. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.36/30.50 apply (zenon_L87_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.36/30.50 apply (zenon_L235_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.36/30.50 apply (zenon_L1803_); trivial. % 30.36/30.50 apply (zenon_L541_); trivial. % 30.36/30.50 (* end of lemma zenon_L1804_ *) % 30.36/30.50 assert (zenon_L1805_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H16f zenon_H68 zenon_H103 zenon_H19a zenon_H182 zenon_H6f. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.36/30.50 apply (zenon_L18_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.36/30.50 exact (zenon_H103 zenon_H37). % 30.36/30.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.36/30.50 apply (zenon_L235_); trivial. % 30.36/30.50 apply (zenon_L758_); trivial. % 30.36/30.50 (* end of lemma zenon_L1805_ *) % 30.36/30.50 assert (zenon_L1806_ : ((op (e3) (e2)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 30.36/30.50 do 0 intro. intros zenon_Hb6 zenon_H40 zenon_H30b. % 30.36/30.50 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 30.36/30.50 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e1)) = (op (e3) (e2)))). % 30.36/30.50 intro zenon_D_pnotp. % 30.36/30.50 apply zenon_H30b. % 30.36/30.50 rewrite <- zenon_D_pnotp. % 30.36/30.50 exact zenon_Hef. % 30.36/30.50 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 30.36/30.50 cut (((op (e3) (e2)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H30c]. % 30.36/30.50 congruence. % 30.36/30.50 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e1)))). % 30.36/30.50 intro zenon_D_pnotp. % 30.36/30.50 apply zenon_H30c. % 30.36/30.50 rewrite <- zenon_D_pnotp. % 30.36/30.50 exact zenon_Hb6. % 30.36/30.50 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 30.36/30.50 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 30.36/30.50 congruence. % 30.36/30.50 apply zenon_Hf0. apply refl_equal. % 30.36/30.50 apply zenon_H41. apply sym_equal. exact zenon_H40. % 30.36/30.50 apply zenon_Hf0. apply refl_equal. % 30.36/30.50 apply zenon_Hf0. apply refl_equal. % 30.36/30.50 (* end of lemma zenon_L1806_ *) % 30.36/30.50 assert (zenon_L1807_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H1ca zenon_Hc3 zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H9d zenon_H222 zenon_H1af zenon_H1c5 zenon_H1c7. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1cb ]. % 30.36/30.50 apply (zenon_L347_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H1cc ]. % 30.36/30.50 apply (zenon_L163_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H55 | zenon_intro zenon_H3d ]. % 30.36/30.50 apply (zenon_L264_); trivial. % 30.36/30.50 apply (zenon_L167_); trivial. % 30.36/30.50 (* end of lemma zenon_L1807_ *) % 30.36/30.50 assert (zenon_L1808_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H102 zenon_H1c7 zenon_H1c5 zenon_H1af zenon_H222 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H9d zenon_H100 zenon_H103. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.36/30.50 apply (zenon_L1807_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.36/30.50 apply (zenon_L1131_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.36/30.50 apply (zenon_L60_); trivial. % 30.36/30.50 exact (zenon_H103 zenon_H37). % 30.36/30.50 (* end of lemma zenon_L1808_ *) % 30.36/30.50 assert (zenon_L1809_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.36/30.50 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_H103 zenon_H100 zenon_H182 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H222 zenon_H1af zenon_H1c5 zenon_H1c7 zenon_H102 zenon_Hb6 zenon_He1 zenon_H90 zenon_H89. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.36/30.50 apply (zenon_L386_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.36/30.50 apply (zenon_L1808_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.36/30.50 apply (zenon_L204_); trivial. % 30.36/30.50 apply (zenon_L538_); trivial. % 30.36/30.50 (* end of lemma zenon_L1809_ *) % 30.36/30.50 assert (zenon_L1810_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hd0 zenon_Hdc zenon_H18c zenon_H135 zenon_H55 zenon_H60 zenon_H23b zenon_H89 zenon_He1 zenon_Hb6 zenon_H102 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H100 zenon_H103 zenon_Hcd zenon_Hf9 zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H182 zenon_H14e. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.36/30.50 apply (zenon_L332_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.36/30.50 apply (zenon_L145_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.36/30.50 apply (zenon_L216_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.36/30.50 apply (zenon_L1809_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.36/30.50 apply (zenon_L336_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.36/30.50 apply (zenon_L337_); trivial. % 30.36/30.50 apply (zenon_L137_); trivial. % 30.36/30.50 (* end of lemma zenon_L1810_ *) % 30.36/30.50 assert (zenon_L1811_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.36/30.50 do 0 intro. intros zenon_H208 zenon_H14e zenon_Hee zenon_H3f zenon_H1f zenon_Hf9 zenon_H103 zenon_H100 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H102 zenon_Hb6 zenon_He1 zenon_H89 zenon_H23b zenon_H60 zenon_H135 zenon_H18c zenon_Hdc zenon_Hd0 zenon_Hd6 zenon_Hc8 zenon_H1d5 zenon_H55 zenon_Hcd zenon_H20e zenon_H19a zenon_H156 zenon_H182. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.36/30.50 apply (zenon_L1810_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.36/30.50 apply (zenon_L212_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.36/30.50 apply (zenon_L225_); trivial. % 30.36/30.50 apply (zenon_L934_); trivial. % 30.36/30.50 (* end of lemma zenon_L1811_ *) % 30.36/30.50 assert (zenon_L1812_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H102 zenon_H1ba zenon_H19e zenon_H159 zenon_H182 zenon_H9d zenon_H100 zenon_H103. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.36/30.50 apply (zenon_L347_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.36/30.50 apply (zenon_L1131_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.36/30.50 apply (zenon_L60_); trivial. % 30.36/30.50 exact (zenon_H103 zenon_H37). % 30.36/30.50 (* end of lemma zenon_L1812_ *) % 30.36/30.50 assert (zenon_L1813_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H23b zenon_H20 zenon_H8b zenon_H1f zenon_H3f zenon_Hb6 zenon_H6f zenon_H182 zenon_H14e. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.36/30.50 apply (zenon_L27_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.36/30.50 apply (zenon_L336_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.36/30.50 apply (zenon_L540_); trivial. % 30.36/30.50 apply (zenon_L137_); trivial. % 30.36/30.50 (* end of lemma zenon_L1813_ *) % 30.36/30.50 assert (zenon_L1814_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H182 zenon_H156 zenon_H142 zenon_H60 zenon_H20d zenon_H1af zenon_H16b zenon_H218. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.36/30.50 apply (zenon_L690_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.36/30.50 apply (zenon_L934_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.36/30.50 apply (zenon_L223_); trivial. % 30.36/30.50 apply (zenon_L245_); trivial. % 30.36/30.50 (* end of lemma zenon_L1814_ *) % 30.36/30.50 assert (zenon_L1815_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H30d zenon_H218 zenon_H20d zenon_H60 zenon_H142 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H6f zenon_H182 zenon_H1c7 zenon_H1af zenon_H222 zenon_H9d zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_Hb1 zenon_H2d. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H30d); [ zenon_intro zenon_H16b | zenon_intro zenon_H30e ]. % 30.36/30.50 apply (zenon_L1814_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H16c | zenon_intro zenon_H30f ]. % 30.36/30.50 apply (zenon_L758_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H1c5 | zenon_intro zenon_Hbc ]. % 30.36/30.50 apply (zenon_L1807_); trivial. % 30.36/30.50 apply (zenon_L107_); trivial. % 30.36/30.50 (* end of lemma zenon_L1815_ *) % 30.36/30.50 assert (zenon_L1816_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_Hbd zenon_H14e zenon_H3f zenon_H1f zenon_H20 zenon_H23b zenon_H100 zenon_Hb6 zenon_H30d zenon_H218 zenon_H20d zenon_H60 zenon_H142 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H6f zenon_H182 zenon_H1c7 zenon_H1af zenon_H222 zenon_H9d zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H2d. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.36/30.50 apply (zenon_L1813_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.36/30.50 apply (zenon_L1497_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.36/30.50 apply (zenon_L304_); trivial. % 30.36/30.50 apply (zenon_L1815_); trivial. % 30.36/30.50 (* end of lemma zenon_L1816_ *) % 30.36/30.50 assert (zenon_L1817_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.36/30.50 do 0 intro. intros zenon_H125 zenon_Hde zenon_H10e zenon_Hfd zenon_Hfc zenon_Hd0 zenon_He1 zenon_Hb6. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.36/30.50 apply (zenon_L192_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.36/30.50 apply (zenon_L58_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.36/30.50 exact (zenon_Hd0 zenon_Hcc). % 30.36/30.50 apply (zenon_L204_); trivial. % 30.36/30.50 (* end of lemma zenon_L1817_ *) % 30.36/30.50 assert (zenon_L1818_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.36/30.50 do 0 intro. intros zenon_Hc0 zenon_H89 zenon_H14e zenon_H6f zenon_Hb6 zenon_H3f zenon_H8b zenon_H20 zenon_H23b zenon_H1a5 zenon_H19a zenon_H182 zenon_H16a. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.36/30.50 apply (zenon_L734_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.36/30.50 apply (zenon_L1813_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.36/30.50 apply (zenon_L136_); trivial. % 30.36/30.50 apply (zenon_L115_); trivial. % 30.36/30.50 (* end of lemma zenon_L1818_ *) % 30.36/30.50 assert (zenon_L1819_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H102 zenon_H95 zenon_H159 zenon_H182 zenon_H9d zenon_H100 zenon_H103. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.36/30.50 apply (zenon_L1497_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.36/30.50 apply (zenon_L1131_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.36/30.50 apply (zenon_L60_); trivial. % 30.36/30.50 exact (zenon_H103 zenon_H37). % 30.36/30.50 (* end of lemma zenon_L1819_ *) % 30.36/30.50 assert (zenon_L1820_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H101 zenon_H14e zenon_H6f zenon_Hb6 zenon_H3f zenon_H1f zenon_Hf9 zenon_Hcd zenon_He1 zenon_H89 zenon_H23b zenon_Hed zenon_Hfc zenon_H1bd zenon_Hc9 zenon_H102 zenon_H95 zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.36/30.50 apply (zenon_L541_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.36/30.50 apply (zenon_L58_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.36/30.50 apply (zenon_L282_); trivial. % 30.36/30.50 apply (zenon_L1819_); trivial. % 30.36/30.50 (* end of lemma zenon_L1820_ *) % 30.36/30.50 assert (zenon_L1821_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.36/30.50 do 0 intro. intros zenon_Hbd zenon_H16a zenon_H19a zenon_H1a5 zenon_H20 zenon_Hc0 zenon_H103 zenon_H100 zenon_H182 zenon_H159 zenon_H102 zenon_Hc9 zenon_H1bd zenon_Hfc zenon_Hed zenon_H23b zenon_H89 zenon_He1 zenon_Hcd zenon_Hf9 zenon_H1f zenon_H3f zenon_Hb6 zenon_H6f zenon_H14e zenon_H101 zenon_H10e zenon_H10d zenon_Hf6 zenon_H1e1. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.36/30.50 apply (zenon_L1818_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.36/30.50 apply (zenon_L1820_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.36/30.50 apply (zenon_L63_); trivial. % 30.36/30.50 apply (zenon_L690_); trivial. % 30.36/30.50 (* end of lemma zenon_L1821_ *) % 30.36/30.50 assert (zenon_L1822_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hd0 zenon_H125 zenon_Hf6 zenon_H10d zenon_H10e zenon_H101 zenon_H14e zenon_H6f zenon_Hb6 zenon_H3f zenon_H1f zenon_Hf9 zenon_He1 zenon_H89 zenon_H23b zenon_Hfc zenon_H1bd zenon_Hc9 zenon_H102 zenon_H159 zenon_H100 zenon_H103 zenon_Hc0 zenon_H20 zenon_H1a5 zenon_H19a zenon_H16a zenon_Hbd zenon_H30d zenon_H218 zenon_H20d zenon_H60 zenon_H156 zenon_H1e6 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H6c zenon_H19e zenon_Hc3 zenon_H1ca zenon_H2d zenon_Hde zenon_H200 zenon_H182 zenon_Hcd. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.36/30.50 apply (zenon_L142_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.36/30.50 apply (zenon_L1817_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.36/30.50 apply (zenon_L541_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.36/30.50 apply (zenon_L58_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.36/30.50 apply (zenon_L282_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.50 apply (zenon_L49_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.50 apply (zenon_L1812_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.50 apply (zenon_L1816_); trivial. % 30.36/30.50 apply (zenon_L1821_); trivial. % 30.36/30.50 apply (zenon_L1135_); trivial. % 30.36/30.50 (* end of lemma zenon_L1822_ *) % 30.36/30.50 assert (zenon_L1823_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.36/30.50 do 0 intro. intros zenon_H135 zenon_Hcd zenon_H182 zenon_H200 zenon_H2d zenon_H1ca zenon_Hc3 zenon_H19e zenon_H6c zenon_H5e zenon_H1af zenon_H1c7 zenon_H1e6 zenon_H156 zenon_H60 zenon_H20d zenon_H218 zenon_H30d zenon_Hbd zenon_H16a zenon_H19a zenon_H1a5 zenon_H20 zenon_Hc0 zenon_H103 zenon_H100 zenon_H159 zenon_H102 zenon_H1bd zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H1f zenon_H3f zenon_Hb6 zenon_H6f zenon_H14e zenon_H101 zenon_H10e zenon_H10d zenon_Hf6 zenon_H125 zenon_H18c zenon_H173 zenon_H9d zenon_H222 zenon_Hd0 zenon_Hde zenon_H1e1. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.36/30.50 apply (zenon_L1822_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.36/30.50 apply (zenon_L264_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.36/30.50 exact (zenon_Hd0 zenon_Hcc). % 30.36/30.50 apply (zenon_L294_); trivial. % 30.36/30.50 (* end of lemma zenon_L1823_ *) % 30.36/30.50 assert (zenon_L1824_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H101 zenon_H6f zenon_Hd1 zenon_H14e zenon_Hee zenon_H19a zenon_H3f zenon_H1f zenon_Hf9 zenon_Hcd zenon_H1ca zenon_H1bd zenon_H6c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_Hb6 zenon_He1 zenon_H89 zenon_H23b zenon_H60 zenon_H135 zenon_H18c zenon_Hdc zenon_Hd0 zenon_Hd6 zenon_Hc8 zenon_H1d5 zenon_H102 zenon_H1ba zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.36/30.50 apply (zenon_L541_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.36/30.50 apply (zenon_L154_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.36/30.50 apply (zenon_L1810_); trivial. % 30.36/30.50 apply (zenon_L1812_); trivial. % 30.36/30.50 (* end of lemma zenon_L1824_ *) % 30.36/30.50 assert (zenon_L1825_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.36/30.50 do 0 intro. intros zenon_H30d zenon_H218 zenon_H20d zenon_H60 zenon_H142 zenon_H156 zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H6f zenon_H103 zenon_H100 zenon_H9d zenon_H182 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H102 zenon_H110 zenon_Hb6. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H30d); [ zenon_intro zenon_H16b | zenon_intro zenon_H30e ]. % 30.36/30.50 apply (zenon_L1814_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H16c | zenon_intro zenon_H30f ]. % 30.36/30.50 apply (zenon_L758_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H1c5 | zenon_intro zenon_Hbc ]. % 30.36/30.50 apply (zenon_L1808_); trivial. % 30.36/30.50 apply (zenon_L1303_); trivial. % 30.36/30.50 (* end of lemma zenon_L1825_ *) % 30.36/30.50 assert (zenon_L1826_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.36/30.50 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H90 zenon_H103 zenon_H100 zenon_H9d zenon_H182 zenon_H159 zenon_H102 zenon_Hb6 zenon_H2d zenon_Hf6 zenon_H1e1. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.36/30.50 apply (zenon_L27_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.36/30.50 apply (zenon_L1819_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.36/30.50 apply (zenon_L304_); trivial. % 30.36/30.50 apply (zenon_L690_); trivial. % 30.36/30.50 (* end of lemma zenon_L1826_ *) % 30.36/30.50 assert (zenon_L1827_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H200 zenon_H17b zenon_Hd0 zenon_Hde zenon_H135 zenon_H156 zenon_H222 zenon_H60 zenon_H5e zenon_H1f zenon_H3c zenon_H1dc zenon_H30d zenon_H218 zenon_H20d zenon_H1e6 zenon_H6f zenon_H1ca zenon_H19e zenon_H1bd zenon_H1af zenon_H1c7 zenon_H110 zenon_H208 zenon_Hbd zenon_H20 zenon_H90 zenon_H103 zenon_H100 zenon_H9d zenon_H182 zenon_H159 zenon_H102 zenon_Hb6 zenon_H2d zenon_Hf6. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.36/30.50 apply (zenon_L406_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.36/30.50 apply (zenon_L1812_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.36/30.50 apply (zenon_L27_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.36/30.50 apply (zenon_L1819_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.36/30.50 apply (zenon_L177_); trivial. % 30.36/30.50 apply (zenon_L1825_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.36/30.50 apply (zenon_L218_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.36/30.50 apply (zenon_L256_); trivial. % 30.36/30.50 apply (zenon_L934_); trivial. % 30.36/30.50 apply (zenon_L1826_); trivial. % 30.36/30.50 (* end of lemma zenon_L1827_ *) % 30.36/30.50 assert (zenon_L1828_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H173 zenon_H18c zenon_H10e zenon_H125 zenon_Hf6 zenon_H2d zenon_Hb6 zenon_H102 zenon_H159 zenon_H100 zenon_H103 zenon_H90 zenon_H20 zenon_Hbd zenon_H208 zenon_H110 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_H1ca zenon_H6f zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H1dc zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H156 zenon_H135 zenon_Hde zenon_Hd0 zenon_H17b zenon_H200 zenon_Hc9 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H182 zenon_Hcd. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.36/30.50 apply (zenon_L142_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.36/30.50 apply (zenon_L1817_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.36/30.50 apply (zenon_L541_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.36/30.50 apply (zenon_L58_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.36/30.50 apply (zenon_L282_); trivial. % 30.36/30.50 apply (zenon_L1827_); trivial. % 30.36/30.50 apply (zenon_L1135_); trivial. % 30.36/30.50 (* end of lemma zenon_L1828_ *) % 30.36/30.50 assert (zenon_L1829_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.36/30.50 do 0 intro. intros zenon_H225 zenon_He4 zenon_Hee zenon_Hd6 zenon_Hc8 zenon_H1d5 zenon_H20e zenon_H19a zenon_H182 zenon_H101 zenon_H14e zenon_H3f zenon_Hf9 zenon_He1 zenon_H89 zenon_H23b zenon_Hfc zenon_H200 zenon_Hd0 zenon_Hde zenon_H135 zenon_H156 zenon_H222 zenon_H60 zenon_H5e zenon_H1f zenon_H3c zenon_H1dc zenon_H30d zenon_H218 zenon_H20d zenon_H1e6 zenon_H6f zenon_H1ca zenon_H19e zenon_H1bd zenon_H1af zenon_H1c7 zenon_H110 zenon_H208 zenon_Hbd zenon_H20 zenon_H103 zenon_H100 zenon_H159 zenon_H102 zenon_Hb6 zenon_H2d zenon_Hf6 zenon_H125 zenon_H10e zenon_H18c zenon_H173 zenon_H90 zenon_Hcd. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.36/30.50 apply (zenon_L232_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.36/30.50 apply (zenon_L541_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.36/30.50 apply (zenon_L192_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.50 apply (zenon_L232_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.36/30.50 apply (zenon_L541_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.36/30.50 apply (zenon_L1817_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.36/30.50 apply (zenon_L1811_); trivial. % 30.36/30.50 apply (zenon_L1827_); trivial. % 30.36/30.50 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.36/30.50 apply (zenon_L1828_); trivial. % 30.36/30.50 apply (zenon_L386_); trivial. % 30.36/30.50 (* end of lemma zenon_L1829_ *) % 30.36/30.51 assert (zenon_L1830_ : (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.36/30.51 do 0 intro. intros zenon_Hcd zenon_H173 zenon_H18c zenon_H10e zenon_H125 zenon_Hf6 zenon_H2d zenon_Hb6 zenon_H102 zenon_H159 zenon_H100 zenon_H103 zenon_H20 zenon_Hbd zenon_H208 zenon_H110 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_H1ca zenon_H6f zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H1dc zenon_H3c zenon_H5e zenon_H60 zenon_H222 zenon_H156 zenon_H135 zenon_Hde zenon_Hd0 zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H20e zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H10d zenon_H16f zenon_H92 zenon_H1a5 zenon_H19a zenon_H182 zenon_H16a. % 30.36/30.51 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.36/30.51 apply (zenon_L734_); trivial. % 30.36/30.51 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.36/30.51 apply (zenon_L734_); trivial. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.36/30.51 apply (zenon_L1805_); trivial. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.36/30.51 apply (zenon_L232_); trivial. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.36/30.51 apply (zenon_L541_); trivial. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.36/30.51 apply (zenon_L192_); trivial. % 30.36/30.51 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.36/30.51 apply (zenon_L232_); trivial. % 30.36/30.51 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.36/30.51 apply (zenon_L4_); trivial. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.36/30.51 exact (zenon_H103 zenon_H37). % 30.36/30.51 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.36/30.51 apply (zenon_L145_); trivial. % 30.36/30.51 apply (zenon_L1806_); trivial. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.36/30.51 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.51 apply (zenon_L541_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.51 apply (zenon_L154_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.51 apply (zenon_L1811_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.51 apply (zenon_L406_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.51 apply (zenon_L1812_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.51 apply (zenon_L1816_); trivial. % 30.42/30.51 apply (zenon_L1823_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.51 apply (zenon_L1824_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.51 apply (zenon_L541_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.51 apply (zenon_L1817_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.51 apply (zenon_L1810_); trivial. % 30.42/30.51 apply (zenon_L1819_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.42/30.51 apply (zenon_L142_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.42/30.51 apply (zenon_L1817_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.51 apply (zenon_L541_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.51 apply (zenon_L58_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.51 apply (zenon_L282_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.51 apply (zenon_L406_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.51 apply (zenon_L1812_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.51 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.42/30.51 apply (zenon_L1818_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.42/30.51 apply (zenon_L1819_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.42/30.51 apply (zenon_L177_); trivial. % 30.42/30.51 apply (zenon_L1825_); trivial. % 30.42/30.51 apply (zenon_L1821_); trivial. % 30.42/30.51 apply (zenon_L1135_); trivial. % 30.42/30.51 apply (zenon_L387_); trivial. % 30.42/30.51 apply (zenon_L1829_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.42/30.51 apply (zenon_L136_); trivial. % 30.42/30.51 apply (zenon_L115_); trivial. % 30.42/30.51 (* end of lemma zenon_L1830_ *) % 30.42/30.51 assert (zenon_L1831_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.42/30.51 do 0 intro. intros zenon_H1fd zenon_H17b zenon_Hcd zenon_H173 zenon_H18c zenon_H10e zenon_H125 zenon_Hf6 zenon_H2d zenon_H102 zenon_H159 zenon_H100 zenon_H103 zenon_H20 zenon_Hbd zenon_H208 zenon_H110 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_H1ca zenon_H6f zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H1dc zenon_H3c zenon_H5e zenon_H60 zenon_H222 zenon_H156 zenon_H135 zenon_Hde zenon_Hd0 zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H20e zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H10d zenon_H16f zenon_H92 zenon_H1a5 zenon_H19a zenon_H182 zenon_H16a. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.42/30.51 apply (zenon_L87_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.42/30.51 apply (zenon_L235_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.42/30.51 apply (zenon_L259_); trivial. % 30.42/30.51 apply (zenon_L1830_); trivial. % 30.42/30.51 (* end of lemma zenon_L1831_ *) % 30.42/30.51 assert (zenon_L1832_ : ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.42/30.51 do 0 intro. intros zenon_H1f zenon_H231 zenon_H267 zenon_H1d8 zenon_H6b zenon_H6c zenon_H1fd zenon_Hcd zenon_H173 zenon_H18c zenon_H10e zenon_H125 zenon_Hf6 zenon_H2d zenon_H102 zenon_H159 zenon_H100 zenon_H103 zenon_H20 zenon_Hbd zenon_H208 zenon_H110 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_H1ca zenon_H6f zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H1dc zenon_H3c zenon_H5e zenon_H60 zenon_H222 zenon_H156 zenon_H135 zenon_Hde zenon_Hd0 zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H20e zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H10d zenon_H16f zenon_H92 zenon_H1a5 zenon_H19a zenon_H182 zenon_H16a. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.51 apply (zenon_L232_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.51 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.51 apply (zenon_L232_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.51 apply (zenon_L1799_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.51 apply (zenon_L1804_); trivial. % 30.42/30.51 apply (zenon_L387_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.51 apply (zenon_L192_); trivial. % 30.42/30.51 apply (zenon_L1831_); trivial. % 30.42/30.51 (* end of lemma zenon_L1832_ *) % 30.42/30.51 assert (zenon_L1833_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.51 do 0 intro. intros zenon_H102 zenon_H25 zenon_H15e zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.42/30.51 apply (zenon_L99_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.42/30.51 apply (zenon_L1131_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.42/30.51 exact (zenon_H13b zenon_Hfd). % 30.42/30.51 exact (zenon_H103 zenon_H37). % 30.42/30.51 (* end of lemma zenon_L1833_ *) % 30.42/30.51 assert (zenon_L1834_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 30.42/30.51 do 0 intro. intros zenon_H1dc zenon_H25 zenon_H1a0. % 30.42/30.51 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 30.42/30.51 intro zenon_D_pnotp. % 30.42/30.51 apply zenon_H1dc. % 30.42/30.51 rewrite <- zenon_D_pnotp. % 30.42/30.51 exact zenon_H25. % 30.42/30.51 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 30.42/30.51 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 30.42/30.51 congruence. % 30.42/30.51 apply zenon_H29. apply refl_equal. % 30.42/30.51 apply zenon_H1a1. apply sym_equal. exact zenon_H1a0. % 30.42/30.51 (* end of lemma zenon_L1834_ *) % 30.42/30.51 assert (zenon_L1835_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 30.42/30.51 do 0 intro. intros zenon_H1d2 zenon_H1e1 zenon_H108 zenon_H1a0 zenon_H1dc zenon_Hd0 zenon_H15e zenon_H20e. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.42/30.51 apply (zenon_L296_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.42/30.51 apply (zenon_L1834_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.42/30.51 exact (zenon_Hd0 zenon_Hcc). % 30.42/30.51 apply (zenon_L1145_); trivial. % 30.42/30.51 (* end of lemma zenon_L1835_ *) % 30.42/30.51 assert (zenon_L1836_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 30.42/30.51 do 0 intro. intros zenon_H1a2 zenon_H27 zenon_H5c zenon_H15a zenon_H16a zenon_H1a5 zenon_H92 zenon_H16f zenon_H10d zenon_Hc0 zenon_H296 zenon_H30b zenon_H42 zenon_Hd1 zenon_H225 zenon_He4 zenon_Hee zenon_Hd6 zenon_Hc8 zenon_H1d5 zenon_H101 zenon_H14e zenon_H3f zenon_Hf9 zenon_He1 zenon_H89 zenon_H23b zenon_Hfc zenon_H200 zenon_Hde zenon_H135 zenon_H156 zenon_H222 zenon_H60 zenon_H5e zenon_H3c zenon_H30d zenon_H218 zenon_H20d zenon_H1e6 zenon_H6f zenon_H1ca zenon_H19e zenon_H1bd zenon_H1af zenon_H1c7 zenon_H110 zenon_H208 zenon_Hbd zenon_H20 zenon_H100 zenon_H2d zenon_Hf6 zenon_H125 zenon_H10e zenon_H18c zenon_H173 zenon_Hcd zenon_H1fd zenon_H6c zenon_H6b zenon_H1d8 zenon_H267 zenon_H231 zenon_H1f zenon_H103 zenon_H13b zenon_H182 zenon_H159 zenon_H102 zenon_H1d2 zenon_H1e1 zenon_H108 zenon_H1dc zenon_Hd0 zenon_H15e zenon_H20e. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.42/30.51 apply (zenon_L1801_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.42/30.51 apply (zenon_L1832_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.42/30.51 apply (zenon_L1833_); trivial. % 30.42/30.51 apply (zenon_L1835_); trivial. % 30.42/30.51 (* end of lemma zenon_L1836_ *) % 30.42/30.51 assert (zenon_L1837_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 30.42/30.51 do 0 intro. intros zenon_H20e zenon_Hd0 zenon_H1dc zenon_H108 zenon_H1e1 zenon_H1d2 zenon_H231 zenon_H267 zenon_H1d8 zenon_H6b zenon_H1fd zenon_Hcd zenon_H173 zenon_H18c zenon_H10e zenon_H125 zenon_Hf6 zenon_H2d zenon_H100 zenon_H20 zenon_Hbd zenon_H208 zenon_H110 zenon_H1c7 zenon_H1bd zenon_H19e zenon_H1ca zenon_H6f zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H60 zenon_H156 zenon_H135 zenon_Hde zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H10d zenon_H16f zenon_H92 zenon_H1a5 zenon_H16a zenon_H15a zenon_H5c zenon_H27 zenon_H1a2 zenon_H3c zenon_H1f zenon_H5e zenon_H103 zenon_H13b zenon_H182 zenon_H159 zenon_H15e zenon_H102 zenon_H222 zenon_H1af zenon_H40. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.51 apply (zenon_L1836_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.51 apply (zenon_L218_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.51 apply (zenon_L1833_); trivial. % 30.42/30.51 apply (zenon_L1337_); trivial. % 30.42/30.51 (* end of lemma zenon_L1837_ *) % 30.42/30.51 assert (zenon_L1838_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 30.42/30.51 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H40 zenon_H20e zenon_H15e zenon_H1d2 zenon_H55 zenon_H60 zenon_H1bd zenon_H27 zenon_H26 zenon_Hd0 zenon_H108. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.51 apply (zenon_L332_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.51 apply (zenon_L775_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.51 apply (zenon_L1145_); trivial. % 30.42/30.51 apply (zenon_L634_); trivial. % 30.42/30.51 (* end of lemma zenon_L1838_ *) % 30.42/30.51 assert (zenon_L1839_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.42/30.51 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H182 zenon_H20 zenon_H20e zenon_H15e zenon_Hd0 zenon_H1dc zenon_H1a0 zenon_H108 zenon_H1d2 zenon_H8b zenon_H17d. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.42/30.51 exact (zenon_H30a zenon_H185). % 30.42/30.51 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.42/30.51 apply (zenon_L658_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.42/30.51 apply (zenon_L1835_); trivial. % 30.42/30.51 apply (zenon_L772_); trivial. % 30.42/30.51 (* end of lemma zenon_L1839_ *) % 30.42/30.51 assert (zenon_L1840_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> False). % 30.42/30.51 do 0 intro. intros zenon_H1d2 zenon_H6b zenon_Hdf zenon_H1dc zenon_Hd0 zenon_Hb1 zenon_H1a0. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.42/30.51 apply (zenon_L303_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.42/30.51 apply (zenon_L1834_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.42/30.51 exact (zenon_Hd0 zenon_Hcc). % 30.42/30.51 apply (zenon_L751_); trivial. % 30.42/30.51 (* end of lemma zenon_L1840_ *) % 30.42/30.51 assert (zenon_L1841_ : (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((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)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 30.42/30.51 do 0 intro. intros zenon_Hd0 zenon_H1dc zenon_Hdf zenon_H6b zenon_H1d2 zenon_H10d zenon_H10e zenon_H2d zenon_H2b4 zenon_H30a zenon_H182 zenon_H20 zenon_H20e zenon_H108 zenon_H17d zenon_Hbd zenon_H1f zenon_H231 zenon_H267 zenon_H1d8 zenon_H1fd zenon_H173 zenon_H18c zenon_H125 zenon_Hf6 zenon_H102 zenon_H159 zenon_H100 zenon_H103 zenon_H208 zenon_H110 zenon_H1c7 zenon_H1bd zenon_H19e zenon_H1ca zenon_H6f zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H3c zenon_H5e zenon_H60 zenon_H156 zenon_H135 zenon_Hde zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H16f zenon_H92 zenon_H1a5 zenon_H16a zenon_H27 zenon_H1a2 zenon_H55 zenon_Hcd zenon_H15e zenon_Hc3 zenon_H222 zenon_H1af zenon_H40. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.42/30.51 apply (zenon_L1838_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.42/30.51 apply (zenon_L1832_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.42/30.51 apply (zenon_L99_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.42/30.51 apply (zenon_L1839_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.42/30.51 apply (zenon_L766_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.42/30.51 apply (zenon_L63_); trivial. % 30.42/30.51 apply (zenon_L1840_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.51 apply (zenon_L212_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.51 apply (zenon_L99_); trivial. % 30.42/30.51 apply (zenon_L1337_); trivial. % 30.42/30.51 (* end of lemma zenon_L1841_ *) % 30.42/30.51 assert (zenon_L1842_ : ((op (e3) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.51 do 0 intro. intros zenon_H40 zenon_H1af zenon_H222 zenon_H15e zenon_Hcd zenon_H55 zenon_H1a2 zenon_H27 zenon_H16a zenon_H1a5 zenon_H92 zenon_H16f zenon_Hc0 zenon_H296 zenon_H30b zenon_H42 zenon_Hd1 zenon_H225 zenon_He4 zenon_Hee zenon_Hd6 zenon_Hc8 zenon_H1d5 zenon_H101 zenon_H14e zenon_H3f zenon_Hf9 zenon_He1 zenon_H89 zenon_H23b zenon_Hfc zenon_H200 zenon_Hde zenon_H135 zenon_H156 zenon_H60 zenon_H5e zenon_H3c zenon_H30d zenon_H218 zenon_H20d zenon_H1e6 zenon_H6f zenon_H1ca zenon_H19e zenon_H1bd zenon_H1c7 zenon_H110 zenon_H208 zenon_H100 zenon_H102 zenon_Hf6 zenon_H125 zenon_H18c zenon_H173 zenon_H1fd zenon_H1d8 zenon_H267 zenon_H231 zenon_H1f zenon_Hbd zenon_H17d zenon_H108 zenon_H20e zenon_H20 zenon_H30a zenon_H2b4 zenon_H2d zenon_H10e zenon_H10d zenon_H1d2 zenon_H6b zenon_Hdf zenon_H1dc zenon_Hd0 zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.42/30.51 apply (zenon_L1841_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.42/30.51 apply (zenon_L1131_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.42/30.51 exact (zenon_H13b zenon_Hfd). % 30.42/30.51 exact (zenon_H103 zenon_H37). % 30.42/30.51 (* end of lemma zenon_L1842_ *) % 30.42/30.51 assert (zenon_L1843_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.51 do 0 intro. intros zenon_H102 zenon_H1ba zenon_H19e zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.42/30.51 apply (zenon_L347_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.42/30.51 apply (zenon_L1131_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.42/30.51 exact (zenon_H13b zenon_Hfd). % 30.42/30.51 exact (zenon_H103 zenon_H37). % 30.42/30.51 (* end of lemma zenon_L1843_ *) % 30.42/30.51 assert (zenon_L1844_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 30.42/30.51 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H17d zenon_H55 zenon_H20e zenon_Hd0 zenon_H1dc zenon_H108 zenon_H1d2 zenon_H231 zenon_H267 zenon_H1d8 zenon_H6b zenon_H1fd zenon_Hcd zenon_H173 zenon_H18c zenon_H10e zenon_H125 zenon_Hf6 zenon_H2d zenon_H100 zenon_H20 zenon_Hbd zenon_H208 zenon_H110 zenon_H1c7 zenon_H1bd zenon_H19e zenon_H1ca zenon_H6f zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H60 zenon_H156 zenon_H135 zenon_Hde zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H10d zenon_H16f zenon_H92 zenon_H1a5 zenon_H16a zenon_H15a zenon_H5c zenon_H27 zenon_H1a2 zenon_H3c zenon_H1f zenon_H5e zenon_H103 zenon_H13b zenon_H182 zenon_H159 zenon_H15e zenon_H102 zenon_H222 zenon_H1af zenon_H40. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.51 apply (zenon_L1842_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.51 apply (zenon_L1843_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.51 apply (zenon_L165_); trivial. % 30.42/30.51 apply (zenon_L1837_); trivial. % 30.42/30.51 (* end of lemma zenon_L1844_ *) % 30.42/30.51 assert (zenon_L1845_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.42/30.51 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_Hdc zenon_H18c zenon_H135 zenon_He1 zenon_H9d. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.51 apply (zenon_L4_); trivial. % 30.42/30.51 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.51 exact (zenon_H103 zenon_H37). % 30.42/30.51 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.51 apply (zenon_L145_); trivial. % 30.42/30.51 apply (zenon_L1354_); trivial. % 30.42/30.51 (* end of lemma zenon_L1845_ *) % 30.42/30.51 assert (zenon_L1846_ : (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H6f zenon_H182 zenon_H2b4 zenon_H30a zenon_H17d zenon_H20e zenon_H1dc zenon_H108 zenon_H1d2 zenon_H231 zenon_H267 zenon_H1d8 zenon_H6b zenon_H1fd zenon_Hcd zenon_H173 zenon_H10e zenon_H125 zenon_Hf6 zenon_H100 zenon_H20 zenon_Hbd zenon_H208 zenon_H110 zenon_H1c7 zenon_H1bd zenon_H19e zenon_H1ca zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H60 zenon_H156 zenon_Hde zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H1d5 zenon_Hc8 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H30b zenon_H296 zenon_Hc0 zenon_H10d zenon_H16f zenon_H92 zenon_H1a5 zenon_H16a zenon_H15a zenon_H5c zenon_H27 zenon_H1a2 zenon_H3c zenon_H1f zenon_H5e zenon_H13b zenon_H159 zenon_H102 zenon_H222 zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_Hd6 zenon_H1af zenon_Hd0 zenon_Hdc zenon_H18c zenon_H135 zenon_He1. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.52 apply (zenon_L241_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.52 apply (zenon_L4_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.52 apply (zenon_L145_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.52 apply (zenon_L363_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.52 apply (zenon_L207_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.52 apply (zenon_L224_); trivial. % 30.42/30.52 apply (zenon_L1837_); trivial. % 30.42/30.52 apply (zenon_L758_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.52 exact (zenon_H13b zenon_Hfd). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.52 apply (zenon_L241_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.52 apply (zenon_L4_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.52 apply (zenon_L145_); trivial. % 30.42/30.52 apply (zenon_L1844_); trivial. % 30.42/30.52 apply (zenon_L758_); trivial. % 30.42/30.52 apply (zenon_L1845_); trivial. % 30.42/30.52 (* end of lemma zenon_L1846_ *) % 30.42/30.52 assert (zenon_L1847_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.52 do 0 intro. intros zenon_H208 zenon_He1 zenon_H1ca zenon_Hc3 zenon_H19e zenon_H1bd zenon_H1c7 zenon_H1af zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_Hdc zenon_H18c zenon_H135 zenon_H1f zenon_H5e zenon_H3c zenon_He9 zenon_H60 zenon_H156 zenon_H182. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.52 apply (zenon_L349_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.52 apply (zenon_L218_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.52 apply (zenon_L219_); trivial. % 30.42/30.52 apply (zenon_L934_); trivial. % 30.42/30.52 (* end of lemma zenon_L1847_ *) % 30.42/30.52 assert (zenon_L1848_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.52 do 0 intro. intros zenon_H208 zenon_He1 zenon_H102 zenon_Hd6 zenon_H1af zenon_H1c7 zenon_H19e zenon_H1ca zenon_H159 zenon_Hdc zenon_Hd1 zenon_H103 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H18c zenon_H135 zenon_H1ba zenon_H5e zenon_H1bd zenon_H3c zenon_He9 zenon_H60 zenon_H156 zenon_H182. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.52 apply (zenon_L1799_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.52 apply (zenon_L608_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.52 apply (zenon_L219_); trivial. % 30.42/30.52 apply (zenon_L934_); trivial. % 30.42/30.52 (* end of lemma zenon_L1848_ *) % 30.42/30.52 assert (zenon_L1849_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H102 zenon_H95 zenon_H100 zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.42/30.52 apply (zenon_L1497_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.42/30.52 apply (zenon_L1131_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.42/30.52 exact (zenon_H13b zenon_Hfd). % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 (* end of lemma zenon_L1849_ *) % 30.42/30.52 assert (zenon_L1850_ : (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H13b zenon_H159 zenon_H100 zenon_H102 zenon_H208 zenon_He1 zenon_Hd6 zenon_H1c7 zenon_H19e zenon_H1ca zenon_Hd1 zenon_H6b zenon_H1d5 zenon_H18c zenon_H5e zenon_H1bd zenon_H60 zenon_H156 zenon_H1f zenon_H2b4 zenon_H30a zenon_H17d zenon_H1dc zenon_H108 zenon_H1d2 zenon_H231 zenon_H267 zenon_H1fd zenon_Hcd zenon_H173 zenon_H125 zenon_Hf6 zenon_H20 zenon_Hbd zenon_H110 zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_Hde zenon_H200 zenon_Hfc zenon_H23b zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_Hc8 zenon_Hee zenon_He4 zenon_H225 zenon_H30b zenon_H296 zenon_Hc0 zenon_H10d zenon_H92 zenon_H1a5 zenon_H16a zenon_H1a2 zenon_H222 zenon_H42 zenon_H2d zenon_H27 zenon_H10e zenon_H5c zenon_H16f zenon_H89 zenon_H15a zenon_H103 zenon_H20e zenon_H1af zenon_Hd0 zenon_He9 zenon_H3c zenon_H1d8 zenon_H135 zenon_H182 zenon_H6f. % 30.42/30.52 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.52 apply (zenon_L232_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.52 apply (zenon_L1846_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.52 apply (zenon_L1847_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.52 apply (zenon_L1848_); trivial. % 30.42/30.52 apply (zenon_L1849_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.52 apply (zenon_L191_); trivial. % 30.42/30.52 apply (zenon_L1800_); trivial. % 30.42/30.52 (* end of lemma zenon_L1850_ *) % 30.42/30.52 assert (zenon_L1851_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H16f zenon_H89 zenon_H15a zenon_H9d zenon_He1 zenon_H135 zenon_He2 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_H20e zenon_H103 zenon_H1e zenon_H2d zenon_H42 zenon_H182 zenon_H6f. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.52 apply (zenon_L241_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.52 apply (zenon_L4_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.52 apply (zenon_L592_); trivial. % 30.42/30.52 apply (zenon_L1354_); trivial. % 30.42/30.52 apply (zenon_L758_); trivial. % 30.42/30.52 (* end of lemma zenon_L1851_ *) % 30.42/30.52 assert (zenon_L1852_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H17d zenon_H1dc zenon_H108 zenon_H1d2 zenon_H231 zenon_H267 zenon_H6b zenon_H1fd zenon_Hcd zenon_H173 zenon_H18c zenon_H10e zenon_H125 zenon_Hf6 zenon_H100 zenon_H20 zenon_Hbd zenon_H208 zenon_H110 zenon_H1c7 zenon_H1bd zenon_H19e zenon_H1ca zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H60 zenon_H156 zenon_Hde zenon_H200 zenon_Hfc zenon_H23b zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H30b zenon_H296 zenon_Hc0 zenon_H10d zenon_H92 zenon_H1a5 zenon_H16a zenon_H5c zenon_H27 zenon_H1a2 zenon_H3c zenon_H1f zenon_H5e zenon_H13b zenon_H159 zenon_H102 zenon_H222 zenon_H16f zenon_H89 zenon_H15a zenon_He1 zenon_H135 zenon_He2 zenon_H1d8 zenon_Hd0 zenon_H1af zenon_H20e zenon_H103 zenon_H1e zenon_H2d zenon_H42 zenon_H182 zenon_H6f. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.52 apply (zenon_L1850_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.52 exact (zenon_H13b zenon_Hfd). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.52 apply (zenon_L241_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.52 apply (zenon_L4_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.52 apply (zenon_L592_); trivial. % 30.42/30.52 apply (zenon_L1844_); trivial. % 30.42/30.52 apply (zenon_L758_); trivial. % 30.42/30.52 apply (zenon_L1851_); trivial. % 30.42/30.52 (* end of lemma zenon_L1852_ *) % 30.42/30.52 assert (zenon_L1853_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H182 zenon_H20 zenon_Hdf zenon_H20d zenon_H95 zenon_H113. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.42/30.52 exact (zenon_H30a zenon_H185). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.42/30.52 apply (zenon_L658_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.42/30.52 apply (zenon_L548_); trivial. % 30.42/30.52 apply (zenon_L798_); trivial. % 30.42/30.52 (* end of lemma zenon_L1853_ *) % 30.42/30.52 assert (zenon_L1854_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e1)) -> False). % 30.42/30.52 do 0 intro. intros zenon_Hbd zenon_H17d zenon_H108 zenon_H15e zenon_H20e zenon_H113 zenon_H20d zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1d2 zenon_H6b zenon_Hdf zenon_H1dc zenon_Hd0 zenon_H1a0. % 30.42/30.52 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.42/30.52 apply (zenon_L1839_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.42/30.52 apply (zenon_L1853_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.42/30.52 apply (zenon_L63_); trivial. % 30.42/30.52 apply (zenon_L1840_); trivial. % 30.42/30.52 (* end of lemma zenon_L1854_ *) % 30.42/30.52 assert (zenon_L1855_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e1)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H1a2 zenon_H27 zenon_H1bd zenon_H60 zenon_H55 zenon_H17b zenon_H218 zenon_He1 zenon_Hc8 zenon_H1d5 zenon_H89 zenon_He2 zenon_Hee zenon_H3f zenon_H1f zenon_Hcd zenon_H23b zenon_H6c zenon_Hbd zenon_H17d zenon_H108 zenon_H15e zenon_H20e zenon_H113 zenon_H20d zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1d2 zenon_H6b zenon_Hdf zenon_H1dc zenon_Hd0. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.42/30.52 apply (zenon_L635_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.42/30.52 apply (zenon_L387_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.42/30.52 apply (zenon_L17_); trivial. % 30.42/30.52 apply (zenon_L1854_); trivial. % 30.42/30.52 (* end of lemma zenon_L1855_ *) % 30.42/30.52 assert (zenon_L1856_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.52 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H1f zenon_H5e zenon_H3c zenon_He9 zenon_H60 zenon_H156 zenon_H182. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.52 apply (zenon_L120_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.52 apply (zenon_L218_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.52 apply (zenon_L219_); trivial. % 30.42/30.52 apply (zenon_L934_); trivial. % 30.42/30.52 (* end of lemma zenon_L1856_ *) % 30.42/30.52 assert (zenon_L1857_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H182 zenon_H20 zenon_H3d zenon_H1af zenon_H1bd zenon_H8b zenon_H17d. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.42/30.52 exact (zenon_H30a zenon_H185). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.42/30.52 apply (zenon_L658_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.42/30.52 apply (zenon_L209_); trivial. % 30.42/30.52 apply (zenon_L772_); trivial. % 30.42/30.52 (* end of lemma zenon_L1857_ *) % 30.42/30.52 assert (zenon_L1858_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.42/30.52 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_H17d zenon_H8b zenon_H1bd zenon_H1af zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_He1 zenon_H9d. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.52 apply (zenon_L4_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.52 apply (zenon_L1857_); trivial. % 30.42/30.52 apply (zenon_L1354_); trivial. % 30.42/30.52 (* end of lemma zenon_L1858_ *) % 30.42/30.52 assert (zenon_L1859_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H101 zenon_H156 zenon_H60 zenon_H3c zenon_H5e zenon_H1f zenon_H18c zenon_H68 zenon_H208 zenon_H13b zenon_Hc9 zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_H17d zenon_H8b zenon_H1bd zenon_H1af zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_He1. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.52 apply (zenon_L1856_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.52 exact (zenon_H13b zenon_Hfd). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.52 apply (zenon_L282_); trivial. % 30.42/30.52 apply (zenon_L1858_); trivial. % 30.42/30.52 (* end of lemma zenon_L1859_ *) % 30.42/30.52 assert (zenon_L1860_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H159 zenon_H142 zenon_H108 zenon_H8b zenon_H17d. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.42/30.52 exact (zenon_H30a zenon_H185). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.42/30.52 apply (zenon_L1458_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.42/30.52 apply (zenon_L296_); trivial. % 30.42/30.52 apply (zenon_L772_); trivial. % 30.42/30.52 (* end of lemma zenon_L1860_ *) % 30.42/30.52 assert (zenon_L1861_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H1e1 zenon_H20e zenon_H15e zenon_H102 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H9d zenon_H100 zenon_H103. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.52 apply (zenon_L332_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.52 apply (zenon_L209_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.52 apply (zenon_L1145_); trivial. % 30.42/30.52 apply (zenon_L1808_); trivial. % 30.42/30.52 (* end of lemma zenon_L1861_ *) % 30.42/30.52 assert (zenon_L1862_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.52 do 0 intro. intros zenon_H208 zenon_H103 zenon_H100 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H1af zenon_H1c7 zenon_H102 zenon_H15e zenon_H20e zenon_H1e1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H60 zenon_H222 zenon_H156 zenon_H182. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.52 apply (zenon_L1861_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.52 apply (zenon_L218_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.52 apply (zenon_L256_); trivial. % 30.42/30.52 apply (zenon_L934_); trivial. % 30.42/30.52 (* end of lemma zenon_L1862_ *) % 30.42/30.52 assert (zenon_L1863_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H101 zenon_H18c zenon_H68 zenon_H13b zenon_H16f zenon_H15a zenon_H156 zenon_H222 zenon_H60 zenon_H5e zenon_H1f zenon_H3c zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H20e zenon_H102 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H100 zenon_H103 zenon_H208 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H108 zenon_H8b zenon_H17d zenon_Hde zenon_Hc9 zenon_H200 zenon_H182 zenon_H6f. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.52 apply (zenon_L1856_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.52 exact (zenon_H13b zenon_Hfd). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.52 apply (zenon_L282_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.52 apply (zenon_L241_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.52 apply (zenon_L49_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.52 apply (zenon_L1812_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.52 apply (zenon_L1860_); trivial. % 30.42/30.52 apply (zenon_L1862_); trivial. % 30.42/30.52 apply (zenon_L758_); trivial. % 30.42/30.52 (* end of lemma zenon_L1863_ *) % 30.42/30.52 assert (zenon_L1864_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H101 zenon_H156 zenon_H60 zenon_H3c zenon_H5e zenon_H1f zenon_H18c zenon_H68 zenon_H208 zenon_H13b zenon_H1bd zenon_Hc9 zenon_H102 zenon_H1ba zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.52 apply (zenon_L1856_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.52 exact (zenon_H13b zenon_Hfd). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.52 apply (zenon_L282_); trivial. % 30.42/30.52 apply (zenon_L1812_); trivial. % 30.42/30.52 (* end of lemma zenon_L1864_ *) % 30.42/30.52 assert (zenon_L1865_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.42/30.52 do 0 intro. intros zenon_He4 zenon_Hcd zenon_H97 zenon_H101 zenon_H156 zenon_H60 zenon_H3c zenon_H5e zenon_H1f zenon_H18c zenon_H68 zenon_H208 zenon_H13b zenon_H1bd zenon_H102 zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103 zenon_H16f zenon_H15a zenon_H222 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H20e zenon_H1c7 zenon_H1af zenon_H1ca zenon_H2b4 zenon_H30a zenon_H108 zenon_H17d zenon_H200 zenon_H6f zenon_H42 zenon_H2d zenon_H20 zenon_He1 zenon_H296 zenon_H8b zenon_Hde. % 30.42/30.52 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.52 apply (zenon_L232_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.52 apply (zenon_L48_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.52 apply (zenon_L1859_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.52 apply (zenon_L1863_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.52 apply (zenon_L1864_); trivial. % 30.42/30.52 apply (zenon_L1287_); trivial. % 30.42/30.52 apply (zenon_L288_); trivial. % 30.42/30.52 (* end of lemma zenon_L1865_ *) % 30.42/30.52 assert (zenon_L1866_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 30.42/30.52 do 0 intro. intros zenon_Haa zenon_H113 zenon_Hb1 zenon_H90 zenon_H97 zenon_H25 zenon_H60 zenon_H222 zenon_H2c zenon_H3f. % 30.42/30.52 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H95 | zenon_intro zenon_Hab ]. % 30.42/30.52 apply (zenon_L798_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H98 | zenon_intro zenon_Hac ]. % 30.42/30.52 apply (zenon_L30_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9d | zenon_intro zenon_H40 ]. % 30.42/30.52 apply (zenon_L256_); trivial. % 30.42/30.52 apply (zenon_L746_); trivial. % 30.42/30.52 (* end of lemma zenon_L1866_ *) % 30.42/30.52 assert (zenon_L1867_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H23b zenon_H2c zenon_H222 zenon_H60 zenon_H97 zenon_Hb1 zenon_H113 zenon_Haa zenon_H1f zenon_H3f zenon_H25 zenon_H1dc zenon_H182 zenon_H14e. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.42/30.52 apply (zenon_L1866_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.42/30.52 apply (zenon_L336_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.42/30.52 apply (zenon_L1834_); trivial. % 30.42/30.52 apply (zenon_L137_); trivial. % 30.42/30.52 (* end of lemma zenon_L1867_ *) % 30.42/30.52 assert (zenon_L1868_ : (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.52 do 0 intro. intros zenon_Hd0 zenon_H6b zenon_H1d2 zenon_H15e zenon_Hee zenon_He2 zenon_H218 zenon_H17b zenon_H55 zenon_H27 zenon_H1a2 zenon_H14e zenon_H1dc zenon_H3f zenon_H1f zenon_Haa zenon_H113 zenon_H97 zenon_H60 zenon_H222 zenon_H2c zenon_H23b zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_Hdf zenon_H20d zenon_He4 zenon_Hcd zenon_H101 zenon_H3c zenon_H5e zenon_H18c zenon_H68 zenon_H208 zenon_H13b zenon_H1bd zenon_H102 zenon_H19e zenon_H159 zenon_H100 zenon_H103 zenon_H16f zenon_H15a zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H20e zenon_H1c7 zenon_H1af zenon_H1ca zenon_H108 zenon_H17d zenon_H200 zenon_H6f zenon_H42 zenon_H2d zenon_He1 zenon_H296 zenon_Hde zenon_Hbd zenon_H156 zenon_H182. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.52 apply (zenon_L1855_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.52 apply (zenon_L218_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.42/30.52 apply (zenon_L1865_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.42/30.52 apply (zenon_L1853_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.42/30.52 apply (zenon_L63_); trivial. % 30.42/30.52 apply (zenon_L1867_); trivial. % 30.42/30.52 apply (zenon_L934_); trivial. % 30.42/30.52 (* end of lemma zenon_L1868_ *) % 30.42/30.52 assert (zenon_L1869_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.52 do 0 intro. intros zenon_H20e zenon_Hd0 zenon_H1dc zenon_H108 zenon_H1e1 zenon_H1d2 zenon_H102 zenon_H159 zenon_H13b zenon_H103 zenon_H1f zenon_H231 zenon_H267 zenon_H1d8 zenon_H6b zenon_H1fd zenon_H173 zenon_H18c zenon_H10e zenon_H125 zenon_Hf6 zenon_H2d zenon_H100 zenon_H20 zenon_Hbd zenon_H208 zenon_H110 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_H1ca zenon_H6f zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H3c zenon_H5e zenon_H60 zenon_H222 zenon_H135 zenon_Hde zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H10d zenon_H16f zenon_H92 zenon_H1a5 zenon_H16a zenon_H15a zenon_H5c zenon_H27 zenon_H1a2 zenon_H55 zenon_Hcd zenon_H15e zenon_Hc3 zenon_H156 zenon_H182. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.52 apply (zenon_L1836_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.52 apply (zenon_L212_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.52 apply (zenon_L99_); trivial. % 30.42/30.52 apply (zenon_L934_); trivial. % 30.42/30.52 (* end of lemma zenon_L1869_ *) % 30.42/30.52 assert (zenon_L1870_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H20 zenon_H108 zenon_H30d zenon_H218 zenon_H20d zenon_H60 zenon_H142 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H6f zenon_H182 zenon_H1c7 zenon_H1af zenon_H222 zenon_H9d zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H2d. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.42/30.52 exact (zenon_H30a zenon_H185). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.42/30.52 apply (zenon_L658_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.42/30.52 apply (zenon_L296_); trivial. % 30.42/30.52 apply (zenon_L1815_); trivial. % 30.42/30.52 (* end of lemma zenon_L1870_ *) % 30.42/30.52 assert (zenon_L1871_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.52 do 0 intro. intros zenon_H208 zenon_H2d zenon_H1ca zenon_Hc3 zenon_H19e zenon_H1bd zenon_H1af zenon_H1c7 zenon_H6f zenon_H1e6 zenon_Hf6 zenon_H142 zenon_H20d zenon_H218 zenon_H30d zenon_H108 zenon_H20 zenon_H30a zenon_H2b4 zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H60 zenon_H222 zenon_H156 zenon_H182. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.52 apply (zenon_L1870_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.52 apply (zenon_L218_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.52 apply (zenon_L256_); trivial. % 30.42/30.52 apply (zenon_L934_); trivial. % 30.42/30.52 (* end of lemma zenon_L1871_ *) % 30.42/30.52 assert (zenon_L1872_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.52 do 0 intro. intros zenon_H16f zenon_H15a zenon_H156 zenon_H222 zenon_H60 zenon_H9d zenon_H5e zenon_H1f zenon_H3c zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H20e zenon_H102 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H100 zenon_H103 zenon_H208 zenon_H2d zenon_Hc3 zenon_H1e6 zenon_Hf6 zenon_H20d zenon_H218 zenon_H30d zenon_H108 zenon_H20 zenon_H30a zenon_H2b4 zenon_H135 zenon_Hde zenon_Hd0 zenon_H200 zenon_H182 zenon_H6f. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.52 apply (zenon_L241_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.52 exact (zenon_H103 zenon_H37). % 30.42/30.52 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.52 apply (zenon_L359_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.52 apply (zenon_L1812_); trivial. % 30.42/30.52 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.53 apply (zenon_L1871_); trivial. % 30.42/30.53 apply (zenon_L1862_); trivial. % 30.42/30.53 apply (zenon_L758_); trivial. % 30.42/30.53 (* end of lemma zenon_L1872_ *) % 30.42/30.53 assert (zenon_L1873_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H16f zenon_H89 zenon_H15a zenon_H103 zenon_H20e zenon_H1af zenon_Hd0 zenon_He9 zenon_H3c zenon_Hde zenon_Hdf zenon_H135 zenon_H182 zenon_H6f. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.53 apply (zenon_L241_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.53 exact (zenon_H103 zenon_H37). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.53 apply (zenon_L363_); trivial. % 30.42/30.53 apply (zenon_L758_); trivial. % 30.42/30.53 (* end of lemma zenon_L1873_ *) % 30.42/30.53 assert (zenon_L1874_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H101 zenon_H6f zenon_H182 zenon_H3c zenon_H1af zenon_H20e zenon_H103 zenon_H15a zenon_H16f zenon_H13b zenon_H108 zenon_H26 zenon_H27 zenon_H1bd zenon_H60 zenon_H1d2 zenon_He1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H135 zenon_Hdf zenon_Hde zenon_H222 zenon_Hd0 zenon_H17b zenon_H218. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.53 apply (zenon_L1873_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.53 exact (zenon_H13b zenon_Hfd). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.53 apply (zenon_L635_); trivial. % 30.42/30.53 apply (zenon_L406_); trivial. % 30.42/30.53 (* end of lemma zenon_L1874_ *) % 30.42/30.53 assert (zenon_L1875_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H225 zenon_H10e zenon_H101 zenon_H6f zenon_H182 zenon_H3c zenon_H1af zenon_H20e zenon_H103 zenon_H15a zenon_H16f zenon_H13b zenon_H108 zenon_H26 zenon_H27 zenon_H1bd zenon_H60 zenon_H1d2 zenon_He1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H135 zenon_Hdf zenon_Hde zenon_H222 zenon_Hd0 zenon_H218. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.53 apply (zenon_L232_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.53 apply (zenon_L1873_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.53 apply (zenon_L192_); trivial. % 30.42/30.53 apply (zenon_L1874_); trivial. % 30.42/30.53 (* end of lemma zenon_L1875_ *) % 30.42/30.53 assert (zenon_L1876_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H1a2 zenon_H27 zenon_H13b zenon_H15a zenon_H16a zenon_H1a5 zenon_H92 zenon_H16f zenon_Hc0 zenon_H296 zenon_H30b zenon_H42 zenon_Hd1 zenon_H225 zenon_He4 zenon_Hee zenon_Hd6 zenon_Hc8 zenon_H1d5 zenon_H101 zenon_H14e zenon_H3f zenon_Hf9 zenon_He1 zenon_H89 zenon_H23b zenon_Hfc zenon_H200 zenon_Hde zenon_H135 zenon_H156 zenon_H222 zenon_H60 zenon_H5e zenon_H3c zenon_H30d zenon_H218 zenon_H20d zenon_H1e6 zenon_H6f zenon_H1ca zenon_H19e zenon_H1bd zenon_H1af zenon_H1c7 zenon_H110 zenon_H208 zenon_H103 zenon_H159 zenon_H102 zenon_H2d zenon_Hf6 zenon_H125 zenon_H18c zenon_H173 zenon_Hcd zenon_H1fd zenon_H6c zenon_H1d8 zenon_H267 zenon_H231 zenon_H1f zenon_Hbd zenon_H17d zenon_H108 zenon_H15e zenon_H20e zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_H1d2 zenon_H6b zenon_Hdf zenon_H1dc zenon_Hd0. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.42/30.53 apply (zenon_L1875_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.42/30.53 apply (zenon_L1832_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.42/30.53 apply (zenon_L99_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.42/30.53 apply (zenon_L1839_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.42/30.53 apply (zenon_L1497_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.42/30.53 apply (zenon_L63_); trivial. % 30.42/30.53 apply (zenon_L1840_); trivial. % 30.42/30.53 (* end of lemma zenon_L1876_ *) % 30.42/30.53 assert (zenon_L1877_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H20e zenon_Hd0 zenon_H1dc zenon_H108 zenon_H1d2 zenon_H102 zenon_H159 zenon_H13b zenon_H103 zenon_H1f zenon_H231 zenon_H267 zenon_H1d8 zenon_H6b zenon_H6c zenon_H1fd zenon_Hcd zenon_H173 zenon_H18c zenon_H10e zenon_H125 zenon_Hf6 zenon_H2d zenon_H100 zenon_H20 zenon_Hbd zenon_H208 zenon_H110 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_H1ca zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H3c zenon_H5e zenon_H60 zenon_H222 zenon_H156 zenon_H135 zenon_Hde zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H10d zenon_H16f zenon_H92 zenon_H1a5 zenon_H16a zenon_H15a zenon_H5c zenon_H27 zenon_H1a2 zenon_H55 zenon_Hc3 zenon_H17d zenon_H30a zenon_H2b4 zenon_H182 zenon_H6f. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.53 apply (zenon_L241_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.53 exact (zenon_H103 zenon_H37). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.53 apply (zenon_L1876_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.53 apply (zenon_L347_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.53 apply (zenon_L165_); trivial. % 30.42/30.53 apply (zenon_L1836_); trivial. % 30.42/30.53 apply (zenon_L758_); trivial. % 30.42/30.53 (* end of lemma zenon_L1877_ *) % 30.42/30.53 assert (zenon_L1878_ : (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H6f zenon_H182 zenon_H1e zenon_H1af zenon_Hcd zenon_H1a2 zenon_H27 zenon_H16a zenon_H1a5 zenon_H92 zenon_H16f zenon_Hc0 zenon_H296 zenon_H30b zenon_H42 zenon_Hd1 zenon_H225 zenon_He4 zenon_Hee zenon_Hd6 zenon_Hc8 zenon_H1d5 zenon_H101 zenon_H14e zenon_H3f zenon_Hf9 zenon_He1 zenon_H89 zenon_H23b zenon_Hfc zenon_H200 zenon_H156 zenon_H60 zenon_H5e zenon_H3c zenon_H30d zenon_H20d zenon_H1e6 zenon_H1ca zenon_H19e zenon_H1bd zenon_H1c7 zenon_H110 zenon_H208 zenon_H100 zenon_H102 zenon_Hf6 zenon_H125 zenon_H18c zenon_H173 zenon_H1fd zenon_H1d8 zenon_H267 zenon_H231 zenon_H1f zenon_Hbd zenon_H17d zenon_H108 zenon_H20e zenon_H20 zenon_H30a zenon_H2b4 zenon_H2d zenon_H10e zenon_H10d zenon_H1d2 zenon_H6b zenon_H1dc zenon_H159 zenon_H13b zenon_H103 zenon_H15a zenon_H135 zenon_Hdf zenon_Hde zenon_H222 zenon_Hd0 zenon_H17b zenon_H218. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.53 apply (zenon_L1873_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.53 exact (zenon_H13b zenon_Hfd). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.53 apply (zenon_L241_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.53 exact (zenon_H103 zenon_H37). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.53 apply (zenon_L4_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.53 exact (zenon_H103 zenon_H37). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.53 apply (zenon_L126_); trivial. % 30.42/30.53 apply (zenon_L1842_); trivial. % 30.42/30.53 apply (zenon_L758_); trivial. % 30.42/30.53 apply (zenon_L406_); trivial. % 30.42/30.53 (* end of lemma zenon_L1878_ *) % 30.42/30.53 assert (zenon_L1879_ : (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((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)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.53 do 0 intro. intros zenon_Hd0 zenon_H1dc zenon_Hdf zenon_H6b zenon_H1d2 zenon_H10d zenon_H10e zenon_H100 zenon_H2b4 zenon_H30a zenon_H20 zenon_H20e zenon_H108 zenon_H17d zenon_Hbd zenon_H231 zenon_H267 zenon_H1d8 zenon_H1fd zenon_Hcd zenon_H173 zenon_H18c zenon_H125 zenon_Hf6 zenon_H2d zenon_H102 zenon_H159 zenon_H103 zenon_H208 zenon_H110 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_H1ca zenon_H6f zenon_H1e6 zenon_H20d zenon_H218 zenon_H30d zenon_H60 zenon_H222 zenon_H135 zenon_Hde zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H16f zenon_H92 zenon_H1a5 zenon_H16a zenon_H15a zenon_H13b zenon_H27 zenon_H1a2 zenon_H3c zenon_H1f zenon_H5e zenon_H15e zenon_Hc3 zenon_H156 zenon_H182. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.53 apply (zenon_L1876_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.53 apply (zenon_L218_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.53 apply (zenon_L99_); trivial. % 30.42/30.53 apply (zenon_L934_); trivial. % 30.42/30.53 (* end of lemma zenon_L1879_ *) % 30.42/30.53 assert (zenon_L1880_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H156 zenon_Hc3 zenon_H5e zenon_H1f zenon_H3c zenon_H1a2 zenon_H27 zenon_H13b zenon_H15a zenon_H16a zenon_H1a5 zenon_H92 zenon_H16f zenon_Hc0 zenon_H296 zenon_H30b zenon_H42 zenon_Hd1 zenon_H225 zenon_He4 zenon_Hee zenon_Hd6 zenon_Hc8 zenon_H1d5 zenon_H101 zenon_H14e zenon_H3f zenon_Hf9 zenon_He1 zenon_H89 zenon_H23b zenon_Hfc zenon_H200 zenon_Hde zenon_H135 zenon_H222 zenon_H60 zenon_H30d zenon_H218 zenon_H20d zenon_H1e6 zenon_H1ca zenon_H19e zenon_H1bd zenon_H1af zenon_H1c7 zenon_H110 zenon_H208 zenon_H103 zenon_H159 zenon_H102 zenon_H2d zenon_Hf6 zenon_H125 zenon_H18c zenon_H173 zenon_Hcd zenon_H1fd zenon_H1d8 zenon_H267 zenon_H231 zenon_Hbd zenon_H17d zenon_H108 zenon_H20e zenon_H20 zenon_H30a zenon_H2b4 zenon_H100 zenon_H10e zenon_H10d zenon_H1d2 zenon_H6b zenon_Hdf zenon_H1dc zenon_Hd0 zenon_H182 zenon_H6f. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.53 apply (zenon_L241_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.53 exact (zenon_H103 zenon_H37). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.53 apply (zenon_L1879_); trivial. % 30.42/30.53 apply (zenon_L758_); trivial. % 30.42/30.53 (* end of lemma zenon_L1880_ *) % 30.42/30.53 assert (zenon_L1881_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 30.42/30.53 do 0 intro. intros zenon_H1d2 zenon_H17d zenon_H8b zenon_H159 zenon_Hc3 zenon_H30a zenon_H2b4 zenon_H27 zenon_H26 zenon_Hd0 zenon_H108 zenon_H1c5. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.42/30.53 apply (zenon_L1860_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.42/30.53 apply (zenon_L3_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.42/30.53 exact (zenon_Hd0 zenon_Hcc). % 30.42/30.53 apply (zenon_L171_); trivial. % 30.42/30.53 (* end of lemma zenon_L1881_ *) % 30.42/30.53 assert (zenon_L1882_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H102 zenon_H1c5 zenon_H108 zenon_Hd0 zenon_H26 zenon_H27 zenon_H2b4 zenon_H30a zenon_H8b zenon_H17d zenon_H1d2 zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.42/30.53 apply (zenon_L1881_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.42/30.53 apply (zenon_L1131_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.42/30.53 exact (zenon_H13b zenon_Hfd). % 30.42/30.53 exact (zenon_H103 zenon_H37). % 30.42/30.53 (* end of lemma zenon_L1882_ *) % 30.42/30.53 assert (zenon_L1883_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_Hd6 zenon_H1af zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H20e zenon_H15e zenon_H102 zenon_H108 zenon_Hd0 zenon_H26 zenon_H27 zenon_H2b4 zenon_H30a zenon_H8b zenon_H17d zenon_H1d2 zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.53 apply (zenon_L332_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.53 apply (zenon_L145_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.53 apply (zenon_L1145_); trivial. % 30.42/30.53 apply (zenon_L1882_); trivial. % 30.42/30.53 (* end of lemma zenon_L1883_ *) % 30.42/30.53 assert (zenon_L1884_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H16f zenon_H15a zenon_H17d zenon_H8b zenon_H1d2 zenon_H108 zenon_H1dc zenon_Hd0 zenon_H20e zenon_H20 zenon_H30a zenon_H2b4 zenon_H6b zenon_H6c zenon_H1d5 zenon_H89 zenon_Hc8 zenon_Hd6 zenon_H1af zenon_He1 zenon_Hdc zenon_H18c zenon_H135 zenon_H102 zenon_H27 zenon_H159 zenon_H13b zenon_H103 zenon_H1a2 zenon_H182 zenon_H6f. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.53 apply (zenon_L241_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.53 exact (zenon_H103 zenon_H37). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.42/30.53 apply (zenon_L1883_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.42/30.53 apply (zenon_L235_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.42/30.53 apply (zenon_L17_); trivial. % 30.42/30.53 apply (zenon_L1839_); trivial. % 30.42/30.53 apply (zenon_L758_); trivial. % 30.42/30.53 (* end of lemma zenon_L1884_ *) % 30.42/30.53 assert (zenon_L1885_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H1ca zenon_Hc3 zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1af zenon_H1c5 zenon_H1c7. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1cb ]. % 30.42/30.53 apply (zenon_L347_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H1cc ]. % 30.42/30.53 apply (zenon_L163_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H55 | zenon_intro zenon_H3d ]. % 30.42/30.53 apply (zenon_L88_); trivial. % 30.42/30.53 apply (zenon_L167_); trivial. % 30.42/30.53 (* end of lemma zenon_L1885_ *) % 30.42/30.53 assert (zenon_L1886_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H102 zenon_H1c7 zenon_H1c5 zenon_H1af zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.42/30.53 apply (zenon_L1885_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.42/30.53 apply (zenon_L1131_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.42/30.53 exact (zenon_H13b zenon_Hfd). % 30.42/30.53 exact (zenon_H103 zenon_H37). % 30.42/30.53 (* end of lemma zenon_L1886_ *) % 30.42/30.53 assert (zenon_L1887_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_H17d zenon_H8b zenon_H20 zenon_H30a zenon_H2b4 zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H102 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.53 apply (zenon_L273_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.53 apply (zenon_L1857_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.53 apply (zenon_L628_); trivial. % 30.42/30.53 apply (zenon_L1886_); trivial. % 30.42/30.53 (* end of lemma zenon_L1887_ *) % 30.42/30.53 assert (zenon_L1888_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H101 zenon_H159 zenon_H1ca zenon_H19e zenon_H6c zenon_H5e zenon_H3c zenon_H1c7 zenon_H102 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_H20d zenon_H231 zenon_H1d5 zenon_H13b zenon_Hc9 zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_H17d zenon_H8b zenon_H1bd zenon_H1af zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_He1. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.53 apply (zenon_L1887_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.53 exact (zenon_H13b zenon_Hfd). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.53 apply (zenon_L282_); trivial. % 30.42/30.53 apply (zenon_L1858_); trivial. % 30.42/30.53 (* end of lemma zenon_L1888_ *) % 30.42/30.53 assert (zenon_L1889_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H1e1 zenon_H20e zenon_H15e zenon_H102 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.53 apply (zenon_L332_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.53 apply (zenon_L209_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.53 apply (zenon_L1145_); trivial. % 30.42/30.53 apply (zenon_L1886_); trivial. % 30.42/30.53 (* end of lemma zenon_L1889_ *) % 30.42/30.53 assert (zenon_L1890_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H16f zenon_H15a zenon_H103 zenon_H13b zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1af zenon_H1c7 zenon_H102 zenon_H20e zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H108 zenon_H8b zenon_H17d zenon_H135 zenon_Hde zenon_Hd0 zenon_H200 zenon_H182 zenon_H6f. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.53 apply (zenon_L241_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.53 exact (zenon_H103 zenon_H37). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.53 apply (zenon_L363_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.53 apply (zenon_L347_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.53 apply (zenon_L1860_); trivial. % 30.42/30.53 apply (zenon_L1889_); trivial. % 30.42/30.53 apply (zenon_L758_); trivial. % 30.42/30.53 (* end of lemma zenon_L1890_ *) % 30.42/30.53 assert (zenon_L1891_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H200 zenon_H8b zenon_H5c zenon_H1d8 zenon_H2d zenon_Hc3 zenon_H6f zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H60 zenon_H20d zenon_H218 zenon_H30d zenon_H108 zenon_H20 zenon_H30a zenon_H2b4 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H20e zenon_H15e zenon_H102 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H9d zenon_H100 zenon_H103. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.53 apply (zenon_L194_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.53 apply (zenon_L347_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.53 apply (zenon_L1870_); trivial. % 30.42/30.53 apply (zenon_L1861_); trivial. % 30.42/30.53 (* end of lemma zenon_L1891_ *) % 30.42/30.53 assert (zenon_L1892_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H16f zenon_H15a zenon_H103 zenon_H100 zenon_H9d zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H102 zenon_H20e zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H2b4 zenon_H30a zenon_H20 zenon_H108 zenon_H30d zenon_H218 zenon_H20d zenon_H60 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_Hc3 zenon_H2d zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H182 zenon_H6f. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.53 apply (zenon_L241_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.53 exact (zenon_H103 zenon_H37). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.53 apply (zenon_L1891_); trivial. % 30.42/30.53 apply (zenon_L758_); trivial. % 30.42/30.53 (* end of lemma zenon_L1892_ *) % 30.42/30.53 assert (zenon_L1893_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H101 zenon_Hd0 zenon_Hde zenon_H135 zenon_H17d zenon_H3c zenon_H13b zenon_Hc9 zenon_H16f zenon_H15a zenon_H103 zenon_H100 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H102 zenon_H20e zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H2b4 zenon_H30a zenon_H20 zenon_H108 zenon_H30d zenon_H218 zenon_H20d zenon_H60 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_Hc3 zenon_H2d zenon_H1d8 zenon_H5c zenon_H8b zenon_H200 zenon_H182 zenon_H6f. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.53 apply (zenon_L1890_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.53 exact (zenon_H13b zenon_Hfd). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.53 apply (zenon_L282_); trivial. % 30.42/30.53 apply (zenon_L1892_); trivial. % 30.42/30.53 (* end of lemma zenon_L1893_ *) % 30.42/30.53 assert (zenon_L1894_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.53 do 0 intro. intros zenon_H101 zenon_H1ca zenon_H6c zenon_H5e zenon_H3c zenon_H1af zenon_H1c7 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_H20d zenon_H231 zenon_H2b4 zenon_H30a zenon_H20 zenon_H8b zenon_H17d zenon_He1 zenon_H1d5 zenon_H13b zenon_H1bd zenon_Hc9 zenon_H102 zenon_H1ba zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.53 apply (zenon_L1887_); trivial. % 30.42/30.53 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.53 exact (zenon_H13b zenon_Hfd). % 30.42/30.53 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.54 apply (zenon_L282_); trivial. % 30.42/30.54 apply (zenon_L1812_); trivial. % 30.42/30.54 (* end of lemma zenon_L1894_ *) % 30.42/30.54 assert (zenon_L1895_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.42/30.54 do 0 intro. intros zenon_H296 zenon_H42 zenon_H6f zenon_H200 zenon_H5c zenon_H1d8 zenon_H2d zenon_H1e6 zenon_Hf6 zenon_H30d zenon_H108 zenon_H89 zenon_Hc8 zenon_H20e zenon_H222 zenon_H15a zenon_H16f zenon_H135 zenon_Hde zenon_Hd0 zenon_H103 zenon_H100 zenon_H182 zenon_H159 zenon_H19e zenon_H102 zenon_Hc9 zenon_H1bd zenon_H13b zenon_H1d5 zenon_He1 zenon_H17d zenon_H20 zenon_H30a zenon_H2b4 zenon_H231 zenon_H20d zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H1c7 zenon_H1af zenon_H3c zenon_H5e zenon_H6c zenon_H1ca zenon_H101 zenon_H97 zenon_H8b. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.54 apply (zenon_L1888_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.54 apply (zenon_L1893_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.54 apply (zenon_L1894_); trivial. % 30.42/30.54 apply (zenon_L1287_); trivial. % 30.42/30.54 (* end of lemma zenon_L1895_ *) % 30.42/30.54 assert (zenon_L1896_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.42/30.54 do 0 intro. intros zenon_H92 zenon_H208 zenon_H1f zenon_Hcd zenon_Hde zenon_H296 zenon_H42 zenon_H6f zenon_H200 zenon_H5c zenon_H1d8 zenon_H2d zenon_H1e6 zenon_Hf6 zenon_H30d zenon_H108 zenon_H89 zenon_Hc8 zenon_H20e zenon_H222 zenon_H15a zenon_H16f zenon_H135 zenon_Hd0 zenon_H103 zenon_H100 zenon_H182 zenon_H159 zenon_H19e zenon_H102 zenon_H1bd zenon_H13b zenon_H1d5 zenon_He1 zenon_H17d zenon_H30a zenon_H2b4 zenon_H231 zenon_H20d zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H1c7 zenon_H1af zenon_H3c zenon_H5e zenon_H1ca zenon_H101 zenon_H97 zenon_H1d2 zenon_H1dc zenon_H6b zenon_Hd6 zenon_H18c zenon_H27 zenon_H1a2 zenon_He4 zenon_H8b zenon_H20. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.42/30.54 apply (zenon_L734_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.42/30.54 apply (zenon_L1865_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.54 apply (zenon_L232_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.54 apply (zenon_L1884_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.54 apply (zenon_L1895_); trivial. % 30.42/30.54 apply (zenon_L288_); trivial. % 30.42/30.54 apply (zenon_L27_); trivial. % 30.42/30.54 (* end of lemma zenon_L1896_ *) % 30.42/30.54 assert (zenon_L1897_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e2)) = (op (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 (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 30.42/30.54 do 0 intro. intros zenon_Hbd zenon_He4 zenon_H1a2 zenon_H27 zenon_H18c zenon_Hd6 zenon_H6b zenon_H1dc zenon_H1d2 zenon_H101 zenon_H1ca zenon_H5e zenon_H3c zenon_H1af zenon_H1c7 zenon_H267 zenon_H218 zenon_H156 zenon_H231 zenon_H17d zenon_He1 zenon_H1d5 zenon_H13b zenon_H1bd zenon_H102 zenon_H19e zenon_H159 zenon_H100 zenon_H103 zenon_Hd0 zenon_H135 zenon_H16f zenon_H15a zenon_H20e zenon_Hc8 zenon_H89 zenon_H108 zenon_H30d zenon_Hf6 zenon_H1e6 zenon_H2d zenon_H1d8 zenon_H5c zenon_H200 zenon_H6f zenon_H42 zenon_H296 zenon_Hde zenon_Hcd zenon_H1f zenon_H208 zenon_H92 zenon_H20d zenon_Hdf zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_Haa zenon_H113 zenon_H90 zenon_H97 zenon_H25 zenon_H60 zenon_H222 zenon_H2c zenon_H3f. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.42/30.54 apply (zenon_L1896_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.42/30.54 apply (zenon_L1853_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.42/30.54 apply (zenon_L63_); trivial. % 30.42/30.54 apply (zenon_L1866_); trivial. % 30.42/30.54 (* end of lemma zenon_L1897_ *) % 30.42/30.54 assert (zenon_L1898_ : (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.42/30.54 do 0 intro. intros zenon_H103 zenon_H100 zenon_H159 zenon_H19e zenon_H102 zenon_H13b zenon_Hd0 zenon_H1dc zenon_H6b zenon_H1d2 zenon_H10d zenon_H10e zenon_H2d zenon_H20e zenon_H108 zenon_H17d zenon_Hbd zenon_H1f zenon_H231 zenon_H267 zenon_H1d8 zenon_H1fd zenon_H173 zenon_H18c zenon_H125 zenon_Hf6 zenon_H208 zenon_H110 zenon_H1c7 zenon_H1bd zenon_H1ca zenon_H1e6 zenon_H218 zenon_H30d zenon_H3c zenon_H5e zenon_H60 zenon_H156 zenon_H135 zenon_Hde zenon_H200 zenon_Hfc zenon_H23b zenon_H89 zenon_He1 zenon_Hf9 zenon_H3f zenon_H14e zenon_H101 zenon_H1d5 zenon_Hc8 zenon_Hd6 zenon_Hee zenon_He4 zenon_H225 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H16f zenon_H92 zenon_H1a5 zenon_H16a zenon_H27 zenon_H1a2 zenon_Hcd zenon_H222 zenon_H1af zenon_Hdc zenon_H17b zenon_H97 zenon_H90 zenon_Haa zenon_H5c zenon_H15a zenon_H6f zenon_H2b4 zenon_H30a zenon_H182 zenon_H20 zenon_Hdf zenon_H20d zenon_H113. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.54 apply (zenon_L1878_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.54 apply (zenon_L1880_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.54 apply (zenon_L1848_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.54 exact (zenon_H13b zenon_Hfd). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.54 apply (zenon_L241_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.42/30.54 apply (zenon_L635_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.42/30.54 apply (zenon_L1832_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.42/30.54 apply (zenon_L1897_); trivial. % 30.42/30.54 apply (zenon_L1854_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.54 apply (zenon_L608_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.54 apply (zenon_L1897_); trivial. % 30.42/30.54 apply (zenon_L934_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.54 apply (zenon_L145_); trivial. % 30.42/30.54 apply (zenon_L1842_); trivial. % 30.42/30.54 apply (zenon_L758_); trivial. % 30.42/30.54 apply (zenon_L1812_); trivial. % 30.42/30.54 apply (zenon_L1853_); trivial. % 30.42/30.54 (* end of lemma zenon_L1898_ *) % 30.42/30.54 assert (zenon_L1899_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.54 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H40 zenon_H20e zenon_H15e zenon_H102 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.54 apply (zenon_L332_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.54 apply (zenon_L775_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.54 apply (zenon_L1145_); trivial. % 30.42/30.54 apply (zenon_L1886_); trivial. % 30.42/30.54 (* end of lemma zenon_L1899_ *) % 30.42/30.54 assert (zenon_L1900_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 30.42/30.54 do 0 intro. intros zenon_H208 zenon_H103 zenon_H13b zenon_H182 zenon_H159 zenon_H1ca zenon_H19e zenon_H3c zenon_He9 zenon_H1c7 zenon_H102 zenon_H15e zenon_H20e zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H1ba zenon_H5e zenon_H1bd zenon_H27 zenon_H26 zenon_H222 zenon_H1af zenon_H40. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.54 apply (zenon_L1899_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.54 apply (zenon_L608_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.54 apply (zenon_L3_); trivial. % 30.42/30.54 apply (zenon_L1337_); trivial. % 30.42/30.54 (* end of lemma zenon_L1900_ *) % 30.42/30.54 assert (zenon_L1901_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.42/30.54 do 0 intro. intros zenon_H135 zenon_H18c zenon_Hdc zenon_H108 zenon_H26 zenon_H27 zenon_H1bd zenon_H60 zenon_H1d2 zenon_H15e zenon_H20e zenon_H40 zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hd0 zenon_Hde zenon_H1e1. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.42/30.54 apply (zenon_L142_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.42/30.54 apply (zenon_L1838_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.42/30.54 exact (zenon_Hd0 zenon_Hcc). % 30.42/30.54 apply (zenon_L294_); trivial. % 30.42/30.54 (* end of lemma zenon_L1901_ *) % 30.42/30.54 assert (zenon_L1902_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> False). % 30.42/30.54 do 0 intro. intros zenon_H200 zenon_H1af zenon_H5e zenon_H102 zenon_H1c7 zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H13b zenon_H103 zenon_H208 zenon_H20d zenon_He9 zenon_H3c zenon_H135 zenon_H18c zenon_Hdc zenon_H108 zenon_H26 zenon_H27 zenon_H1bd zenon_H60 zenon_H1d2 zenon_H15e zenon_H20e zenon_H40 zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hd0 zenon_Hde. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.54 apply (zenon_L363_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.54 apply (zenon_L1900_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.54 apply (zenon_L224_); trivial. % 30.42/30.54 apply (zenon_L1901_); trivial. % 30.42/30.54 (* end of lemma zenon_L1902_ *) % 30.42/30.54 assert (zenon_L1903_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.54 do 0 intro. intros zenon_H16f zenon_H15a zenon_Hde zenon_Hd0 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H20e zenon_H1d2 zenon_H60 zenon_H1bd zenon_H27 zenon_H26 zenon_H108 zenon_Hdc zenon_H18c zenon_H135 zenon_H3c zenon_He9 zenon_H20d zenon_H208 zenon_H103 zenon_H13b zenon_H159 zenon_H1ca zenon_H19e zenon_H1c7 zenon_H102 zenon_H5e zenon_H1af zenon_H200 zenon_He1 zenon_Hd6 zenon_H1e zenon_H2d zenon_H42 zenon_H182 zenon_H6f. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.54 apply (zenon_L241_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.54 apply (zenon_L4_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.54 apply (zenon_L145_); trivial. % 30.42/30.54 apply (zenon_L1902_); trivial. % 30.42/30.54 apply (zenon_L758_); trivial. % 30.42/30.54 (* end of lemma zenon_L1903_ *) % 30.42/30.54 assert (zenon_L1904_ : (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.42/30.54 do 0 intro. intros zenon_Hcd zenon_H100 zenon_H159 zenon_H19e zenon_H102 zenon_H1dc zenon_H6b zenon_H10d zenon_H2d zenon_H17d zenon_Hbd zenon_H231 zenon_H267 zenon_H1d8 zenon_H1fd zenon_H173 zenon_H18c zenon_H125 zenon_Hf6 zenon_H208 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H1e6 zenon_H30d zenon_H5e zenon_H156 zenon_H200 zenon_Hfc zenon_H23b zenon_Hf9 zenon_H3f zenon_H14e zenon_Hd6 zenon_Hee zenon_He4 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H92 zenon_H1a5 zenon_H1a2 zenon_H97 zenon_Haa zenon_H5c zenon_H2b4 zenon_H30a zenon_H20 zenon_H20d zenon_H113 zenon_H218 zenon_Hd0 zenon_H222 zenon_Hde zenon_Hdf zenon_H135 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_He1 zenon_H1d2 zenon_H60 zenon_H1bd zenon_H27 zenon_H108 zenon_H13b zenon_H16f zenon_H15a zenon_H103 zenon_H20e zenon_H1af zenon_H3c zenon_H6f zenon_H101 zenon_H10e zenon_H225 zenon_H182 zenon_H16a. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.42/30.54 apply (zenon_L734_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.42/30.54 apply (zenon_L734_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.54 apply (zenon_L232_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.54 apply (zenon_L1873_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.54 apply (zenon_L192_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.54 apply (zenon_L232_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.54 apply (zenon_L48_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.54 apply (zenon_L49_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.54 apply (zenon_L1878_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.54 apply (zenon_L1880_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.54 apply (zenon_L1873_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.54 exact (zenon_H13b zenon_Hfd). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.54 apply (zenon_L241_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.54 apply (zenon_L1868_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.54 apply (zenon_L126_); trivial. % 30.42/30.54 apply (zenon_L1842_); trivial. % 30.42/30.54 apply (zenon_L758_); trivial. % 30.42/30.54 apply (zenon_L1812_); trivial. % 30.42/30.54 apply (zenon_L1853_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.54 apply (zenon_L232_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.54 apply (zenon_L1873_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.54 apply (zenon_L192_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.54 apply (zenon_L232_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.54 apply (zenon_L1799_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.54 exact (zenon_H13b zenon_Hfd). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.54 apply (zenon_L241_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.42/30.54 apply (zenon_L635_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.42/30.54 apply (zenon_L235_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.42/30.54 apply (zenon_L17_); trivial. % 30.42/30.54 apply (zenon_L1854_); trivial. % 30.42/30.54 apply (zenon_L758_); trivial. % 30.42/30.54 apply (zenon_L406_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.54 apply (zenon_L49_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.54 apply (zenon_L1878_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.54 apply (zenon_L1880_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.54 apply (zenon_L1873_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.54 exact (zenon_H13b zenon_Hfd). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.54 apply (zenon_L241_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.54 apply (zenon_L1855_); trivial. % 30.42/30.54 apply (zenon_L758_); trivial. % 30.42/30.54 apply (zenon_L1812_); trivial. % 30.42/30.54 apply (zenon_L1853_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.54 apply (zenon_L232_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.54 apply (zenon_L1873_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.54 apply (zenon_L192_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.54 apply (zenon_L232_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.54 apply (zenon_L1898_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.54 apply (zenon_L49_); trivial. % 30.42/30.54 apply (zenon_L386_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.42/30.54 apply (zenon_L1875_); trivial. % 30.42/30.54 apply (zenon_L115_); trivial. % 30.42/30.54 (* end of lemma zenon_L1904_ *) % 30.42/30.54 assert (zenon_L1905_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.42/30.54 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H1af zenon_H1bd zenon_H20e zenon_H15e zenon_Hbd zenon_H108 zenon_Hd0 zenon_H26 zenon_H27 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H17d zenon_H1d2 zenon_H103 zenon_H13b zenon_H182 zenon_H159 zenon_H100 zenon_H102 zenon_H10e zenon_H10d zenon_Hf6 zenon_H1e1. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.54 apply (zenon_L332_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.54 apply (zenon_L209_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.54 apply (zenon_L1145_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.42/30.54 apply (zenon_L1881_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.42/30.54 apply (zenon_L1849_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.42/30.54 apply (zenon_L63_); trivial. % 30.42/30.54 apply (zenon_L690_); trivial. % 30.42/30.54 (* end of lemma zenon_L1905_ *) % 30.42/30.54 assert (zenon_L1906_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.54 do 0 intro. intros zenon_Hf6 zenon_H10d zenon_H10e zenon_H102 zenon_H100 zenon_H159 zenon_H13b zenon_H103 zenon_H1d2 zenon_H17d zenon_Hc3 zenon_H30a zenon_H2b4 zenon_H27 zenon_H26 zenon_Hd0 zenon_H108 zenon_Hbd zenon_H20e zenon_H1bd zenon_H1af zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H135 zenon_H18c zenon_Hdc zenon_H3c zenon_He9 zenon_H20d zenon_H60 zenon_H5e zenon_Hd5 zenon_Hcd zenon_H19e zenon_H1dc zenon_H6b zenon_H2d zenon_H231 zenon_H267 zenon_H1d8 zenon_H1fd zenon_H173 zenon_H125 zenon_H208 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H1e6 zenon_H30d zenon_H156 zenon_H200 zenon_Hfc zenon_H23b zenon_Hf9 zenon_H3f zenon_H14e zenon_Hd6 zenon_Hee zenon_He4 zenon_Hd1 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H92 zenon_H1a5 zenon_H1a2 zenon_H97 zenon_Haa zenon_H5c zenon_H20 zenon_H113 zenon_H218 zenon_H222 zenon_Hde zenon_He1 zenon_H16f zenon_H15a zenon_H101 zenon_H225 zenon_H16a zenon_H182 zenon_H6f. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.54 apply (zenon_L241_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.54 apply (zenon_L1904_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.54 apply (zenon_L608_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.54 apply (zenon_L224_); trivial. % 30.42/30.54 apply (zenon_L1905_); trivial. % 30.42/30.54 apply (zenon_L758_); trivial. % 30.42/30.54 (* end of lemma zenon_L1906_ *) % 30.42/30.54 assert (zenon_L1907_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.54 do 0 intro. intros zenon_H16f zenon_H89 zenon_H15a zenon_H103 zenon_Hee zenon_Hb6 zenon_H182 zenon_H6f. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.54 apply (zenon_L241_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.54 apply (zenon_L490_); trivial. % 30.42/30.54 apply (zenon_L758_); trivial. % 30.42/30.54 (* end of lemma zenon_L1907_ *) % 30.42/30.54 assert (zenon_L1908_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 30.42/30.54 do 0 intro. intros zenon_H200 zenon_H218 zenon_H17b zenon_Hd0 zenon_Hde zenon_H135 zenon_H19e zenon_H2d zenon_H16f zenon_H89 zenon_H15a zenon_H103 zenon_Hee zenon_H182 zenon_H6f zenon_H222 zenon_H90 zenon_Hb8 zenon_H1dc zenon_H102 zenon_H159 zenon_H9d zenon_H100 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H108 zenon_H17d zenon_Hbd zenon_H1bd zenon_H1af zenon_H3d. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.54 apply (zenon_L406_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.54 apply (zenon_L1812_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.42/30.54 apply (zenon_L1860_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.42/30.54 apply (zenon_L1819_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.42/30.54 apply (zenon_L177_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.42/30.54 apply (zenon_L39_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.42/30.54 apply (zenon_L775_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.42/30.54 apply (zenon_L1907_); trivial. % 30.42/30.54 apply (zenon_L107_); trivial. % 30.42/30.54 apply (zenon_L209_); trivial. % 30.42/30.54 (* end of lemma zenon_L1908_ *) % 30.42/30.54 assert (zenon_L1909_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.42/30.54 do 0 intro. intros zenon_Hb8 zenon_He7 zenon_H89 zenon_H9d zenon_He1 zenon_Hee zenon_H15e zenon_Hb1 zenon_H2d. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.42/30.54 apply (zenon_L199_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.42/30.54 apply (zenon_L1354_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.42/30.54 apply (zenon_L490_); trivial. % 30.42/30.54 apply (zenon_L107_); trivial. % 30.42/30.54 (* end of lemma zenon_L1909_ *) % 30.42/30.54 assert (zenon_L1910_ : (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.54 do 0 intro. intros zenon_H2d zenon_Hee zenon_He1 zenon_H9d zenon_H89 zenon_He7 zenon_Hb8 zenon_H10d zenon_H10e zenon_H102 zenon_H159 zenon_H100 zenon_H103 zenon_H1d2 zenon_H17d zenon_Hc3 zenon_H30a zenon_H2b4 zenon_H27 zenon_H26 zenon_Hd0 zenon_H108 zenon_Hbd zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hc9 zenon_H20d zenon_H231 zenon_H200 zenon_H17b zenon_Hde zenon_H135 zenon_H19e zenon_H16f zenon_H15a zenon_H222 zenon_H90 zenon_H1dc zenon_H1bd zenon_H1af zenon_H1d5 zenon_H182 zenon_H6f. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.54 apply (zenon_L241_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.54 exact (zenon_H103 zenon_H37). % 30.42/30.54 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.54 apply (zenon_L273_); trivial. % 30.42/30.54 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.55 apply (zenon_L1908_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.55 apply (zenon_L628_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.42/30.55 apply (zenon_L1881_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.42/30.55 apply (zenon_L1819_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.42/30.55 apply (zenon_L63_); trivial. % 30.42/30.55 apply (zenon_L1909_); trivial. % 30.42/30.55 apply (zenon_L758_); trivial. % 30.42/30.55 (* end of lemma zenon_L1910_ *) % 30.42/30.55 assert (zenon_L1911_ : (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H6f zenon_H182 zenon_H1d5 zenon_H1af zenon_H1dc zenon_H90 zenon_H222 zenon_H15a zenon_H16f zenon_H19e zenon_H135 zenon_Hde zenon_H200 zenon_H231 zenon_H20d zenon_H156 zenon_H267 zenon_Hbd zenon_H108 zenon_H26 zenon_H27 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H17d zenon_H1d2 zenon_H103 zenon_H100 zenon_H159 zenon_H102 zenon_H10e zenon_H10d zenon_Hb8 zenon_He7 zenon_H89 zenon_H9d zenon_He1 zenon_Hee zenon_H2d zenon_H142 zenon_H60 zenon_H1bd zenon_Hd0 zenon_H17b zenon_H218. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.42/30.55 apply (zenon_L1910_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.42/30.55 apply (zenon_L165_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.42/30.55 exact (zenon_Hd0 zenon_Hcc). % 30.42/30.55 apply (zenon_L405_); trivial. % 30.42/30.55 (* end of lemma zenon_L1911_ *) % 30.42/30.55 assert (zenon_L1912_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H16a zenon_H225 zenon_H101 zenon_H3c zenon_H113 zenon_H20 zenon_H5c zenon_Haa zenon_H97 zenon_H1a2 zenon_H1a5 zenon_H92 zenon_Hc0 zenon_H296 zenon_H30b zenon_H42 zenon_Hd1 zenon_He4 zenon_Hd6 zenon_H14e zenon_H3f zenon_Hf9 zenon_H23b zenon_Hfc zenon_H30d zenon_H1e6 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H208 zenon_H125 zenon_H18c zenon_H173 zenon_H1fd zenon_H1d8 zenon_H6b zenon_Hcd zenon_Hd5 zenon_H5e zenon_H218 zenon_H17b zenon_H60 zenon_H2d zenon_Hee zenon_He1 zenon_H9d zenon_He7 zenon_Hb8 zenon_H267 zenon_H156 zenon_H20d zenon_H231 zenon_H200 zenon_Hde zenon_H135 zenon_H19e zenon_H16f zenon_H15a zenon_H222 zenon_H90 zenon_H1dc zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H1af zenon_H1bd zenon_H20e zenon_H15e zenon_Hbd zenon_H108 zenon_Hd0 zenon_H26 zenon_H27 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H17d zenon_H1d2 zenon_H103 zenon_H13b zenon_H182 zenon_H159 zenon_H100 zenon_H102 zenon_H10e zenon_H10d zenon_Hf6. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.55 apply (zenon_L1904_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.55 apply (zenon_L608_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.55 apply (zenon_L1911_); trivial. % 30.42/30.55 apply (zenon_L1905_); trivial. % 30.42/30.55 (* end of lemma zenon_L1912_ *) % 30.42/30.55 assert (zenon_L1913_ : (~((e1) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.42/30.55 do 0 intro. intros zenon_Hcd zenon_H5c zenon_H10e zenon_H27 zenon_H97 zenon_Hf6 zenon_H10d zenon_H17d zenon_H30a zenon_H2b4 zenon_Hbd zenon_H20e zenon_H1dc zenon_H222 zenon_H15a zenon_H16f zenon_Hde zenon_H200 zenon_H231 zenon_H20d zenon_H267 zenon_Hb8 zenon_He7 zenon_Hee zenon_H2d zenon_H1d8 zenon_H1fd zenon_H173 zenon_H125 zenon_H110 zenon_H1e6 zenon_H30d zenon_Hfc zenon_H23b zenon_Hf9 zenon_H3f zenon_H14e zenon_He4 zenon_H42 zenon_H30b zenon_H296 zenon_Hc0 zenon_H92 zenon_H1a5 zenon_H1a2 zenon_Haa zenon_H20 zenon_H113 zenon_H225 zenon_H6f zenon_H124 zenon_H19e zenon_H1d5 zenon_H89 zenon_Hc8 zenon_He1 zenon_H218 zenon_H1d2 zenon_H60 zenon_H1bd zenon_Hd0 zenon_H108 zenon_H208 zenon_Hd6 zenon_H1af zenon_H1c7 zenon_H1ca zenon_Hd1 zenon_H6b zenon_H18c zenon_H135 zenon_H5e zenon_H3c zenon_H156 zenon_H101 zenon_H102 zenon_H100 zenon_H159 zenon_H13b zenon_H103 zenon_Hd9 zenon_H182 zenon_H16a. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.42/30.55 apply (zenon_L734_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.42/30.55 apply (zenon_L734_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.55 apply (zenon_L232_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.55 apply (zenon_L1850_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.55 apply (zenon_L192_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.55 apply (zenon_L232_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.55 apply (zenon_L48_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.55 apply (zenon_L191_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.55 apply (zenon_L1852_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1800_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.55 apply (zenon_L18_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.55 apply (zenon_L1868_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.55 apply (zenon_L347_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.55 apply (zenon_L165_); trivial. % 30.42/30.55 apply (zenon_L1869_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.55 apply (zenon_L592_); trivial. % 30.42/30.55 apply (zenon_L1844_); trivial. % 30.42/30.55 apply (zenon_L758_); trivial. % 30.42/30.55 apply (zenon_L1872_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.55 apply (zenon_L1843_); trivial. % 30.42/30.55 apply (zenon_L1849_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.55 apply (zenon_L232_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.55 apply (zenon_L1846_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L349_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L1877_); trivial. % 30.42/30.55 apply (zenon_L1872_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.55 apply (zenon_L1843_); trivial. % 30.42/30.55 apply (zenon_L1849_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.55 apply (zenon_L191_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.55 apply (zenon_L1852_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1800_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L1877_); trivial. % 30.42/30.55 apply (zenon_L1872_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.55 apply (zenon_L1843_); trivial. % 30.42/30.55 apply (zenon_L1849_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.55 apply (zenon_L232_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.55 apply (zenon_L1850_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.55 apply (zenon_L192_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.55 apply (zenon_L232_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.55 apply (zenon_L1846_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1847_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.55 apply (zenon_L241_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.55 apply (zenon_L1898_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.55 apply (zenon_L347_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.55 apply (zenon_L165_); trivial. % 30.42/30.55 apply (zenon_L1869_); trivial. % 30.42/30.55 apply (zenon_L758_); trivial. % 30.42/30.55 apply (zenon_L1872_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.55 apply (zenon_L1843_); trivial. % 30.42/30.55 apply (zenon_L1849_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.55 apply (zenon_L191_); trivial. % 30.42/30.55 apply (zenon_L386_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.42/30.55 apply (zenon_L797_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.55 apply (zenon_L232_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.55 apply (zenon_L232_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.55 apply (zenon_L48_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.55 apply (zenon_L191_); trivial. % 30.42/30.55 apply (zenon_L1800_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.55 apply (zenon_L192_); trivial. % 30.42/30.55 apply (zenon_L636_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.42/30.55 apply (zenon_L1801_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.55 apply (zenon_L232_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.55 apply (zenon_L232_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.55 apply (zenon_L1903_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.42/30.55 apply (zenon_L1847_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.42/30.55 apply (zenon_L906_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.42/30.55 apply (zenon_L1906_); trivial. % 30.42/30.55 apply (zenon_L30_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.55 apply (zenon_L1848_); trivial. % 30.42/30.55 apply (zenon_L1849_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.55 apply (zenon_L191_); trivial. % 30.42/30.55 apply (zenon_L386_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.55 apply (zenon_L192_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.55 apply (zenon_L232_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1903_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L635_); trivial. % 30.42/30.55 apply (zenon_L1845_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1847_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L635_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.55 apply (zenon_L241_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.55 apply (zenon_L1879_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.55 apply (zenon_L1812_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.55 apply (zenon_L1911_); trivial. % 30.42/30.55 apply (zenon_L1905_); trivial. % 30.42/30.55 apply (zenon_L758_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.42/30.55 apply (zenon_L906_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1906_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L212_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.55 apply (zenon_L241_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.55 apply (zenon_L1912_); trivial. % 30.42/30.55 apply (zenon_L758_); trivial. % 30.42/30.55 apply (zenon_L30_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1848_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L635_); trivial. % 30.42/30.55 apply (zenon_L1812_); trivial. % 30.42/30.55 apply (zenon_L1849_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.55 apply (zenon_L191_); trivial. % 30.42/30.55 apply (zenon_L386_); trivial. % 30.42/30.55 apply (zenon_L115_); trivial. % 30.42/30.55 (* end of lemma zenon_L1913_ *) % 30.42/30.55 assert (zenon_L1914_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H182 zenon_H20 zenon_H3d zenon_H1af zenon_H1bd zenon_Hb8 zenon_He7 zenon_H89 zenon_H9d zenon_He1 zenon_Hee zenon_H15e zenon_H2d. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.42/30.55 exact (zenon_H30a zenon_H185). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.42/30.55 apply (zenon_L658_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.42/30.55 apply (zenon_L209_); trivial. % 30.42/30.55 apply (zenon_L1909_); trivial. % 30.42/30.55 (* end of lemma zenon_L1914_ *) % 30.42/30.55 assert (zenon_L1915_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H16f zenon_H15a zenon_H9d zenon_He1 zenon_H2b4 zenon_H30a zenon_H20 zenon_H1af zenon_H1bd zenon_Hb8 zenon_He7 zenon_H89 zenon_Hee zenon_H2d zenon_H103 zenon_H1e zenon_H42 zenon_H182 zenon_H6f. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.55 apply (zenon_L241_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.55 apply (zenon_L4_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.55 apply (zenon_L1914_); trivial. % 30.42/30.55 apply (zenon_L1354_); trivial. % 30.42/30.55 apply (zenon_L758_); trivial. % 30.42/30.55 (* end of lemma zenon_L1915_ *) % 30.42/30.55 assert (zenon_L1916_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H182 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H3d zenon_H1c7. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.42/30.55 apply (zenon_L690_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.42/30.55 apply (zenon_L934_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.42/30.55 apply (zenon_L550_); trivial. % 30.42/30.55 apply (zenon_L167_); trivial. % 30.42/30.55 (* end of lemma zenon_L1916_ *) % 30.42/30.55 assert (zenon_L1917_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H20 zenon_H1bd zenon_H1e6 zenon_Hf6 zenon_H182 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H3d zenon_H1c7. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.42/30.55 exact (zenon_H30a zenon_H185). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.42/30.55 apply (zenon_L658_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.42/30.55 apply (zenon_L209_); trivial. % 30.42/30.55 apply (zenon_L1916_); trivial. % 30.42/30.55 (* end of lemma zenon_L1917_ *) % 30.42/30.55 assert (zenon_L1918_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H16f zenon_H15a zenon_H103 zenon_H13b zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1af zenon_H1c7 zenon_H102 zenon_H20e zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H2b4 zenon_H30a zenon_H20 zenon_H1e6 zenon_Hf6 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1e zenon_H2d zenon_H42 zenon_H182 zenon_H6f. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.55 apply (zenon_L241_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.55 apply (zenon_L4_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.55 apply (zenon_L1917_); trivial. % 30.42/30.55 apply (zenon_L1899_); trivial. % 30.42/30.55 apply (zenon_L758_); trivial. % 30.42/30.55 (* end of lemma zenon_L1918_ *) % 30.42/30.55 assert (zenon_L1919_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H101 zenon_H108 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_H20e zenon_H102 zenon_H1c7 zenon_H3c zenon_H5e zenon_H6c zenon_H19e zenon_H1ca zenon_H159 zenon_H13b zenon_Hd6 zenon_Hcc zenon_H60 zenon_H16f zenon_H15a zenon_He1 zenon_H2b4 zenon_H30a zenon_H20 zenon_H1af zenon_H1bd zenon_Hb8 zenon_He7 zenon_H89 zenon_Hee zenon_H2d zenon_H103 zenon_H1e zenon_H42 zenon_H182 zenon_H6f. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1918_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L575_); trivial. % 30.42/30.55 apply (zenon_L1915_); trivial. % 30.42/30.55 (* end of lemma zenon_L1919_ *) % 30.42/30.55 assert (zenon_L1920_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H101 zenon_H231 zenon_H1dc zenon_H60 zenon_H3f zenon_H90 zenon_Hcd zenon_Hf9 zenon_H13b zenon_Hcc zenon_Hd6 zenon_H16f zenon_H15a zenon_He1 zenon_H2b4 zenon_H30a zenon_H20 zenon_H1af zenon_H1bd zenon_Hb8 zenon_He7 zenon_H89 zenon_Hee zenon_H2d zenon_H103 zenon_H1e zenon_H42 zenon_H182 zenon_H6f. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1105_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L555_); trivial. % 30.42/30.55 apply (zenon_L1915_); trivial. % 30.42/30.55 (* end of lemma zenon_L1920_ *) % 30.42/30.55 assert (zenon_L1921_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H92 zenon_H208 zenon_H18c zenon_H1f zenon_H159 zenon_H1ca zenon_H19e zenon_H5e zenon_H3c zenon_H1c7 zenon_H102 zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H108 zenon_H101 zenon_H231 zenon_H1dc zenon_H60 zenon_H3f zenon_Hcd zenon_Hf9 zenon_H13b zenon_Hcc zenon_Hd6 zenon_H16f zenon_H15a zenon_He1 zenon_H2b4 zenon_H30a zenon_H20 zenon_H1af zenon_H1bd zenon_Hb8 zenon_He7 zenon_H89 zenon_Hee zenon_H2d zenon_H103 zenon_H1e zenon_H42 zenon_H182 zenon_H6f. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.42/30.55 apply (zenon_L734_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1856_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L575_); trivial. % 30.42/30.55 apply (zenon_L1915_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.42/30.55 apply (zenon_L1919_); trivial. % 30.42/30.55 apply (zenon_L1920_); trivial. % 30.42/30.55 (* end of lemma zenon_L1921_ *) % 30.42/30.55 assert (zenon_L1922_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.42/30.55 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_H1c7 zenon_H1af zenon_H108 zenon_H60 zenon_Hcc zenon_H156 zenon_H182 zenon_Hf6 zenon_H1e6 zenon_H1bd zenon_H20 zenon_H30a zenon_H2b4 zenon_H23b zenon_Hcd zenon_H6f zenon_H26 zenon_H10d zenon_He2 zenon_H89. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.55 apply (zenon_L4_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.55 apply (zenon_L1917_); trivial. % 30.42/30.55 apply (zenon_L1389_); trivial. % 30.42/30.55 (* end of lemma zenon_L1922_ *) % 30.42/30.55 assert (zenon_L1923_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H92 zenon_Hd9 zenon_H10d zenon_H26 zenon_H23b zenon_H6b zenon_H74 zenon_He4 zenon_H159 zenon_H1ca zenon_H19e zenon_H5e zenon_H3c zenon_H1c7 zenon_H102 zenon_H20e zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H108 zenon_H101 zenon_H231 zenon_H1dc zenon_H60 zenon_H3f zenon_Hcd zenon_Hf9 zenon_H13b zenon_Hcc zenon_Hd6 zenon_H16f zenon_H15a zenon_He1 zenon_H2b4 zenon_H30a zenon_H20 zenon_H1af zenon_H1bd zenon_Hb8 zenon_He7 zenon_H89 zenon_Hee zenon_H2d zenon_H103 zenon_H1e zenon_H42 zenon_H182 zenon_H6f. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.42/30.55 apply (zenon_L797_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.55 exact (zenon_H74 zenon_H73). % 30.42/30.55 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.55 apply (zenon_L48_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.55 apply (zenon_L552_); trivial. % 30.42/30.55 apply (zenon_L1922_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.42/30.55 apply (zenon_L1919_); trivial. % 30.42/30.55 apply (zenon_L1920_); trivial. % 30.42/30.55 (* end of lemma zenon_L1923_ *) % 30.42/30.55 assert (zenon_L1924_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (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). % 30.42/30.55 do 0 intro. intros zenon_Hc0 zenon_H18c zenon_H208 zenon_H6f zenon_H42 zenon_H1e zenon_H103 zenon_H2d zenon_Hee zenon_H89 zenon_He7 zenon_Hb8 zenon_H1bd zenon_H1af zenon_H20 zenon_H30a zenon_H2b4 zenon_He1 zenon_H15a zenon_H16f zenon_Hd6 zenon_Hcc zenon_H13b zenon_Hf9 zenon_Hcd zenon_H3f zenon_H60 zenon_H1dc zenon_H231 zenon_H101 zenon_H108 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_H20e zenon_H102 zenon_H1c7 zenon_H3c zenon_H5e zenon_H19e zenon_H1ca zenon_H159 zenon_He4 zenon_H74 zenon_H6b zenon_H23b zenon_H10d zenon_Hd9 zenon_H92 zenon_H182 zenon_H16a. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.42/30.55 apply (zenon_L734_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.42/30.55 apply (zenon_L1921_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.42/30.55 apply (zenon_L1923_); trivial. % 30.42/30.55 apply (zenon_L115_); trivial. % 30.42/30.55 (* end of lemma zenon_L1924_ *) % 30.42/30.55 assert (zenon_L1925_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.42/30.55 do 0 intro. intros zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_Hdf zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H182 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H3d zenon_H1c7. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.42/30.55 apply (zenon_L194_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.42/30.55 apply (zenon_L1853_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.42/30.55 apply (zenon_L63_); trivial. % 30.42/30.55 apply (zenon_L1916_); trivial. % 30.42/30.55 (* end of lemma zenon_L1925_ *) % 30.42/30.55 assert (zenon_L1926_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.42/30.55 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_H1c7 zenon_H1af zenon_H108 zenon_H60 zenon_Hcc zenon_H156 zenon_H182 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_Hdf zenon_H20d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_He1 zenon_H9d. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.42/30.55 apply (zenon_L4_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.42/30.55 exact (zenon_H103 zenon_H37). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.42/30.55 apply (zenon_L1925_); trivial. % 30.42/30.55 apply (zenon_L1354_); trivial. % 30.42/30.55 (* end of lemma zenon_L1926_ *) % 30.42/30.55 assert (zenon_L1927_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H108 zenon_Hcc zenon_H156 zenon_H182 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_Hdf zenon_H20d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_H218 zenon_H17b zenon_H60 zenon_H1ca zenon_Hc3 zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H9d zenon_H222 zenon_H1af zenon_H1c7. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.55 apply (zenon_L332_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.55 apply (zenon_L1925_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.55 apply (zenon_L259_); trivial. % 30.42/30.55 apply (zenon_L1807_); trivial. % 30.42/30.55 (* end of lemma zenon_L1927_ *) % 30.42/30.55 assert (zenon_L1928_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.55 do 0 intro. intros zenon_H208 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H17b zenon_H218 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_Hdf zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_Hcc zenon_H108 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H60 zenon_H222 zenon_H156 zenon_H182. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.42/30.55 apply (zenon_L1927_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.42/30.55 apply (zenon_L218_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.42/30.55 apply (zenon_L256_); trivial. % 30.42/30.55 apply (zenon_L934_); trivial. % 30.42/30.55 (* end of lemma zenon_L1928_ *) % 30.42/30.55 assert (zenon_L1929_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.55 do 0 intro. intros zenon_H101 zenon_H18c zenon_H68 zenon_H13b zenon_Hd6 zenon_H208 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H17b zenon_H218 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_Hdf zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_Hcc zenon_H108 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H156 zenon_H182. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1856_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L555_); trivial. % 30.42/30.55 apply (zenon_L1928_); trivial. % 30.42/30.55 (* end of lemma zenon_L1929_ *) % 30.42/30.55 assert (zenon_L1930_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.55 do 0 intro. intros zenon_H101 zenon_H156 zenon_H3c zenon_H5e zenon_H1f zenon_H18c zenon_H68 zenon_H208 zenon_H13b zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H1ba zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.55 apply (zenon_L1856_); trivial. % 30.42/30.55 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.55 exact (zenon_H13b zenon_Hfd). % 30.42/30.55 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.55 apply (zenon_L575_); trivial. % 30.42/30.55 apply (zenon_L1812_); trivial. % 30.42/30.55 (* end of lemma zenon_L1930_ *) % 30.42/30.55 assert (zenon_L1931_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H108 zenon_H60 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_Hdf zenon_H20d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hcc zenon_He1 zenon_H102 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.56 apply (zenon_L332_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.56 apply (zenon_L1925_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.56 apply (zenon_L544_); trivial. % 30.42/30.56 apply (zenon_L1886_); trivial. % 30.42/30.56 (* end of lemma zenon_L1931_ *) % 30.42/30.56 assert (zenon_L1932_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H108 zenon_Hcc zenon_H156 zenon_H182 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_Hdf zenon_H20d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_H218 zenon_H17b zenon_H60 zenon_H1ca zenon_Hc3 zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1af zenon_H1c7. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.56 apply (zenon_L332_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.56 apply (zenon_L1925_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.56 apply (zenon_L259_); trivial. % 30.42/30.56 apply (zenon_L1885_); trivial. % 30.42/30.56 (* end of lemma zenon_L1932_ *) % 30.42/30.56 assert (zenon_L1933_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.56 do 0 intro. intros zenon_H101 zenon_H6c zenon_Hde zenon_Hd6 zenon_H208 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H17b zenon_H218 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_Hdf zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_Hcc zenon_H108 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H156 zenon_H182. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1932_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 apply (zenon_L782_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L575_); trivial. % 30.42/30.56 apply (zenon_L1928_); trivial. % 30.42/30.56 (* end of lemma zenon_L1933_ *) % 30.42/30.56 assert (zenon_L1934_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H101 zenon_H231 zenon_H1dc zenon_H3f zenon_H90 zenon_Hcd zenon_Hf9 zenon_Hdc zenon_Hd1 zenon_Hd6 zenon_H42 zenon_H2d zenon_H1e zenon_H103 zenon_H1c7 zenon_H1af zenon_H108 zenon_H60 zenon_Hcc zenon_H156 zenon_H182 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_Hdf zenon_H20d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_He1. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1105_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 apply (zenon_L154_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L555_); trivial. % 30.42/30.56 apply (zenon_L1926_); trivial. % 30.42/30.56 (* end of lemma zenon_L1934_ *) % 30.42/30.56 assert (zenon_L1935_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.42/30.56 do 0 intro. intros zenon_H101 zenon_H231 zenon_H1dc zenon_H3f zenon_H90 zenon_Hcd zenon_Hf9 zenon_Hde zenon_Hd6 zenon_H208 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H17b zenon_H218 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_Hdf zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_Hcc zenon_H108 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H3c zenon_H1f zenon_H5e zenon_H60 zenon_H222 zenon_H156 zenon_H182. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1105_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 apply (zenon_L782_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L555_); trivial. % 30.42/30.56 apply (zenon_L1928_); trivial. % 30.42/30.56 (* end of lemma zenon_L1935_ *) % 30.42/30.56 assert (zenon_L1936_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H101 zenon_H231 zenon_H1dc zenon_H3f zenon_H90 zenon_Hcd zenon_Hf9 zenon_Hdc zenon_Hd1 zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H1ba zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1105_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 apply (zenon_L154_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L575_); trivial. % 30.42/30.56 apply (zenon_L1812_); trivial. % 30.42/30.56 (* end of lemma zenon_L1936_ *) % 30.42/30.56 assert (zenon_L1937_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H296 zenon_He1 zenon_H2d zenon_H42 zenon_H156 zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H108 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H1d8 zenon_H5c zenon_Hbd zenon_H218 zenon_H17b zenon_H1ca zenon_H1bd zenon_H1af zenon_H1c7 zenon_H208 zenon_Hde zenon_H103 zenon_H100 zenon_H159 zenon_H19e zenon_H102 zenon_H60 zenon_Hcc zenon_Hd6 zenon_Hd1 zenon_Hdc zenon_Hf9 zenon_Hcd zenon_H90 zenon_H3f zenon_H1dc zenon_H231 zenon_H101 zenon_H2b4 zenon_H30a zenon_H182 zenon_H20 zenon_Hdf zenon_H20d zenon_H113. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.56 apply (zenon_L1934_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.56 apply (zenon_L1935_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.56 apply (zenon_L1936_); trivial. % 30.42/30.56 apply (zenon_L1853_); trivial. % 30.42/30.56 (* end of lemma zenon_L1937_ *) % 30.42/30.56 assert (zenon_L1938_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.42/30.56 do 0 intro. intros zenon_He4 zenon_H113 zenon_H20d zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_H101 zenon_H231 zenon_H1dc zenon_H3f zenon_Hf9 zenon_Hd1 zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H19e zenon_H159 zenon_H100 zenon_H103 zenon_H208 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H1ca zenon_H17b zenon_H218 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H108 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H156 zenon_H42 zenon_H2d zenon_He1 zenon_H296 zenon_Hdf zenon_Hde zenon_H90 zenon_Hcd. % 30.42/30.56 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.42/30.56 apply (zenon_L232_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.42/30.56 apply (zenon_L1937_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.42/30.56 apply (zenon_L49_); trivial. % 30.42/30.56 apply (zenon_L386_); trivial. % 30.42/30.56 (* end of lemma zenon_L1938_ *) % 30.42/30.56 assert (zenon_L1939_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (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 (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H225 zenon_H27 zenon_He4 zenon_H113 zenon_H20d zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_H101 zenon_H231 zenon_H1dc zenon_H3f zenon_Hf9 zenon_Hd1 zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H19e zenon_H159 zenon_H100 zenon_H103 zenon_H208 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H1ca zenon_H218 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H108 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H156 zenon_H42 zenon_H2d zenon_He1 zenon_H296 zenon_Hdf zenon_Hde zenon_H90 zenon_Hcd. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.56 apply (zenon_L232_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.56 apply (zenon_L1105_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.56 apply (zenon_L554_); trivial. % 30.42/30.56 apply (zenon_L1938_); trivial. % 30.42/30.56 (* end of lemma zenon_L1939_ *) % 30.42/30.56 assert (zenon_L1940_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (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 (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H92 zenon_H6f zenon_H18c zenon_H13b zenon_H225 zenon_H27 zenon_He4 zenon_H113 zenon_H20d zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_H101 zenon_H231 zenon_H1dc zenon_H3f zenon_Hf9 zenon_Hd1 zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H19e zenon_H159 zenon_H100 zenon_H103 zenon_H208 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H1ca zenon_H218 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H108 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H156 zenon_H42 zenon_H2d zenon_He1 zenon_H296 zenon_Hdf zenon_Hde zenon_Hcd. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.42/30.56 apply (zenon_L734_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.56 apply (zenon_L232_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.56 apply (zenon_L1856_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.56 apply (zenon_L554_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1856_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 exact (zenon_H13b zenon_Hfd). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L555_); trivial. % 30.42/30.56 apply (zenon_L1926_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.56 apply (zenon_L1929_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.56 apply (zenon_L1930_); trivial. % 30.42/30.56 apply (zenon_L1853_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.42/30.56 apply (zenon_L232_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.42/30.56 apply (zenon_L1931_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.42/30.56 apply (zenon_L192_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1931_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 exact (zenon_H13b zenon_Hfd). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L575_); trivial. % 30.42/30.56 apply (zenon_L1926_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.56 apply (zenon_L1933_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1931_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 exact (zenon_H13b zenon_Hfd). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L555_); trivial. % 30.42/30.56 apply (zenon_L1812_); trivial. % 30.42/30.56 apply (zenon_L1853_); trivial. % 30.42/30.56 apply (zenon_L1939_); trivial. % 30.42/30.56 (* end of lemma zenon_L1940_ *) % 30.42/30.56 assert (zenon_L1941_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H310 zenon_H1e1 zenon_H103 zenon_H100 zenon_H9d zenon_H182 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H5e zenon_H222 zenon_H1c7 zenon_H102 zenon_Hcc zenon_H6b zenon_H1af zenon_H1c5 zenon_H20d. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_Hdf | zenon_intro zenon_H311 ]. % 30.42/30.56 apply (zenon_L548_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H6c | zenon_intro zenon_H312 ]. % 30.42/30.56 apply (zenon_L1808_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H76 ]. % 30.42/30.56 apply (zenon_L552_); trivial. % 30.42/30.56 apply (zenon_L1343_); trivial. % 30.42/30.56 (* end of lemma zenon_L1941_ *) % 30.42/30.56 assert (zenon_L1942_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H1d5 zenon_Hc8 zenon_H2d zenon_H15e zenon_Hee zenon_He1 zenon_H89 zenon_He7 zenon_Hb8 zenon_H20 zenon_H218 zenon_H17b zenon_H60 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H20d zenon_H1af zenon_H6b zenon_Hcc zenon_H102 zenon_H1c7 zenon_H222 zenon_H5e zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H9d zenon_H100 zenon_H103 zenon_H310 zenon_H9c zenon_H110. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.56 apply (zenon_L332_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.56 apply (zenon_L1914_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.56 apply (zenon_L259_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.42/30.56 exact (zenon_H30a zenon_H185). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.42/30.56 apply (zenon_L1458_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.42/30.56 apply (zenon_L1941_); trivial. % 30.42/30.56 apply (zenon_L65_); trivial. % 30.42/30.56 (* end of lemma zenon_L1942_ *) % 30.42/30.56 assert (zenon_L1943_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H14b zenon_Hcd zenon_Hdf zenon_H296 zenon_H42 zenon_H156 zenon_H1f zenon_H3c zenon_H108 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H1d8 zenon_H5c zenon_Hbd zenon_H208 zenon_Hd6 zenon_Hd1 zenon_Hf9 zenon_H3f zenon_H1dc zenon_H231 zenon_H101 zenon_H113 zenon_He4 zenon_H27 zenon_H225 zenon_H13b zenon_H18c zenon_H6f zenon_H92 zenon_Hfc zenon_Hde zenon_H1d5 zenon_Hc8 zenon_H2d zenon_H15e zenon_Hee zenon_He1 zenon_H89 zenon_He7 zenon_Hb8 zenon_H20 zenon_H218 zenon_H17b zenon_H60 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H20d zenon_H1af zenon_H6b zenon_Hcc zenon_H102 zenon_H1c7 zenon_H222 zenon_H5e zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H9d zenon_H100 zenon_H103 zenon_H310 zenon_H110. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.42/30.56 apply (zenon_L1940_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.42/30.56 apply (zenon_L59_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.42/30.56 apply (zenon_L89_); trivial. % 30.42/30.56 apply (zenon_L1942_); trivial. % 30.42/30.56 (* end of lemma zenon_L1943_ *) % 30.42/30.56 assert (zenon_L1944_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H16f zenon_H68 zenon_H156 zenon_H222 zenon_H60 zenon_H5e zenon_H1f zenon_H3c zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H20e zenon_H102 zenon_H1c7 zenon_H1af zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H100 zenon_H103 zenon_H208 zenon_H2d zenon_Hc3 zenon_H1e6 zenon_Hf6 zenon_H20d zenon_H218 zenon_H30d zenon_H108 zenon_H20 zenon_H30a zenon_H2b4 zenon_H14b zenon_Hcd zenon_H296 zenon_H42 zenon_H10d zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hd6 zenon_Hd1 zenon_Hf9 zenon_H3f zenon_H1dc zenon_H231 zenon_H101 zenon_H113 zenon_He4 zenon_H27 zenon_H225 zenon_H13b zenon_H18c zenon_H92 zenon_Hfc zenon_Hde zenon_Hee zenon_He1 zenon_He7 zenon_Hb8 zenon_H17b zenon_H6b zenon_Hcc zenon_H310 zenon_H110 zenon_H200 zenon_H182 zenon_H6f. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1856_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 exact (zenon_H13b zenon_Hfd). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L555_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.56 apply (zenon_L18_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.56 exact (zenon_H103 zenon_H37). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.56 apply (zenon_L1943_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.56 apply (zenon_L1812_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.56 apply (zenon_L1871_); trivial. % 30.42/30.56 apply (zenon_L1862_); trivial. % 30.42/30.56 apply (zenon_L758_); trivial. % 30.42/30.56 (* end of lemma zenon_L1944_ *) % 30.42/30.56 assert (zenon_L1945_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H16f zenon_H15a zenon_H103 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H20e zenon_H2b4 zenon_H30a zenon_H20 zenon_H1e6 zenon_Hf6 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H182 zenon_H6f. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.56 apply (zenon_L241_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.56 exact (zenon_H103 zenon_H37). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.56 apply (zenon_L332_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.56 apply (zenon_L1917_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.56 apply (zenon_L1145_); trivial. % 30.42/30.56 apply (zenon_L1885_); trivial. % 30.42/30.56 apply (zenon_L758_); trivial. % 30.42/30.56 (* end of lemma zenon_L1945_ *) % 30.42/30.56 assert (zenon_L1946_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H16f zenon_H15a zenon_H103 zenon_H100 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H102 zenon_H20e zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H208 zenon_H2d zenon_Hc3 zenon_H1e6 zenon_Hf6 zenon_H20d zenon_H218 zenon_H30d zenon_H108 zenon_H20 zenon_H30a zenon_H2b4 zenon_H3c zenon_H1f zenon_H60 zenon_H156 zenon_H14b zenon_Hcd zenon_H296 zenon_H42 zenon_H10d zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hd6 zenon_Hd1 zenon_Hf9 zenon_H3f zenon_H1dc zenon_H231 zenon_H101 zenon_H113 zenon_He4 zenon_H27 zenon_H225 zenon_H13b zenon_H18c zenon_H92 zenon_Hfc zenon_Hde zenon_Hee zenon_He1 zenon_He7 zenon_Hb8 zenon_H17b zenon_H6b zenon_Hcc zenon_H310 zenon_H110 zenon_H200 zenon_H182 zenon_H6f. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1945_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 exact (zenon_H13b zenon_Hfd). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L575_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.56 apply (zenon_L241_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.56 exact (zenon_H103 zenon_H37). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.56 apply (zenon_L1943_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.42/30.56 apply (zenon_L1812_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.42/30.56 apply (zenon_L1871_); trivial. % 30.42/30.56 apply (zenon_L1861_); trivial. % 30.42/30.56 apply (zenon_L758_); trivial. % 30.42/30.56 (* end of lemma zenon_L1946_ *) % 30.42/30.56 assert (zenon_L1947_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H182 zenon_H20 zenon_H3d zenon_H1af zenon_H1bd zenon_H95 zenon_H113. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.42/30.56 exact (zenon_H30a zenon_H185). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.42/30.56 apply (zenon_L658_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.42/30.56 apply (zenon_L209_); trivial. % 30.42/30.56 apply (zenon_L798_); trivial. % 30.42/30.56 (* end of lemma zenon_L1947_ *) % 30.42/30.56 assert (zenon_L1948_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H113 zenon_H95 zenon_H20 zenon_H30a zenon_H2b4 zenon_Hcc zenon_He1 zenon_H102 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H13b zenon_H103. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.56 apply (zenon_L332_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.56 apply (zenon_L1947_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.56 apply (zenon_L544_); trivial. % 30.42/30.56 apply (zenon_L1886_); trivial. % 30.42/30.56 (* end of lemma zenon_L1948_ *) % 30.42/30.56 assert (zenon_L1949_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H101 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H3c zenon_H1af zenon_H1c7 zenon_He1 zenon_H2b4 zenon_H30a zenon_H20 zenon_H113 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H13b zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H95 zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1948_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 exact (zenon_H13b zenon_Hfd). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L575_); trivial. % 30.42/30.56 apply (zenon_L1819_); trivial. % 30.42/30.56 (* end of lemma zenon_L1949_ *) % 30.42/30.56 assert (zenon_L1950_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H101 zenon_H231 zenon_H1dc zenon_H60 zenon_H3f zenon_H90 zenon_Hcd zenon_Hf9 zenon_H13b zenon_Hcc zenon_Hd6 zenon_H102 zenon_H95 zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1105_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 exact (zenon_H13b zenon_Hfd). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L555_); trivial. % 30.42/30.56 apply (zenon_L1819_); trivial. % 30.42/30.56 (* end of lemma zenon_L1950_ *) % 30.42/30.56 assert (zenon_L1951_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H296 zenon_H6f zenon_H42 zenon_H2d zenon_Hee zenon_H89 zenon_He7 zenon_Hb8 zenon_H1bd zenon_H1af zenon_H20 zenon_H30a zenon_H2b4 zenon_He1 zenon_H15a zenon_H16f zenon_Hfe zenon_Hfc zenon_H19e zenon_H101 zenon_H231 zenon_H1dc zenon_H60 zenon_H3f zenon_H90 zenon_Hcd zenon_Hf9 zenon_H13b zenon_Hcc zenon_Hd6 zenon_H102 zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.42/30.56 apply (zenon_L1920_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.42/30.56 apply (zenon_L59_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.42/30.56 apply (zenon_L1843_); trivial. % 30.42/30.56 apply (zenon_L1950_); trivial. % 30.42/30.56 (* end of lemma zenon_L1951_ *) % 30.42/30.56 assert (zenon_L1952_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_He1 zenon_H310 zenon_H1e1 zenon_H103 zenon_H100 zenon_H9d zenon_H182 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H5e zenon_H222 zenon_H1c7 zenon_H102 zenon_Hcc zenon_H6b zenon_H1af zenon_H20d. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.42/30.56 apply (zenon_L332_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.42/30.56 apply (zenon_L209_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.42/30.56 apply (zenon_L544_); trivial. % 30.42/30.56 apply (zenon_L1941_); trivial. % 30.42/30.56 (* end of lemma zenon_L1952_ *) % 30.42/30.56 assert (zenon_L1953_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (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 (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.42/30.56 do 0 intro. intros zenon_H20d zenon_H1af zenon_H6b zenon_Hcc zenon_H102 zenon_H1c7 zenon_H222 zenon_H5e zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H100 zenon_H103 zenon_H310 zenon_He1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde zenon_Hc3 zenon_H14b zenon_H10d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hd6 zenon_H13b zenon_Hf9 zenon_Hcd zenon_H90 zenon_H3f zenon_H1dc zenon_H231 zenon_H101 zenon_Hfc zenon_H16f zenon_H15a zenon_H42 zenon_H296 zenon_H156 zenon_H1f zenon_H3c zenon_H108 zenon_H30d zenon_Hf6 zenon_H1e6 zenon_H208 zenon_H2d zenon_Hee zenon_He7 zenon_Hb8 zenon_H20 zenon_H218 zenon_H17b zenon_H60 zenon_H2b4 zenon_H30a zenon_H110 zenon_H200 zenon_H182 zenon_H6f. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.42/30.56 apply (zenon_L1105_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.42/30.56 exact (zenon_H13b zenon_Hfd). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.42/30.56 apply (zenon_L575_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.42/30.56 apply (zenon_L241_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.42/30.56 exact (zenon_H103 zenon_H37). % 30.42/30.56 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.42/30.56 apply (zenon_L1935_); trivial. % 30.42/30.56 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.57 apply (zenon_L1951_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.57 apply (zenon_L1871_); trivial. % 30.48/30.57 apply (zenon_L1942_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.57 apply (zenon_L347_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.57 apply (zenon_L89_); trivial. % 30.48/30.57 apply (zenon_L1952_); trivial. % 30.48/30.57 apply (zenon_L758_); trivial. % 30.48/30.57 (* end of lemma zenon_L1953_ *) % 30.48/30.57 assert (zenon_L1954_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.48/30.57 do 0 intro. intros zenon_H2b7 zenon_H10e zenon_H26 zenon_H10d zenon_Hcc zenon_H60 zenon_H1dc zenon_H8a zenon_Hb5. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.48/30.57 apply (zenon_L63_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.48/30.57 apply (zenon_L699_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.48/30.57 apply (zenon_L567_); trivial. % 30.48/30.57 apply (zenon_L461_); trivial. % 30.48/30.57 (* end of lemma zenon_L1954_ *) % 30.48/30.57 assert (zenon_L1955_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_Hb8 zenon_Hb5 zenon_H1dc zenon_H60 zenon_Hcc zenon_H10d zenon_H26 zenon_H10e zenon_H2b7 zenon_H3f zenon_H2c zenon_Hee zenon_H15e zenon_Hb1 zenon_H2d. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.48/30.57 apply (zenon_L1954_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.48/30.57 apply (zenon_L746_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.48/30.57 apply (zenon_L490_); trivial. % 30.48/30.57 apply (zenon_L107_); trivial. % 30.48/30.57 (* end of lemma zenon_L1955_ *) % 30.48/30.57 assert (zenon_L1956_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_Hbd zenon_Hde zenon_He2 zenon_H113 zenon_H20d zenon_Hdf zenon_H20 zenon_H182 zenon_H30a zenon_H2b4 zenon_Hb8 zenon_Hb5 zenon_H1dc zenon_H60 zenon_Hcc zenon_H10d zenon_H26 zenon_H10e zenon_H2b7 zenon_H3f zenon_H2c zenon_Hee zenon_H15e zenon_H2d. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.57 apply (zenon_L288_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.57 apply (zenon_L1853_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.57 apply (zenon_L63_); trivial. % 30.48/30.57 apply (zenon_L1955_); trivial. % 30.48/30.57 (* end of lemma zenon_L1956_ *) % 30.48/30.57 assert (zenon_L1957_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_H16f zenon_H15a zenon_H89 zenon_He2 zenon_H10d zenon_H26 zenon_Hcd zenon_H23b zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_Hdf zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H1e6 zenon_Hf6 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H1c7 zenon_H103 zenon_Hde zenon_Hb8 zenon_Hb5 zenon_H1dc zenon_H2b7 zenon_H3f zenon_Hee zenon_H2d zenon_H42 zenon_H182 zenon_H6f. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.57 apply (zenon_L241_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.57 exact (zenon_H103 zenon_H37). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.57 apply (zenon_L1956_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.57 exact (zenon_H103 zenon_H37). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.57 apply (zenon_L1925_); trivial. % 30.48/30.57 apply (zenon_L1389_); trivial. % 30.48/30.57 apply (zenon_L758_); trivial. % 30.48/30.57 (* end of lemma zenon_L1957_ *) % 30.48/30.57 assert (zenon_L1958_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_He4 zenon_He1 zenon_H68 zenon_H16f zenon_H15a zenon_H89 zenon_H10d zenon_H26 zenon_Hcd zenon_H23b zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_Hdf zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H1e6 zenon_Hf6 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H1c7 zenon_H103 zenon_Hde zenon_Hb8 zenon_Hb5 zenon_H1dc zenon_H2b7 zenon_H3f zenon_Hee zenon_H2d zenon_H42 zenon_H182 zenon_H6f. % 30.48/30.57 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.57 apply (zenon_L232_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.57 apply (zenon_L48_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.57 apply (zenon_L49_); trivial. % 30.48/30.57 apply (zenon_L1957_); trivial. % 30.48/30.57 (* end of lemma zenon_L1958_ *) % 30.48/30.57 assert (zenon_L1959_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((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 (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.48/30.57 do 0 intro. intros zenon_Hb8 zenon_H10e zenon_H9d zenon_He1 zenon_Hee zenon_H15e zenon_H2b7 zenon_H8b zenon_Hb5 zenon_H26 zenon_H10d zenon_Hcc zenon_H60 zenon_H1dc zenon_H110. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.48/30.57 apply (zenon_L1954_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.48/30.57 apply (zenon_L1354_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.48/30.57 apply (zenon_L490_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.48/30.57 apply (zenon_L297_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.48/30.57 apply (zenon_L699_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.48/30.57 apply (zenon_L567_); trivial. % 30.48/30.57 apply (zenon_L1303_); trivial. % 30.48/30.57 (* end of lemma zenon_L1959_ *) % 30.48/30.57 assert (zenon_L1960_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_H16f zenon_H89 zenon_H15a zenon_H103 zenon_H110 zenon_H1dc zenon_H60 zenon_Hcc zenon_H10d zenon_H26 zenon_Hb5 zenon_H8b zenon_H2b7 zenon_Hee zenon_He1 zenon_H9d zenon_H10e zenon_Hb8 zenon_H182 zenon_H6f. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.57 apply (zenon_L241_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.57 exact (zenon_H103 zenon_H37). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.57 apply (zenon_L1959_); trivial. % 30.48/30.57 apply (zenon_L758_); trivial. % 30.48/30.57 (* end of lemma zenon_L1960_ *) % 30.48/30.57 assert (zenon_L1961_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_Hbd zenon_H6f zenon_H182 zenon_H9d zenon_He1 zenon_H110 zenon_H103 zenon_H15a zenon_H89 zenon_H16f zenon_Hc3 zenon_H100 zenon_Hb8 zenon_Hb5 zenon_H1dc zenon_H60 zenon_Hcc zenon_H10d zenon_H26 zenon_H10e zenon_H2b7 zenon_H3f zenon_H2c zenon_Hee zenon_H15e zenon_H2d. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.57 apply (zenon_L1960_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.57 apply (zenon_L1497_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.57 apply (zenon_L63_); trivial. % 30.48/30.57 apply (zenon_L1955_); trivial. % 30.48/30.57 (* end of lemma zenon_L1961_ *) % 30.48/30.57 assert (zenon_L1962_ : ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_H9d zenon_He1 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_Hdf zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H1c7 zenon_H103 zenon_H110 zenon_H15a zenon_H89 zenon_H16f zenon_Hc3 zenon_H100 zenon_Hb8 zenon_Hb5 zenon_H1dc zenon_H26 zenon_H2b7 zenon_H3f zenon_Hee zenon_H2d zenon_H42 zenon_H182 zenon_H6f. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.57 apply (zenon_L241_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.57 exact (zenon_H103 zenon_H37). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.57 apply (zenon_L1961_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.57 exact (zenon_H103 zenon_H37). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.57 apply (zenon_L1925_); trivial. % 30.48/30.57 apply (zenon_L1354_); trivial. % 30.48/30.57 apply (zenon_L758_); trivial. % 30.48/30.57 (* end of lemma zenon_L1962_ *) % 30.48/30.57 assert (zenon_L1963_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_H101 zenon_H231 zenon_H90 zenon_Hf9 zenon_H13b zenon_Hd5 zenon_Hcd zenon_He1 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_Hdf zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H1c7 zenon_H103 zenon_H110 zenon_H15a zenon_H89 zenon_H16f zenon_Hc3 zenon_H100 zenon_Hb8 zenon_Hb5 zenon_H1dc zenon_H26 zenon_H2b7 zenon_H3f zenon_Hee zenon_H2d zenon_H42 zenon_H182 zenon_H6f. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.57 apply (zenon_L1105_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.57 exact (zenon_H13b zenon_Hfd). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.57 apply (zenon_L212_); trivial. % 30.48/30.57 apply (zenon_L1962_); trivial. % 30.48/30.57 (* end of lemma zenon_L1963_ *) % 30.48/30.57 assert (zenon_L1964_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_H20d zenon_H1af zenon_H6b zenon_Hcc zenon_H102 zenon_H1c7 zenon_H222 zenon_H5e zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H100 zenon_H103 zenon_H310 zenon_He1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde zenon_H14b zenon_H42 zenon_H3f zenon_H2b7 zenon_H26 zenon_H1dc zenon_Hb5 zenon_H16f zenon_H15a zenon_H108 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hcd zenon_Hd5 zenon_H13b zenon_Hf9 zenon_H90 zenon_H231 zenon_H101 zenon_Hfc zenon_H2d zenon_Hee zenon_He7 zenon_Hb8 zenon_H20 zenon_H218 zenon_H17b zenon_H60 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H110 zenon_H200 zenon_H182 zenon_H6f. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.57 apply (zenon_L1105_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.57 exact (zenon_H13b zenon_Hfd). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.57 apply (zenon_L212_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.57 apply (zenon_L241_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.57 exact (zenon_H103 zenon_H37). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.57 apply (zenon_L1963_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.57 apply (zenon_L59_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.57 apply (zenon_L89_); trivial. % 30.48/30.57 apply (zenon_L1942_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.57 apply (zenon_L1812_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.57 apply (zenon_L89_); trivial. % 30.48/30.57 apply (zenon_L1952_); trivial. % 30.48/30.57 apply (zenon_L758_); trivial. % 30.48/30.57 (* end of lemma zenon_L1964_ *) % 30.48/30.57 assert (zenon_L1965_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.48/30.57 do 0 intro. intros zenon_H124 zenon_H208 zenon_H30d zenon_H3c zenon_H296 zenon_Hd6 zenon_H6f zenon_H182 zenon_H200 zenon_H110 zenon_Hc3 zenon_H30a zenon_H2b4 zenon_H60 zenon_H17b zenon_H218 zenon_H20 zenon_Hb8 zenon_He7 zenon_Hee zenon_H2d zenon_Hfc zenon_H101 zenon_H231 zenon_Hf9 zenon_H13b zenon_Hcd zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H108 zenon_H15a zenon_H16f zenon_Hb5 zenon_H1dc zenon_H26 zenon_H2b7 zenon_H3f zenon_H42 zenon_H14b zenon_Hde zenon_H1d5 zenon_H89 zenon_Hc8 zenon_He1 zenon_H310 zenon_H103 zenon_H100 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H5e zenon_H222 zenon_H1c7 zenon_H102 zenon_Hcc zenon_H6b zenon_H1af zenon_H20d zenon_H97 zenon_H90. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.57 apply (zenon_L1953_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.57 apply (zenon_L906_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.57 apply (zenon_L1964_); trivial. % 30.48/30.57 apply (zenon_L30_); trivial. % 30.48/30.57 (* end of lemma zenon_L1965_ *) % 30.48/30.57 assert (zenon_L1966_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.48/30.57 do 0 intro. intros zenon_H225 zenon_H27 zenon_H103 zenon_H13b zenon_H182 zenon_H159 zenon_H100 zenon_H102 zenon_H101 zenon_H231 zenon_H1dc zenon_H3f zenon_Hf9 zenon_Hd1 zenon_Hd6 zenon_H60 zenon_H19e zenon_H124 zenon_H208 zenon_H30d zenon_H3c zenon_H296 zenon_H6f zenon_H200 zenon_H110 zenon_H30a zenon_H2b4 zenon_H218 zenon_H20 zenon_Hb8 zenon_He7 zenon_Hee zenon_H2d zenon_Hfc zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H108 zenon_H15a zenon_H16f zenon_Hb5 zenon_H26 zenon_H2b7 zenon_H42 zenon_H14b zenon_Hde zenon_H1d5 zenon_H89 zenon_Hc8 zenon_He1 zenon_H310 zenon_H1ca zenon_H1bd zenon_H5e zenon_H222 zenon_H1c7 zenon_H1af zenon_H20d zenon_H97 zenon_Hc0 zenon_H18c zenon_H20e zenon_He4 zenon_H74 zenon_H23b zenon_Hd9 zenon_H92 zenon_H16a zenon_Hcc zenon_H6b zenon_H90 zenon_Hcd. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.57 exact (zenon_H74 zenon_H73). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.57 apply (zenon_L1105_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.57 apply (zenon_L554_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.57 exact (zenon_H74 zenon_H73). % 30.48/30.57 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.57 apply (zenon_L1924_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.57 apply (zenon_L1965_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.57 apply (zenon_L1936_); trivial. % 30.48/30.57 apply (zenon_L1849_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.57 apply (zenon_L552_); trivial. % 30.48/30.57 apply (zenon_L386_); trivial. % 30.48/30.57 (* end of lemma zenon_L1966_ *) % 30.48/30.57 assert (zenon_L1967_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.57 do 0 intro. intros zenon_H208 zenon_H103 zenon_H13b zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H3c zenon_He9 zenon_H1af zenon_H1c7 zenon_H102 zenon_H15e zenon_H20e zenon_H1e1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H98 zenon_H5e zenon_H222 zenon_H27 zenon_H26 zenon_H156 zenon_H182. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.57 apply (zenon_L1889_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.57 apply (zenon_L514_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.57 apply (zenon_L3_); trivial. % 30.48/30.57 apply (zenon_L934_); trivial. % 30.48/30.57 (* end of lemma zenon_L1967_ *) % 30.48/30.57 assert (zenon_L1968_ : (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (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) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.48/30.57 do 0 intro. intros zenon_Hcd zenon_H6b zenon_Hcc zenon_H16a zenon_H92 zenon_Hd9 zenon_H23b zenon_H74 zenon_He4 zenon_H18c zenon_Hc0 zenon_H97 zenon_H20d zenon_H310 zenon_He1 zenon_Hde zenon_H14b zenon_H42 zenon_H2b7 zenon_Hb5 zenon_H16f zenon_H15a zenon_H108 zenon_Hf6 zenon_H1e6 zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hfc zenon_H2d zenon_Hee zenon_He7 zenon_Hb8 zenon_H20 zenon_H218 zenon_H2b4 zenon_H30a zenon_H110 zenon_H200 zenon_H6f zenon_H296 zenon_H30d zenon_H124 zenon_H60 zenon_Hd6 zenon_Hd1 zenon_Hf9 zenon_H3f zenon_H1dc zenon_H231 zenon_H101 zenon_H100 zenon_H225 zenon_H182 zenon_H156 zenon_H27 zenon_H222 zenon_H5e zenon_H1d5 zenon_Hc8 zenon_H1e1 zenon_H20e zenon_H15e zenon_H102 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H13b zenon_H103 zenon_H208 zenon_H26 zenon_H10d zenon_He2 zenon_H89. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.48/30.57 apply (zenon_L1966_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.48/30.57 apply (zenon_L1967_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.48/30.57 apply (zenon_L699_); trivial. % 30.48/30.57 apply (zenon_L252_); trivial. % 30.48/30.57 (* end of lemma zenon_L1968_ *) % 30.48/30.57 assert (zenon_L1969_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.57 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H98 zenon_H5e zenon_H222 zenon_Hcd zenon_Hcc zenon_H156 zenon_H182. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.57 apply (zenon_L120_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.57 apply (zenon_L514_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.57 apply (zenon_L44_); trivial. % 30.48/30.57 apply (zenon_L934_); trivial. % 30.48/30.57 (* end of lemma zenon_L1969_ *) % 30.48/30.57 assert (zenon_L1970_ : (~((e1) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (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) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.57 do 0 intro. intros zenon_H6f zenon_Hc3 zenon_H6b zenon_H16a zenon_H92 zenon_Hd9 zenon_H23b zenon_H74 zenon_He4 zenon_Hc0 zenon_H97 zenon_H20d zenon_H310 zenon_He1 zenon_Hde zenon_H14b zenon_H42 zenon_H2b7 zenon_Hb5 zenon_H16f zenon_H15a zenon_H108 zenon_Hf6 zenon_H1e6 zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hfc zenon_H2d zenon_Hee zenon_He7 zenon_Hb8 zenon_H20 zenon_H218 zenon_H2b4 zenon_H30a zenon_H110 zenon_H200 zenon_H296 zenon_H30d zenon_H124 zenon_H60 zenon_Hd6 zenon_Hd1 zenon_Hf9 zenon_H3f zenon_H1dc zenon_H231 zenon_H101 zenon_H100 zenon_H225 zenon_H27 zenon_H1d5 zenon_Hc8 zenon_H20e zenon_H102 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H13b zenon_H103 zenon_H26 zenon_H10d zenon_He2 zenon_H89 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_Hcd zenon_Hcc zenon_H156 zenon_H182. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.57 apply (zenon_L1856_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.57 apply (zenon_L906_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.57 apply (zenon_L18_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.57 exact (zenon_H103 zenon_H37). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.57 apply (zenon_L1958_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.57 apply (zenon_L59_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.57 apply (zenon_L89_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.48/30.57 exact (zenon_H30a zenon_H185). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.48/30.57 apply (zenon_L658_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.48/30.57 apply (zenon_L1968_); trivial. % 30.48/30.57 apply (zenon_L65_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.57 apply (zenon_L608_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.57 apply (zenon_L89_); trivial. % 30.48/30.57 apply (zenon_L1968_); trivial. % 30.48/30.57 apply (zenon_L758_); trivial. % 30.48/30.57 apply (zenon_L1969_); trivial. % 30.48/30.57 (* end of lemma zenon_L1970_ *) % 30.48/30.57 assert (zenon_L1971_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.48/30.57 do 0 intro. intros zenon_H14b zenon_H6f zenon_H42 zenon_H3f zenon_H2b7 zenon_H26 zenon_H1dc zenon_Hb5 zenon_H16f zenon_H15a zenon_H108 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_Hdf zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hfc zenon_Hde zenon_H1d5 zenon_Hc8 zenon_H2d zenon_H15e zenon_Hee zenon_He1 zenon_H89 zenon_He7 zenon_Hb8 zenon_H20 zenon_H218 zenon_H17b zenon_H60 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H20d zenon_H1af zenon_H6b zenon_Hcc zenon_H102 zenon_H1c7 zenon_H222 zenon_H5e zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H9d zenon_H100 zenon_H103 zenon_H310 zenon_H110. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.57 apply (zenon_L1962_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.57 apply (zenon_L59_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.57 apply (zenon_L89_); trivial. % 30.48/30.57 apply (zenon_L1942_); trivial. % 30.48/30.57 (* end of lemma zenon_L1971_ *) % 30.48/30.57 assert (zenon_L1972_ : ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_H68 zenon_H20d zenon_H1af zenon_H6b zenon_Hcc zenon_H102 zenon_H1c7 zenon_H222 zenon_H5e zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H9d zenon_H100 zenon_H103 zenon_H310 zenon_He1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde zenon_H14b zenon_H42 zenon_H3f zenon_H2b7 zenon_H26 zenon_H1dc zenon_Hb5 zenon_H16f zenon_H15a zenon_H108 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hfc zenon_H2d zenon_Hee zenon_He7 zenon_Hb8 zenon_H20 zenon_H218 zenon_H17b zenon_H60 zenon_H2b4 zenon_H30a zenon_Hc3 zenon_H110 zenon_H200 zenon_H182 zenon_H6f. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.57 apply (zenon_L18_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.57 exact (zenon_H103 zenon_H37). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.57 apply (zenon_L1971_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.57 apply (zenon_L1812_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.57 apply (zenon_L89_); trivial. % 30.48/30.57 apply (zenon_L1952_); trivial. % 30.48/30.57 apply (zenon_L758_); trivial. % 30.48/30.57 (* end of lemma zenon_L1972_ *) % 30.48/30.57 assert (zenon_L1973_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.57 do 0 intro. intros zenon_H101 zenon_H231 zenon_H1dc zenon_H60 zenon_Hcc zenon_H3f zenon_H90 zenon_Hf9 zenon_H13b zenon_Hd5 zenon_Hcd zenon_H102 zenon_H95 zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.57 apply (zenon_L1105_); trivial. % 30.48/30.57 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.57 exact (zenon_H13b zenon_Hfd). % 30.48/30.57 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.57 apply (zenon_L212_); trivial. % 30.48/30.57 apply (zenon_L1819_); trivial. % 30.48/30.57 (* end of lemma zenon_L1973_ *) % 30.48/30.57 assert (zenon_L1974_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.48/30.58 do 0 intro. intros zenon_H23b zenon_H100 zenon_H95 zenon_Hcd zenon_Hd5 zenon_Hf9 zenon_H3f zenon_Hcc zenon_H60 zenon_H1dc zenon_H231 zenon_H101 zenon_H182 zenon_H156 zenon_H27 zenon_H222 zenon_H5e zenon_H1d5 zenon_Hc8 zenon_H1e1 zenon_H20e zenon_H15e zenon_H102 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H13b zenon_H103 zenon_H208 zenon_H26 zenon_H10d zenon_He2 zenon_H89. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.48/30.58 apply (zenon_L1973_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.48/30.58 apply (zenon_L1967_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.48/30.58 apply (zenon_L699_); trivial. % 30.48/30.58 apply (zenon_L252_); trivial. % 30.48/30.58 (* end of lemma zenon_L1974_ *) % 30.48/30.58 assert (zenon_L1975_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.58 do 0 intro. intros zenon_Hf6 zenon_H10d zenon_H10e zenon_H23b zenon_H100 zenon_Hcd zenon_Hd5 zenon_Hf9 zenon_H3f zenon_Hcc zenon_H60 zenon_H1dc zenon_H231 zenon_H101 zenon_H156 zenon_H27 zenon_H222 zenon_H5e zenon_H1d5 zenon_Hc8 zenon_H20e zenon_H102 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H13b zenon_H103 zenon_H208 zenon_H26 zenon_He2 zenon_H89 zenon_Hde zenon_Hbd zenon_Hc3 zenon_He4 zenon_He1 zenon_H68 zenon_H16f zenon_H15a zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_H20 zenon_H30a zenon_H2b4 zenon_H1e6 zenon_H108 zenon_Hb8 zenon_Hb5 zenon_H2b7 zenon_Hee zenon_H2d zenon_H42 zenon_H200 zenon_H182 zenon_H6f. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.58 apply (zenon_L241_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.58 exact (zenon_H103 zenon_H37). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.58 apply (zenon_L1958_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.58 apply (zenon_L347_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.58 apply (zenon_L89_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.58 apply (zenon_L288_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.58 apply (zenon_L1974_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.58 apply (zenon_L63_); trivial. % 30.48/30.58 apply (zenon_L690_); trivial. % 30.48/30.58 apply (zenon_L758_); trivial. % 30.48/30.58 (* end of lemma zenon_L1975_ *) % 30.48/30.58 assert (zenon_L1976_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.48/30.58 do 0 intro. intros zenon_H23b zenon_H6f zenon_H200 zenon_H110 zenon_Hc3 zenon_H30a zenon_H2b4 zenon_H60 zenon_H17b zenon_H218 zenon_H20 zenon_Hb8 zenon_He7 zenon_Hee zenon_H2d zenon_Hfc zenon_H101 zenon_H231 zenon_Hf9 zenon_Hd5 zenon_Hcd zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H1e6 zenon_Hf6 zenon_H108 zenon_H15a zenon_H16f zenon_Hb5 zenon_H1dc zenon_H2b7 zenon_H3f zenon_H42 zenon_H14b zenon_Hde zenon_He1 zenon_H310 zenon_H100 zenon_Hcc zenon_H6b zenon_H20d zenon_H156 zenon_H27 zenon_H222 zenon_H5e zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H1e1 zenon_H20e zenon_H15e zenon_H102 zenon_H1c7 zenon_H1af zenon_He9 zenon_H3c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H13b zenon_H103 zenon_H208 zenon_H26 zenon_H10d zenon_H182 zenon_H14e. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.48/30.58 apply (zenon_L1964_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.48/30.58 apply (zenon_L1967_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.48/30.58 apply (zenon_L699_); trivial. % 30.48/30.58 apply (zenon_L137_); trivial. % 30.48/30.58 (* end of lemma zenon_L1976_ *) % 30.48/30.58 assert (zenon_L1977_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.58 do 0 intro. intros zenon_H124 zenon_Hd6 zenon_H6f zenon_H200 zenon_H110 zenon_Hc3 zenon_H30a zenon_H2b4 zenon_H60 zenon_H17b zenon_H218 zenon_H20 zenon_Hb8 zenon_He7 zenon_Hee zenon_H2d zenon_Hfc zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H108 zenon_H15a zenon_H16f zenon_Hb5 zenon_H1dc zenon_H26 zenon_H2b7 zenon_H3f zenon_H42 zenon_H14b zenon_Hde zenon_H1d5 zenon_H89 zenon_Hc8 zenon_He1 zenon_H310 zenon_H103 zenon_H100 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H1c7 zenon_H102 zenon_H6b zenon_H1af zenon_H20d zenon_H13b zenon_H23b zenon_H101 zenon_H231 zenon_Hf9 zenon_H27 zenon_H20e zenon_H3c zenon_H14e zenon_He2 zenon_He4 zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_Hcd zenon_Hcc zenon_H156 zenon_H182. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.58 apply (zenon_L1856_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.58 exact (zenon_H13b zenon_Hfd). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.58 apply (zenon_L555_); trivial. % 30.48/30.58 apply (zenon_L1972_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.58 apply (zenon_L1131_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.58 apply (zenon_L241_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.58 exact (zenon_H103 zenon_H37). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.58 apply (zenon_L1975_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.58 apply (zenon_L59_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.58 apply (zenon_L89_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.48/30.58 exact (zenon_H30a zenon_H185). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.48/30.58 apply (zenon_L658_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.48/30.58 apply (zenon_L1976_); trivial. % 30.48/30.58 apply (zenon_L65_); trivial. % 30.48/30.58 apply (zenon_L758_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.58 exact (zenon_H13b zenon_Hfd). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.58 apply (zenon_L212_); trivial. % 30.48/30.58 apply (zenon_L1972_); trivial. % 30.48/30.58 apply (zenon_L1969_); trivial. % 30.48/30.58 (* end of lemma zenon_L1977_ *) % 30.48/30.58 assert (zenon_L1978_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.58 do 0 intro. intros zenon_H101 zenon_H3c zenon_H13b zenon_Hd6 zenon_H103 zenon_H100 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H102 zenon_H20e zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H2b4 zenon_H30a zenon_H20 zenon_H108 zenon_H30d zenon_H218 zenon_H20d zenon_H60 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_Hc3 zenon_H2d zenon_H14b zenon_H42 zenon_H3f zenon_H2b7 zenon_H26 zenon_H1dc zenon_Hb5 zenon_H16f zenon_H15a zenon_H10d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hfc zenon_Hde zenon_Hee zenon_He1 zenon_He7 zenon_Hb8 zenon_H17b zenon_H6b zenon_Hcc zenon_H310 zenon_H110 zenon_H200 zenon_H182 zenon_H6f. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.58 apply (zenon_L1945_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.58 exact (zenon_H13b zenon_Hfd). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.58 apply (zenon_L555_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.58 apply (zenon_L241_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.58 exact (zenon_H103 zenon_H37). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.58 apply (zenon_L1971_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.58 apply (zenon_L1812_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.58 apply (zenon_L1870_); trivial. % 30.48/30.58 apply (zenon_L1861_); trivial. % 30.48/30.58 apply (zenon_L758_); trivial. % 30.48/30.58 (* end of lemma zenon_L1978_ *) % 30.48/30.58 assert (zenon_L1979_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 30.48/30.58 do 0 intro. intros zenon_H200 zenon_H1c7 zenon_H108 zenon_H60 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_H20d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_H103 zenon_H100 zenon_H9d zenon_H182 zenon_H159 zenon_H19e zenon_H102 zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H3d. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.58 apply (zenon_L1925_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.58 apply (zenon_L1812_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.58 apply (zenon_L89_); trivial. % 30.48/30.58 apply (zenon_L209_); trivial. % 30.48/30.58 (* end of lemma zenon_L1979_ *) % 30.48/30.58 assert (zenon_L1980_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.48/30.58 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H102 zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H60 zenon_H108 zenon_H1c7 zenon_H200 zenon_He1 zenon_H9d. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.58 apply (zenon_L4_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.58 exact (zenon_H103 zenon_H37). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.58 apply (zenon_L1979_); trivial. % 30.48/30.58 apply (zenon_L1354_); trivial. % 30.48/30.58 (* end of lemma zenon_L1980_ *) % 30.48/30.58 assert (zenon_L1981_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.48/30.58 do 0 intro. intros zenon_H101 zenon_H3c zenon_H5e zenon_H1f zenon_H18c zenon_H68 zenon_H208 zenon_H13b zenon_Hd6 zenon_H42 zenon_H2d zenon_H1e zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H102 zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H60 zenon_H108 zenon_H1c7 zenon_H200 zenon_He1. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.58 apply (zenon_L1856_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.58 exact (zenon_H13b zenon_Hfd). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.58 apply (zenon_L555_); trivial. % 30.48/30.58 apply (zenon_L1980_); trivial. % 30.48/30.58 (* end of lemma zenon_L1981_ *) % 30.48/30.58 assert (zenon_L1982_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.58 do 0 intro. intros zenon_H124 zenon_H103 zenon_H100 zenon_H19e zenon_H102 zenon_H60 zenon_Hd6 zenon_H13b zenon_H3c zenon_H101 zenon_H159 zenon_H1ba zenon_H1bd zenon_H208 zenon_H68 zenon_H18c zenon_H5e zenon_H222 zenon_Hcd zenon_Hcc zenon_H156 zenon_H182. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.58 apply (zenon_L1930_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.58 apply (zenon_L1131_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.58 apply (zenon_L608_); trivial. % 30.48/30.58 apply (zenon_L1969_); trivial. % 30.48/30.58 (* end of lemma zenon_L1982_ *) % 30.48/30.58 assert (zenon_L1983_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.58 do 0 intro. intros zenon_H101 zenon_H156 zenon_H60 zenon_H3c zenon_H5e zenon_H1f zenon_H18c zenon_H68 zenon_H208 zenon_H13b zenon_Hcc zenon_Hd6 zenon_H102 zenon_H95 zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.58 apply (zenon_L1856_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.58 exact (zenon_H13b zenon_Hfd). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.58 apply (zenon_L555_); trivial. % 30.48/30.58 apply (zenon_L1819_); trivial. % 30.48/30.58 (* end of lemma zenon_L1983_ *) % 30.48/30.58 assert (zenon_L1984_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.48/30.58 do 0 intro. intros zenon_Hf9 zenon_Hde zenon_H8b zenon_He9 zenon_H3f zenon_Hcc zenon_H60 zenon_H1dc zenon_H231. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.48/30.58 apply (zenon_L288_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.48/30.58 apply (zenon_L53_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.48/30.58 apply (zenon_L567_); trivial. % 30.48/30.58 exact (zenon_H231 zenon_Hf4). % 30.48/30.58 (* end of lemma zenon_L1984_ *) % 30.48/30.58 assert (zenon_L1985_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.58 do 0 intro. intros zenon_H101 zenon_H231 zenon_H1dc zenon_H60 zenon_H3f zenon_H8b zenon_Hde zenon_Hf9 zenon_Hdc zenon_Hd1 zenon_Hcc zenon_Hd6 zenon_H102 zenon_H1ba zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.58 apply (zenon_L1984_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.58 apply (zenon_L154_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.58 apply (zenon_L555_); trivial. % 30.48/30.58 apply (zenon_L1812_); trivial. % 30.48/30.58 (* end of lemma zenon_L1985_ *) % 30.48/30.58 assert (zenon_L1986_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 30.48/30.58 do 0 intro. intros zenon_H200 zenon_H1c7 zenon_H108 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_H20d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_H103 zenon_H100 zenon_H182 zenon_H159 zenon_H19e zenon_H102 zenon_Hd6 zenon_Hd1 zenon_Hdc zenon_Hf9 zenon_H8b zenon_H3f zenon_H60 zenon_H1dc zenon_H231 zenon_H101 zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H3d. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.58 apply (zenon_L1925_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.58 apply (zenon_L1985_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.58 apply (zenon_L89_); trivial. % 30.48/30.58 apply (zenon_L209_); trivial. % 30.48/30.58 (* end of lemma zenon_L1986_ *) % 30.48/30.58 assert (zenon_L1987_ : (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.48/30.58 do 0 intro. intros zenon_Hde zenon_H101 zenon_H231 zenon_H1dc zenon_H3f zenon_Hf9 zenon_Hdc zenon_Hd1 zenon_Hd6 zenon_H102 zenon_H19e zenon_H159 zenon_H100 zenon_H103 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H20d zenon_H200 zenon_H113 zenon_H1bd zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H182 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H3d zenon_H1c7. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.58 apply (zenon_L1986_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.58 apply (zenon_L1947_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.58 apply (zenon_L63_); trivial. % 30.48/30.58 apply (zenon_L1916_); trivial. % 30.48/30.58 (* end of lemma zenon_L1987_ *) % 30.48/30.58 assert (zenon_L1988_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.58 do 0 intro. intros zenon_H16f zenon_H15a zenon_H103 zenon_H13b zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1af zenon_H1c7 zenon_H102 zenon_H20e zenon_Hde zenon_H101 zenon_H231 zenon_H1dc zenon_H3f zenon_Hf9 zenon_Hdc zenon_Hd1 zenon_Hd6 zenon_H100 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H20d zenon_H200 zenon_H113 zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H182 zenon_H6f. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.58 apply (zenon_L241_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.58 exact (zenon_H103 zenon_H37). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.48/30.58 apply (zenon_L332_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.48/30.58 apply (zenon_L1987_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.48/30.58 apply (zenon_L1145_); trivial. % 30.48/30.58 apply (zenon_L1886_); trivial. % 30.48/30.58 apply (zenon_L758_); trivial. % 30.48/30.58 (* end of lemma zenon_L1988_ *) % 30.48/30.58 assert (zenon_L1989_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.48/30.58 do 0 intro. intros zenon_Hbd zenon_Hde zenon_He2 zenon_H103 zenon_H13b zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H102 zenon_He1 zenon_H2b4 zenon_H30a zenon_H20 zenon_H113 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H182 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H3d zenon_H1c7. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.58 apply (zenon_L288_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.58 apply (zenon_L1948_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.58 apply (zenon_L63_); trivial. % 30.48/30.58 apply (zenon_L1916_); trivial. % 30.48/30.58 (* end of lemma zenon_L1989_ *) % 30.48/30.58 assert (zenon_L1990_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.58 do 0 intro. intros zenon_H16f zenon_H15a zenon_H103 zenon_H13b zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1af zenon_H1c7 zenon_H102 zenon_H20e zenon_Hbd zenon_Hde zenon_He2 zenon_He1 zenon_H2b4 zenon_H30a zenon_H20 zenon_H113 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H182 zenon_H6f. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.58 apply (zenon_L241_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.58 exact (zenon_H103 zenon_H37). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.48/30.58 apply (zenon_L332_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.48/30.58 apply (zenon_L1989_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.48/30.58 apply (zenon_L1145_); trivial. % 30.48/30.58 apply (zenon_L1886_); trivial. % 30.48/30.58 apply (zenon_L758_); trivial. % 30.48/30.58 (* end of lemma zenon_L1990_ *) % 30.48/30.58 assert (zenon_L1991_ : (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.48/30.58 do 0 intro. intros zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_Hd1 zenon_Hdc zenon_Hf9 zenon_H3f zenon_H1dc zenon_H231 zenon_H101 zenon_H20e zenon_H3c zenon_H5e zenon_H6c zenon_H1ca zenon_H15a zenon_H16f zenon_H13b zenon_Hd6 zenon_H42 zenon_H2d zenon_H1e zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H102 zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H60 zenon_H108 zenon_H1c7 zenon_H200 zenon_He1. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.58 apply (zenon_L1988_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.58 exact (zenon_H13b zenon_Hfd). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.58 apply (zenon_L575_); trivial. % 30.48/30.58 apply (zenon_L1980_); trivial. % 30.48/30.58 (* end of lemma zenon_L1991_ *) % 30.48/30.58 assert (zenon_L1992_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.58 do 0 intro. intros zenon_H16f zenon_H15a zenon_H103 zenon_H100 zenon_H9d zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H102 zenon_H20e zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hcc zenon_Hde zenon_H108 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_H20d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_H218 zenon_H17b zenon_H60 zenon_Hc3 zenon_H200 zenon_H182 zenon_H6f. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.58 apply (zenon_L241_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.58 exact (zenon_H103 zenon_H37). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.58 apply (zenon_L1927_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.58 apply (zenon_L1812_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.58 apply (zenon_L89_); trivial. % 30.48/30.58 apply (zenon_L1861_); trivial. % 30.48/30.58 apply (zenon_L758_); trivial. % 30.48/30.58 (* end of lemma zenon_L1992_ *) % 30.48/30.58 assert (zenon_L1993_ : (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.58 do 0 intro. intros zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H108 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_H113 zenon_H200 zenon_H20d zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hd1 zenon_Hdc zenon_Hf9 zenon_H3f zenon_H1dc zenon_H231 zenon_H101 zenon_Hde zenon_H20e zenon_H1c7 zenon_H1af zenon_H3c zenon_H5e zenon_H6c zenon_H1bd zenon_H1ca zenon_H15a zenon_H16f zenon_H13b zenon_Hd6 zenon_Hcc zenon_H60 zenon_H102 zenon_H1ba zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.58 apply (zenon_L1988_); trivial. % 30.48/30.58 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.58 exact (zenon_H13b zenon_Hfd). % 30.48/30.58 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.58 apply (zenon_L575_); trivial. % 30.48/30.58 apply (zenon_L1812_); trivial. % 30.48/30.58 (* end of lemma zenon_L1993_ *) % 30.48/30.58 assert (zenon_L1994_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H101 zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_He2 zenon_H20e zenon_H3c zenon_H5e zenon_H6c zenon_H1ca zenon_H15a zenon_H16f zenon_H13b zenon_Hd6 zenon_H42 zenon_H2d zenon_H1e zenon_H1af zenon_H1bd zenon_Hcc zenon_Hde zenon_H102 zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103 zenon_Hbd zenon_H5c zenon_H1d8 zenon_H113 zenon_H20d zenon_H20 zenon_H30a zenon_H2b4 zenon_H10e zenon_H10d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H60 zenon_H108 zenon_H1c7 zenon_H200 zenon_He1. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1990_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L555_); trivial. % 30.48/30.59 apply (zenon_L1980_); trivial. % 30.48/30.59 (* end of lemma zenon_L1994_ *) % 30.48/30.59 assert (zenon_L1995_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H101 zenon_H6f zenon_H108 zenon_H60 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H113 zenon_H20 zenon_H30a zenon_H2b4 zenon_He1 zenon_He2 zenon_Hde zenon_Hbd zenon_H20e zenon_H1c7 zenon_H1af zenon_H3c zenon_H5e zenon_H6c zenon_H1bd zenon_H1ca zenon_H15a zenon_H16f zenon_H13b zenon_Hcc zenon_Hd6 zenon_H102 zenon_H1ba zenon_H19e zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1990_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L555_); trivial. % 30.48/30.59 apply (zenon_L1812_); trivial. % 30.48/30.59 (* end of lemma zenon_L1995_ *) % 30.48/30.59 assert (zenon_L1996_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 30.48/30.59 do 0 intro. intros zenon_H200 zenon_H1c7 zenon_H108 zenon_H60 zenon_H156 zenon_H182 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_H20d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_Hd5 zenon_H5e zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H3d. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.59 apply (zenon_L1925_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.59 apply (zenon_L608_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.59 apply (zenon_L89_); trivial. % 30.48/30.59 apply (zenon_L209_); trivial. % 30.48/30.59 (* end of lemma zenon_L1996_ *) % 30.48/30.59 assert (zenon_L1997_ : ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H9d zenon_He1 zenon_H200 zenon_H1c7 zenon_H108 zenon_H60 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H10d zenon_H10e zenon_H2b4 zenon_H30a zenon_H20 zenon_H20d zenon_H113 zenon_H1d8 zenon_H5c zenon_Hbd zenon_H103 zenon_H100 zenon_H159 zenon_H19e zenon_H102 zenon_Hde zenon_Hcc zenon_H1bd zenon_H1af zenon_H110 zenon_H15a zenon_H89 zenon_H16f zenon_Hc3 zenon_Hb8 zenon_Hb5 zenon_H1dc zenon_H26 zenon_H2b7 zenon_H3f zenon_Hee zenon_H2d zenon_H42 zenon_H182 zenon_H6f. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.59 apply (zenon_L241_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.59 apply (zenon_L1961_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.59 apply (zenon_L1979_); trivial. % 30.48/30.59 apply (zenon_L1354_); trivial. % 30.48/30.59 apply (zenon_L758_); trivial. % 30.48/30.59 (* end of lemma zenon_L1997_ *) % 30.48/30.59 assert (zenon_L1998_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H25b zenon_H6f zenon_H89 zenon_H92 zenon_He4 zenon_H6b zenon_H15a zenon_Hf9 zenon_H1dc zenon_H3f zenon_Hd1 zenon_H27 zenon_He1 zenon_H208 zenon_H182 zenon_H156 zenon_H60 zenon_H5e zenon_H3c zenon_H18c zenon_Hde zenon_H10e zenon_H296 zenon_Hcd zenon_H124 zenon_H16f zenon_Hc8 zenon_H218 zenon_H1ca zenon_H222 zenon_H1d5 zenon_H20e zenon_H13b zenon_Hd6 zenon_Hcc zenon_H42 zenon_Hbd zenon_Hf6 zenon_H108 zenon_H1c7 zenon_H1af zenon_H1e6 zenon_H10d zenon_H30a zenon_H20 zenon_H20d zenon_H113 zenon_H2b4 zenon_H5c zenon_H1d8 zenon_H102 zenon_H100 zenon_H159 zenon_H19e zenon_H1bd zenon_H200 zenon_H103 zenon_H2d zenon_H101 zenon_H225 zenon_H2b7 zenon_Hb5 zenon_Hee zenon_H110 zenon_Hb8 zenon_H23b zenon_Hd9 zenon_H16a zenon_Hc0. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.48/30.59 apply (zenon_L734_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.59 apply (zenon_L734_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.59 apply (zenon_L1856_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.59 apply (zenon_L192_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.59 apply (zenon_L1981_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1856_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L555_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.59 apply (zenon_L18_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.59 apply (zenon_L1928_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.59 apply (zenon_L1812_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.59 apply (zenon_L89_); trivial. % 30.48/30.59 apply (zenon_L1862_); trivial. % 30.48/30.59 apply (zenon_L758_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.59 apply (zenon_L1982_); trivial. % 30.48/30.59 apply (zenon_L1983_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.59 apply (zenon_L1988_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.59 apply (zenon_L552_); trivial. % 30.48/30.59 apply (zenon_L1990_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.59 apply (zenon_L554_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.59 apply (zenon_L1991_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1988_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L575_); trivial. % 30.48/30.59 apply (zenon_L1992_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.59 apply (zenon_L1993_); trivial. % 30.48/30.59 apply (zenon_L1949_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.59 apply (zenon_L552_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.59 apply (zenon_L1994_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1990_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L555_); trivial. % 30.48/30.59 apply (zenon_L1992_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.59 apply (zenon_L1995_); trivial. % 30.48/30.59 apply (zenon_L1949_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.59 apply (zenon_L1105_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.59 apply (zenon_L192_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1105_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L575_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.59 apply (zenon_L241_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.59 apply (zenon_L1937_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.59 apply (zenon_L1812_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.59 apply (zenon_L89_); trivial. % 30.48/30.59 apply (zenon_L1862_); trivial. % 30.48/30.59 apply (zenon_L758_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.59 apply (zenon_L552_); trivial. % 30.48/30.59 apply (zenon_L386_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.59 apply (zenon_L797_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.59 apply (zenon_L48_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.59 apply (zenon_L552_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.59 apply (zenon_L1981_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.59 apply (zenon_L1131_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.59 apply (zenon_L4_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.59 apply (zenon_L1996_); trivial. % 30.48/30.59 apply (zenon_L1389_); trivial. % 30.48/30.59 apply (zenon_L1969_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1856_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L555_); trivial. % 30.48/30.59 apply (zenon_L1997_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.59 apply (zenon_L1131_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1975_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L212_); trivial. % 30.48/30.59 apply (zenon_L1997_); trivial. % 30.48/30.59 apply (zenon_L1969_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.59 apply (zenon_L1982_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.59 apply (zenon_L1983_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.59 apply (zenon_L1131_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.59 apply (zenon_L18_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.59 apply (zenon_L1958_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.59 apply (zenon_L608_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.59 apply (zenon_L89_); trivial. % 30.48/30.59 apply (zenon_L1974_); trivial. % 30.48/30.59 apply (zenon_L758_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L212_); trivial. % 30.48/30.59 apply (zenon_L1819_); trivial. % 30.48/30.59 apply (zenon_L1969_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.59 apply (zenon_L1991_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1988_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L555_); trivial. % 30.48/30.59 apply (zenon_L1997_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.59 apply (zenon_L1993_); trivial. % 30.48/30.59 apply (zenon_L1949_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.59 apply (zenon_L552_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.59 apply (zenon_L1994_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1990_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L575_); trivial. % 30.48/30.59 apply (zenon_L1997_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.59 apply (zenon_L1995_); trivial. % 30.48/30.59 apply (zenon_L1949_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1105_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L555_); trivial. % 30.48/30.59 apply (zenon_L1980_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L1105_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 exact (zenon_H13b zenon_Hfd). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L555_); trivial. % 30.48/30.59 apply (zenon_L1997_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.59 apply (zenon_L1936_); trivial. % 30.48/30.59 apply (zenon_L1950_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.59 apply (zenon_L552_); trivial. % 30.48/30.59 apply (zenon_L386_); trivial. % 30.48/30.59 apply (zenon_L115_); trivial. % 30.48/30.59 apply (zenon_L1907_); trivial. % 30.48/30.59 (* end of lemma zenon_L1998_ *) % 30.48/30.59 assert (zenon_L1999_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H16f zenon_H89 zenon_H15a zenon_H103 zenon_H19a zenon_H182 zenon_H6f. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.59 apply (zenon_L241_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.59 apply (zenon_L235_); trivial. % 30.48/30.59 apply (zenon_L758_); trivial. % 30.48/30.59 (* end of lemma zenon_L1999_ *) % 30.48/30.59 assert (zenon_L2000_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H3c zenon_He9 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_H103 zenon_Hd1 zenon_Hdc zenon_H182 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H1c7 zenon_H60 zenon_H1af zenon_Hd6 zenon_H102 zenon_He1. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.48/30.59 apply (zenon_L49_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.48/30.59 apply (zenon_L88_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.48/30.59 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.59 apply (zenon_L1798_); trivial. % 30.48/30.59 (* end of lemma zenon_L2000_ *) % 30.48/30.59 assert (zenon_L2001_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 30.48/30.59 do 0 intro. intros zenon_H208 zenon_He1 zenon_H102 zenon_Hd6 zenon_H60 zenon_H1c7 zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_Hdc zenon_Hd1 zenon_H103 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_He9 zenon_Hde zenon_Hdf zenon_H135 zenon_H3c zenon_H1f zenon_H5e zenon_H20e zenon_H19a zenon_H222 zenon_H1af zenon_H40. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.59 apply (zenon_L2000_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.59 apply (zenon_L218_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.59 apply (zenon_L225_); trivial. % 30.48/30.59 apply (zenon_L1337_); trivial. % 30.48/30.59 (* end of lemma zenon_L2001_ *) % 30.48/30.59 assert (zenon_L2002_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.48/30.59 do 0 intro. intros zenon_H135 zenon_H14e zenon_H182 zenon_H6f zenon_H3f zenon_H1f zenon_Hf9 zenon_Hcd zenon_He1 zenon_H89 zenon_H23b zenon_H1d8 zenon_H20d zenon_H1fd zenon_H2d zenon_H10e zenon_H19a zenon_H156 zenon_H60 zenon_H218 zenon_H267 zenon_H231 zenon_H3c zenon_He9 zenon_Hd0 zenon_Hde zenon_H1e1. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.48/30.59 apply (zenon_L1804_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.48/30.59 apply (zenon_L88_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.48/30.59 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.59 apply (zenon_L294_); trivial. % 30.48/30.59 (* end of lemma zenon_L2002_ *) % 30.48/30.59 assert (zenon_L2003_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H2b7 zenon_H10e zenon_H10d zenon_H19a zenon_Hcc zenon_H60 zenon_H1dc zenon_H15e zenon_Hee. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.48/30.59 apply (zenon_L63_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.48/30.59 apply (zenon_L337_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.48/30.59 apply (zenon_L567_); trivial. % 30.48/30.59 apply (zenon_L490_); trivial. % 30.48/30.59 (* end of lemma zenon_L2003_ *) % 30.48/30.59 assert (zenon_L2004_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.48/30.59 do 0 intro. intros zenon_Hbd zenon_H14e zenon_H6f zenon_H3f zenon_H1f zenon_H20 zenon_H23b zenon_Hc3 zenon_H100 zenon_Hb6 zenon_H2d zenon_H1e6 zenon_Hf6 zenon_H182 zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H3d zenon_H1c7. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.59 apply (zenon_L1813_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.59 apply (zenon_L1497_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.59 apply (zenon_L304_); trivial. % 30.48/30.59 apply (zenon_L1916_); trivial. % 30.48/30.59 (* end of lemma zenon_L2004_ *) % 30.48/30.59 assert (zenon_L2005_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H102 zenon_H1c7 zenon_H3d zenon_H1af zenon_H108 zenon_H60 zenon_Hcc zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H2d zenon_Hb6 zenon_H100 zenon_H23b zenon_H20 zenon_H1f zenon_H3f zenon_H6f zenon_H14e zenon_Hbd zenon_H159 zenon_H182 zenon_Hdc zenon_Hd1 zenon_H103. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.48/30.59 apply (zenon_L2004_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.48/30.59 apply (zenon_L1131_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.48/30.59 apply (zenon_L154_); trivial. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 (* end of lemma zenon_L2005_ *) % 30.48/30.59 assert (zenon_L2006_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H1fd zenon_Hee zenon_H1dc zenon_H19a zenon_H10d zenon_H10e zenon_H2b7 zenon_He1 zenon_H102 zenon_H1c7 zenon_H3d zenon_H1af zenon_H108 zenon_H60 zenon_Hcc zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H2d zenon_H100 zenon_H23b zenon_H20 zenon_H1f zenon_H3f zenon_H6f zenon_H14e zenon_Hbd zenon_H159 zenon_H182 zenon_Hdc zenon_Hd1 zenon_H103. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.59 apply (zenon_L87_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.59 apply (zenon_L2003_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.59 apply (zenon_L544_); trivial. % 30.48/30.59 apply (zenon_L2005_); trivial. % 30.48/30.59 (* end of lemma zenon_L2006_ *) % 30.48/30.59 assert (zenon_L2007_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_Hd1 zenon_Hdc zenon_Hbd zenon_H14e zenon_H6f zenon_H3f zenon_H1f zenon_H20 zenon_H23b zenon_Hb6 zenon_H2d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_Hcc zenon_H108 zenon_H218 zenon_H17b zenon_H60 zenon_H102 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H9d zenon_H100 zenon_H103. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.48/30.59 apply (zenon_L332_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.48/30.59 apply (zenon_L2005_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.48/30.59 apply (zenon_L259_); trivial. % 30.48/30.59 apply (zenon_L1808_); trivial. % 30.48/30.59 (* end of lemma zenon_L2007_ *) % 30.48/30.59 assert (zenon_L2008_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H101 zenon_Hf9 zenon_Hcd zenon_He1 zenon_Hd6 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_Hd1 zenon_Hdc zenon_Hbd zenon_H14e zenon_H6f zenon_H3f zenon_H1f zenon_H20 zenon_H23b zenon_Hb6 zenon_H2d zenon_H1e6 zenon_Hf6 zenon_H156 zenon_Hcc zenon_H108 zenon_H218 zenon_H17b zenon_H60 zenon_H102 zenon_H1c7 zenon_H1af zenon_H222 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H159 zenon_H182 zenon_H100 zenon_H103. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.59 apply (zenon_L541_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.59 apply (zenon_L154_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.59 apply (zenon_L555_); trivial. % 30.48/30.59 apply (zenon_L2007_); trivial. % 30.48/30.59 (* end of lemma zenon_L2008_ *) % 30.48/30.59 assert (zenon_L2009_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> False). % 30.48/30.59 do 0 intro. intros zenon_H225 zenon_H27 zenon_He4 zenon_H103 zenon_H100 zenon_H182 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H222 zenon_H1af zenon_H1c7 zenon_H102 zenon_H60 zenon_H218 zenon_H108 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H2d zenon_Hb6 zenon_H20 zenon_H6f zenon_H14e zenon_Hbd zenon_Hd1 zenon_Hc8 zenon_H1d5 zenon_Hd6 zenon_He1 zenon_Hf9 zenon_H101 zenon_Hcc zenon_H6b zenon_H23b zenon_Hcd zenon_H1f zenon_H3f zenon_H19a zenon_Hee zenon_H89. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.59 apply (zenon_L541_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.59 apply (zenon_L554_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.59 apply (zenon_L2008_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.59 apply (zenon_L552_); trivial. % 30.48/30.59 apply (zenon_L387_); trivial. % 30.48/30.59 (* end of lemma zenon_L2009_ *) % 30.48/30.59 assert (zenon_L2010_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.59 do 0 intro. intros zenon_H208 zenon_H103 zenon_H100 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H222 zenon_H1af zenon_H1c7 zenon_H102 zenon_H60 zenon_H17b zenon_H218 zenon_H108 zenon_Hf6 zenon_H1e6 zenon_H2d zenon_H23b zenon_H20 zenon_H3f zenon_H6f zenon_H14e zenon_Hbd zenon_Hdc zenon_Hd1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hd6 zenon_He1 zenon_Hf9 zenon_H101 zenon_H2b7 zenon_H10e zenon_H10d zenon_H19a zenon_H1dc zenon_Hee zenon_H1fd zenon_H3c zenon_H1f zenon_H5e zenon_Hcd zenon_Hcc zenon_H156 zenon_H182. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.59 apply (zenon_L87_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.59 apply (zenon_L2003_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.59 apply (zenon_L259_); trivial. % 30.48/30.59 apply (zenon_L2008_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.59 apply (zenon_L218_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.59 apply (zenon_L44_); trivial. % 30.48/30.59 apply (zenon_L934_); trivial. % 30.48/30.59 (* end of lemma zenon_L2010_ *) % 30.48/30.59 assert (zenon_L2011_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.48/30.59 do 0 intro. intros zenon_Hc0 zenon_Hcd zenon_H6b zenon_Hcc zenon_H208 zenon_H103 zenon_H100 zenon_H159 zenon_H1ca zenon_H19e zenon_H1bd zenon_H222 zenon_H1af zenon_H1c7 zenon_H102 zenon_H60 zenon_H218 zenon_H108 zenon_Hf6 zenon_H1e6 zenon_H2d zenon_H23b zenon_H20 zenon_H3f zenon_H6f zenon_H14e zenon_Hbd zenon_Hd1 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hd6 zenon_He1 zenon_Hf9 zenon_H101 zenon_H2b7 zenon_H10e zenon_H10d zenon_H1dc zenon_Hee zenon_H1fd zenon_H3c zenon_H5e zenon_H156 zenon_He4 zenon_H27 zenon_H231 zenon_H225 zenon_H16f zenon_H92 zenon_H1a5 zenon_H19a zenon_H182 zenon_H16a. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.48/30.59 apply (zenon_L734_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.59 apply (zenon_L734_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.59 apply (zenon_L1805_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.48/30.59 apply (zenon_L332_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.48/30.59 apply (zenon_L2006_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.48/30.59 apply (zenon_L544_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.59 apply (zenon_L87_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.59 apply (zenon_L235_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.59 apply (zenon_L171_); trivial. % 30.48/30.59 apply (zenon_L2009_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.59 apply (zenon_L552_); trivial. % 30.48/30.59 apply (zenon_L387_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.59 apply (zenon_L1105_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.59 apply (zenon_L554_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.48/30.59 apply (zenon_L232_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.48/30.59 apply (zenon_L2010_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.48/30.59 apply (zenon_L552_); trivial. % 30.48/30.59 apply (zenon_L386_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.48/30.59 apply (zenon_L136_); trivial. % 30.48/30.59 apply (zenon_L115_); trivial. % 30.48/30.59 (* end of lemma zenon_L2011_ *) % 30.48/30.59 assert (zenon_L2012_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 30.48/30.59 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_H25 zenon_H60 zenon_H222 zenon_Hb6 zenon_He1 zenon_H90 zenon_H89. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.48/30.59 apply (zenon_L386_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.48/30.59 apply (zenon_L256_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.48/30.59 apply (zenon_L204_); trivial. % 30.48/30.59 apply (zenon_L538_); trivial. % 30.48/30.59 (* end of lemma zenon_L2012_ *) % 30.48/30.59 assert (zenon_L2013_ : (((op (e3) (op (e3) (e0))) = (e0))/\(((op (e3) (op (e3) (e1))) = (e1))/\(((op (e3) (op (e3) (e2))) = (e2))/\(((op (e3) (op (e3) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0)))/\(((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1)))/\(((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3)))))))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e0) (e0)) = (e3)) -> False). % 30.48/30.59 do 0 intro. intros zenon_H270 zenon_H30a zenon_H89. % 30.48/30.59 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.48/30.59 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.48/30.59 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.48/30.59 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.48/30.59 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H85 | zenon_intro zenon_H185 ]. % 30.48/30.59 exact (zenon_H85 zenon_H89). % 30.48/30.59 exact (zenon_H30a zenon_H185). % 30.48/30.59 (* end of lemma zenon_L2013_ *) % 30.48/30.59 assert (zenon_L2014_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H102 zenon_H19f zenon_H159 zenon_H182 zenon_H35 zenon_He9 zenon_H103. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.48/30.59 exact (zenon_H19f zenon_Hc3). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.48/30.59 apply (zenon_L1131_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.48/30.59 apply (zenon_L95_); trivial. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 (* end of lemma zenon_L2014_ *) % 30.48/30.59 assert (zenon_L2015_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H102 zenon_H19f zenon_H159 zenon_H182 zenon_H55 zenon_H19e zenon_H103. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.48/30.59 exact (zenon_H19f zenon_Hc3). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.48/30.59 apply (zenon_L1131_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.48/30.59 apply (zenon_L787_); trivial. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 (* end of lemma zenon_L2015_ *) % 30.48/30.59 assert (zenon_L2016_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H16f zenon_H36 zenon_Ha4 zenon_H27 zenon_H16a zenon_H15a zenon_H2bd zenon_H1dc zenon_H2c zenon_H3f zenon_Had zenon_Hb8 zenon_H103 zenon_H20e zenon_H1b9 zenon_H182 zenon_H6f. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.59 apply (zenon_L1144_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.59 apply (zenon_L1145_); trivial. % 30.48/30.59 apply (zenon_L758_); trivial. % 30.48/30.59 (* end of lemma zenon_L2016_ *) % 30.48/30.59 assert (zenon_L2017_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.59 do 0 intro. intros zenon_H16f zenon_Had zenon_H8a zenon_H103 zenon_H20e zenon_H1b9 zenon_H182 zenon_H6f. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.59 apply (zenon_L34_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.59 exact (zenon_H103 zenon_H37). % 30.48/30.59 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.59 apply (zenon_L1145_); trivial. % 30.48/30.59 apply (zenon_L758_); trivial. % 30.48/30.59 (* end of lemma zenon_L2017_ *) % 30.48/30.59 assert (zenon_L2018_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.48/30.59 do 0 intro. intros zenon_Hb8 zenon_H6f zenon_H182 zenon_H20e zenon_H103 zenon_Had zenon_H16f zenon_H222 zenon_H3d zenon_H1dc zenon_H1b9 zenon_Ha4 zenon_H36 zenon_H16b. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.48/30.59 apply (zenon_L2017_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.48/30.59 apply (zenon_L775_); trivial. % 30.48/30.59 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.48/30.59 apply (zenon_L200_); trivial. % 30.48/30.59 apply (zenon_L1142_); trivial. % 30.48/30.59 (* end of lemma zenon_L2018_ *) % 30.48/30.59 assert (zenon_L2019_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.48/30.59 do 0 intro. intros zenon_H42 zenon_H3f zenon_H2bd zenon_H15a zenon_H16a zenon_H27 zenon_H16b zenon_H36 zenon_Ha4 zenon_H1b9 zenon_H1dc zenon_H222 zenon_H16f zenon_Had zenon_H103 zenon_H20e zenon_H182 zenon_H6f zenon_Hb8 zenon_He1 zenon_H9d. % 30.48/30.59 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.60 apply (zenon_L2016_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.60 apply (zenon_L2018_); trivial. % 30.48/30.60 apply (zenon_L1354_); trivial. % 30.48/30.60 (* end of lemma zenon_L2019_ *) % 30.48/30.60 assert (zenon_L2020_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H101 zenon_H138 zenon_Hda zenon_H198 zenon_Hdc zenon_Hd1 zenon_H19e zenon_H159 zenon_H19f zenon_H102 zenon_H42 zenon_H3f zenon_H2bd zenon_H15a zenon_H16a zenon_H27 zenon_H16b zenon_H36 zenon_Ha4 zenon_H1b9 zenon_H1dc zenon_H222 zenon_H16f zenon_Had zenon_H103 zenon_H20e zenon_H182 zenon_H6f zenon_Hb8 zenon_He1. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.60 apply (zenon_L1041_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.60 apply (zenon_L154_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.60 apply (zenon_L2015_); trivial. % 30.48/30.60 apply (zenon_L2019_); trivial. % 30.48/30.60 (* end of lemma zenon_L2020_ *) % 30.48/30.60 assert (zenon_L2021_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H83 zenon_H1b3 zenon_H6c zenon_Hc8 zenon_Hda zenon_Hd9 zenon_H218 zenon_H2d6 zenon_H1e1. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H64 | zenon_intro zenon_H86 ]. % 30.48/30.60 exact (zenon_H1b3 zenon_H64). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 30.48/30.60 apply (zenon_L809_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H73 | zenon_intro zenon_H89 ]. % 30.48/30.60 apply (zenon_L47_); trivial. % 30.48/30.60 apply (zenon_L1563_); trivial. % 30.48/30.60 (* end of lemma zenon_L2021_ *) % 30.48/30.60 assert (zenon_L2022_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H101 zenon_H35 zenon_Hdc zenon_Hd1 zenon_H19e zenon_H159 zenon_H19f zenon_H102 zenon_H16f zenon_He1 zenon_H200 zenon_H2e6 zenon_Hde zenon_H135 zenon_H1e zenon_H3c zenon_H260 zenon_H83 zenon_H1b3 zenon_H6c zenon_Hc8 zenon_Hda zenon_Hd9 zenon_H218 zenon_H2d6 zenon_Hb8 zenon_Had zenon_H3f zenon_H1dc zenon_H2bd zenon_H15a zenon_H16a zenon_H27 zenon_Ha4 zenon_H36 zenon_H42 zenon_H103 zenon_H20e zenon_H1b9 zenon_H182 zenon_H6f. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.60 apply (zenon_L2014_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.60 apply (zenon_L154_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.60 apply (zenon_L2015_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.60 apply (zenon_L1144_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.48/30.60 apply (zenon_L49_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.48/30.60 apply (zenon_L126_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.48/30.60 apply (zenon_L544_); trivial. % 30.48/30.60 exact (zenon_H2e6 zenon_Hf5). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.60 apply (zenon_L207_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.60 exact (zenon_H260 zenon_H142). % 30.48/30.60 apply (zenon_L2021_); trivial. % 30.48/30.60 apply (zenon_L1354_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.60 apply (zenon_L1145_); trivial. % 30.48/30.60 apply (zenon_L758_); trivial. % 30.48/30.60 (* end of lemma zenon_L2022_ *) % 30.48/30.60 assert (zenon_L2023_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_Hfd zenon_H2d zenon_H1b9 zenon_H83 zenon_H1b3 zenon_H6c zenon_Hc8 zenon_Hda zenon_Hd9 zenon_H218 zenon_H2d6. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.60 apply (zenon_L49_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.60 apply (zenon_L777_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.60 apply (zenon_L175_); trivial. % 30.48/30.60 apply (zenon_L2021_); trivial. % 30.48/30.60 (* end of lemma zenon_L2023_ *) % 30.48/30.60 assert (zenon_L2024_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H35 zenon_H198 zenon_H26 zenon_Hfd. % 30.48/30.60 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_H35. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H198. % 30.48/30.60 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 30.48/30.60 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 30.48/30.60 congruence. % 30.48/30.60 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 30.48/30.60 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e1)))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_H199. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H3a. % 30.48/30.60 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 30.48/30.60 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 30.48/30.60 congruence. % 30.48/30.60 apply (zenon_L128_); trivial. % 30.48/30.60 apply zenon_H3b. apply refl_equal. % 30.48/30.60 apply zenon_H3b. apply refl_equal. % 30.48/30.60 apply zenon_H149. apply sym_equal. exact zenon_Hfd. % 30.48/30.60 (* end of lemma zenon_L2024_ *) % 30.48/30.60 assert (zenon_L2025_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H3c zenon_H198 zenon_H26 zenon_H55. % 30.48/30.60 cut (((op (e0) (op (e0) (e2))) = (e2)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_H3c. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H198. % 30.48/30.60 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 30.48/30.60 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 30.48/30.60 congruence. % 30.48/30.60 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H3b ]. % 30.48/30.60 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (op (e0) (e2))) = (op (e0) (e1)))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_H199. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H3a. % 30.48/30.60 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 30.48/30.60 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 30.48/30.60 congruence. % 30.48/30.60 apply (zenon_L128_); trivial. % 30.48/30.60 apply zenon_H3b. apply refl_equal. % 30.48/30.60 apply zenon_H3b. apply refl_equal. % 30.48/30.60 apply zenon_H1c2. apply sym_equal. exact zenon_H55. % 30.48/30.60 (* end of lemma zenon_L2025_ *) % 30.48/30.60 assert (zenon_L2026_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e1)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H101 zenon_H138 zenon_Hda zenon_H35 zenon_H3c zenon_H3f zenon_H198 zenon_H26. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.60 apply (zenon_L1041_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.60 apply (zenon_L2024_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.60 apply (zenon_L2025_); trivial. % 30.48/30.60 apply (zenon_L129_); trivial. % 30.48/30.60 (* end of lemma zenon_L2026_ *) % 30.48/30.60 assert (zenon_L2027_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H225 zenon_H6c zenon_H103 zenon_H182 zenon_H159 zenon_H19f zenon_H102 zenon_H26 zenon_H198 zenon_H3f zenon_H3c zenon_H35 zenon_H138 zenon_H101 zenon_H27 zenon_H36 zenon_H1b9. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.60 apply (zenon_L244_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.60 apply (zenon_L2014_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.60 apply (zenon_L2026_); trivial. % 30.48/30.60 apply (zenon_L1141_); trivial. % 30.48/30.60 (* end of lemma zenon_L2027_ *) % 30.48/30.60 assert (zenon_L2028_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e0)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H92 zenon_Hd9 zenon_H15a zenon_H1b9 zenon_H36 zenon_H27 zenon_H101 zenon_H138 zenon_H35 zenon_H3c zenon_H3f zenon_H198 zenon_H26 zenon_H102 zenon_H19f zenon_H159 zenon_H182 zenon_H103 zenon_H225 zenon_He7 zenon_H188 zenon_H1e. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.60 apply (zenon_L797_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.60 apply (zenon_L119_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.60 apply (zenon_L2027_); trivial. % 30.48/30.60 apply (zenon_L1444_); trivial. % 30.48/30.60 (* end of lemma zenon_L2028_ *) % 30.48/30.60 assert (zenon_L2029_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H225 zenon_Hcd zenon_H88 zenon_H103 zenon_H35 zenon_H182 zenon_H159 zenon_H19f zenon_H102 zenon_Hde zenon_H10e zenon_H27 zenon_H36 zenon_H1b9. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.60 apply (zenon_L998_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.60 apply (zenon_L2014_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.60 apply (zenon_L192_); trivial. % 30.48/30.60 apply (zenon_L1141_); trivial. % 30.48/30.60 (* end of lemma zenon_L2029_ *) % 30.48/30.60 assert (zenon_L2030_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H16f zenon_H68 zenon_H103 zenon_H20e zenon_H1b9 zenon_H182 zenon_H6f. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.60 apply (zenon_L18_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.60 apply (zenon_L1145_); trivial. % 30.48/30.60 apply (zenon_L758_); trivial. % 30.48/30.60 (* end of lemma zenon_L2030_ *) % 30.48/30.60 assert (zenon_L2031_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H225 zenon_H6c zenon_H198 zenon_H65 zenon_Hde zenon_H10e zenon_H27 zenon_H36 zenon_H1b9. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.60 apply (zenon_L244_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.60 apply (zenon_L818_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.60 apply (zenon_L192_); trivial. % 30.48/30.60 apply (zenon_L1141_); trivial. % 30.48/30.60 (* end of lemma zenon_L2031_ *) % 30.48/30.60 assert (zenon_L2032_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H102 zenon_H19f zenon_H159 zenon_H182 zenon_H1ba zenon_H1b9 zenon_H103. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.48/30.60 exact (zenon_H19f zenon_Hc3). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.48/30.60 apply (zenon_L1131_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.48/30.60 apply (zenon_L777_); trivial. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 (* end of lemma zenon_L2032_ *) % 30.48/30.60 assert (zenon_L2033_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_Hb8 zenon_Had zenon_H6e zenon_H95 zenon_H2d zenon_H1dc zenon_H1b9 zenon_Ha4 zenon_H36 zenon_H16b. % 30.48/30.60 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.48/30.60 apply (zenon_L34_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.48/30.60 apply (zenon_L766_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.48/30.60 apply (zenon_L200_); trivial. % 30.48/30.60 apply (zenon_L1142_); trivial. % 30.48/30.60 (* end of lemma zenon_L2033_ *) % 30.48/30.60 assert (zenon_L2034_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H16f zenon_Ha4 zenon_H1dc zenon_H2d zenon_H95 zenon_Had zenon_Hb8 zenon_H103 zenon_H20e zenon_H1b9 zenon_H16a zenon_H36 zenon_H16b. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.60 apply (zenon_L2033_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.60 apply (zenon_L1145_); trivial. % 30.48/30.60 apply (zenon_L1541_); trivial. % 30.48/30.60 (* end of lemma zenon_L2034_ *) % 30.48/30.60 assert (zenon_L2035_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H296 zenon_H90 zenon_H188 zenon_He7 zenon_H182 zenon_H159 zenon_H19f zenon_H102 zenon_H16f zenon_Ha4 zenon_H1dc zenon_H2d zenon_Had zenon_Hb8 zenon_H103 zenon_H20e zenon_H1b9 zenon_H16a zenon_H36 zenon_H16b. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.60 apply (zenon_L1444_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.60 exact (zenon_H19f zenon_Hc3). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.60 apply (zenon_L2032_); trivial. % 30.48/30.60 apply (zenon_L2034_); trivial. % 30.48/30.60 (* end of lemma zenon_L2035_ *) % 30.48/30.60 assert (zenon_L2036_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H16f zenon_H185 zenon_H36 zenon_H15a zenon_H103 zenon_H20e zenon_H1b9 zenon_H182 zenon_H6f. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.60 apply (zenon_L1000_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.60 apply (zenon_L1145_); trivial. % 30.48/30.60 apply (zenon_L758_); trivial. % 30.48/30.60 (* end of lemma zenon_L2036_ *) % 30.48/30.60 assert (zenon_L2037_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H8d zenon_Hcd zenon_H1a5 zenon_H198 zenon_Hda zenon_H88 zenon_Hc9 zenon_H18c zenon_H173 zenon_H6b zenon_H16f zenon_Had zenon_H103 zenon_H20e zenon_H1b9 zenon_H182 zenon_H6f. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.60 apply (zenon_L734_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.60 apply (zenon_L142_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.60 apply (zenon_L795_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.60 apply (zenon_L1030_); trivial. % 30.48/30.60 apply (zenon_L1135_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.60 apply (zenon_L1149_); trivial. % 30.48/30.60 apply (zenon_L2017_); trivial. % 30.48/30.60 (* end of lemma zenon_L2037_ *) % 30.48/30.60 assert (zenon_L2038_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H225 zenon_H35 zenon_H159 zenon_H19f zenon_H102 zenon_H6f zenon_H182 zenon_H20e zenon_H103 zenon_Had zenon_H16f zenon_H6b zenon_H173 zenon_H18c zenon_Hc9 zenon_H88 zenon_H198 zenon_H1a5 zenon_Hcd zenon_H8d zenon_H27 zenon_H36 zenon_H1b9. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.60 apply (zenon_L998_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.60 apply (zenon_L2014_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.60 apply (zenon_L2037_); trivial. % 30.48/30.60 apply (zenon_L1141_); trivial. % 30.48/30.60 (* end of lemma zenon_L2038_ *) % 30.48/30.60 assert (zenon_L2039_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H225 zenon_H103 zenon_H35 zenon_H159 zenon_H19f zenon_H102 zenon_Hcd zenon_H182 zenon_H1a5 zenon_H198 zenon_H200 zenon_Hc9 zenon_Hde zenon_H2d zenon_H83 zenon_H1b3 zenon_H6c zenon_Hc8 zenon_Hd9 zenon_H218 zenon_H2d6 zenon_H18c zenon_H173 zenon_H27 zenon_H36 zenon_H1b9. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.60 apply (zenon_L244_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.60 apply (zenon_L2014_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.60 apply (zenon_L142_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.60 apply (zenon_L2023_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.60 apply (zenon_L1030_); trivial. % 30.48/30.60 apply (zenon_L1135_); trivial. % 30.48/30.60 apply (zenon_L1141_); trivial. % 30.48/30.60 (* end of lemma zenon_L2039_ *) % 30.48/30.60 assert (zenon_L2040_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((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). % 30.48/30.60 do 0 intro. intros zenon_Hc0 zenon_H8d zenon_H6b zenon_H16f zenon_Had zenon_H20e zenon_H6f zenon_Hcd zenon_H1a5 zenon_H200 zenon_Hc9 zenon_Hde zenon_H2d zenon_H83 zenon_H1b3 zenon_Hc8 zenon_H218 zenon_H2d6 zenon_H18c zenon_H173 zenon_H65 zenon_H1e zenon_H188 zenon_He7 zenon_H225 zenon_H103 zenon_H159 zenon_H19f zenon_H102 zenon_H198 zenon_H3f zenon_H3c zenon_H35 zenon_H138 zenon_H101 zenon_H27 zenon_H36 zenon_H1b9 zenon_H15a zenon_Hd9 zenon_H92 zenon_H182 zenon_H16a. % 30.48/30.60 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.48/30.60 apply (zenon_L2038_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.60 apply (zenon_L1035_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.60 apply (zenon_L119_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.60 apply (zenon_L2039_); trivial. % 30.48/30.60 apply (zenon_L1444_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.48/30.60 apply (zenon_L2028_); trivial. % 30.48/30.60 apply (zenon_L115_); trivial. % 30.48/30.60 (* end of lemma zenon_L2040_ *) % 30.48/30.60 assert (zenon_L2041_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 30.48/30.60 do 0 intro. intros zenon_He7 zenon_H2d6 zenon_H64 zenon_H8b. % 30.48/30.60 cut (((op (e0) (op (e0) (e0))) = (e0)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_He7. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H2d6. % 30.48/30.60 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 30.48/30.60 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2d7]. % 30.48/30.60 congruence. % 30.48/30.60 elim (classic ((op (e0) (e0)) = (op (e0) (e0)))); [ zenon_intro zenon_H18b | zenon_intro zenon_Hcb ]. % 30.48/30.60 cut (((op (e0) (e0)) = (op (e0) (e0))) = ((op (e0) (op (e0) (e0))) = (op (e0) (e0)))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_H2d7. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H18b. % 30.48/30.60 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 30.48/30.60 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2d5]. % 30.48/30.60 congruence. % 30.48/30.60 apply (zenon_L1049_); trivial. % 30.48/30.60 apply zenon_Hcb. apply refl_equal. % 30.48/30.60 apply zenon_Hcb. apply refl_equal. % 30.48/30.60 apply zenon_H1ed. apply sym_equal. exact zenon_H8b. % 30.48/30.60 (* end of lemma zenon_L2041_ *) % 30.48/30.60 assert (zenon_L2042_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H2fc zenon_H9c zenon_Hb5 zenon_H1e zenon_H188 zenon_He7 zenon_Hc9 zenon_H1d8 zenon_H40 zenon_H97. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H8b | zenon_intro zenon_H2fd ]. % 30.48/30.60 apply (zenon_L297_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H90 | zenon_intro zenon_H2fe ]. % 30.48/30.60 apply (zenon_L1444_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_He2 | zenon_intro zenon_H8a ]. % 30.48/30.60 apply (zenon_L307_); trivial. % 30.48/30.60 apply (zenon_L862_); trivial. % 30.48/30.60 (* end of lemma zenon_L2042_ *) % 30.48/30.60 assert (zenon_L2043_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.48/30.60 do 0 intro. intros zenon_Hbd zenon_H64 zenon_H2d6 zenon_H3f zenon_H97 zenon_H40 zenon_H1d8 zenon_Hc9 zenon_He7 zenon_H188 zenon_H1e zenon_Hb5 zenon_H2fc zenon_H122. % 30.48/30.60 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.60 apply (zenon_L2041_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.60 apply (zenon_L29_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.60 apply (zenon_L2042_); trivial. % 30.48/30.60 exact (zenon_H122 zenon_Hb1). % 30.48/30.60 (* end of lemma zenon_L2043_ *) % 30.48/30.60 assert (zenon_L2044_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H42 zenon_H2d zenon_H16b zenon_H36 zenon_Ha4 zenon_H1dc zenon_H222 zenon_H16f zenon_Had zenon_H103 zenon_H20e zenon_H182 zenon_H6f zenon_Hb8 zenon_H135 zenon_H122 zenon_H2fc zenon_Hb5 zenon_H1e zenon_H188 zenon_He7 zenon_H1d8 zenon_H97 zenon_H3f zenon_H2d6 zenon_H64 zenon_Hbd zenon_Hfd zenon_H19e zenon_H1b9 zenon_He1 zenon_H2e6. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.60 apply (zenon_L4_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.60 apply (zenon_L2018_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.48/30.60 apply (zenon_L2043_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.48/30.60 apply (zenon_L787_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.48/30.60 apply (zenon_L544_); trivial. % 30.48/30.60 exact (zenon_H2e6 zenon_Hf5). % 30.48/30.60 (* end of lemma zenon_L2044_ *) % 30.48/30.60 assert (zenon_L2045_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H296 zenon_He1 zenon_H6f zenon_H20e zenon_H16f zenon_H222 zenon_H27 zenon_H16a zenon_H15a zenon_H2bd zenon_H3f zenon_H42 zenon_H19e zenon_H135 zenon_H122 zenon_H2fc zenon_Hb5 zenon_H188 zenon_He7 zenon_H1d8 zenon_H97 zenon_H2d6 zenon_H64 zenon_Hbd zenon_H2e6 zenon_H198 zenon_Hda zenon_H138 zenon_H101 zenon_H103 zenon_H182 zenon_H159 zenon_H19f zenon_H102 zenon_Hb8 zenon_Had zenon_H6e zenon_H2d zenon_H1dc zenon_H1b9 zenon_Ha4 zenon_H36 zenon_H16b. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.60 apply (zenon_L1041_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.60 apply (zenon_L2044_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.60 apply (zenon_L2015_); trivial. % 30.48/30.60 apply (zenon_L2019_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.60 exact (zenon_H19f zenon_Hc3). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.60 apply (zenon_L2032_); trivial. % 30.48/30.60 apply (zenon_L2033_); trivial. % 30.48/30.60 (* end of lemma zenon_L2045_ *) % 30.48/30.60 assert (zenon_L2046_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H102 zenon_H90 zenon_Had zenon_H18f zenon_H1a5 zenon_H26 zenon_H4a zenon_H103. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.48/30.60 apply (zenon_L769_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.48/30.60 exact (zenon_H18f zenon_Hd2). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.48/30.60 apply (zenon_L748_); trivial. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 (* end of lemma zenon_L2046_ *) % 30.48/30.60 assert (zenon_L2047_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H23b zenon_H103 zenon_H4a zenon_H1a5 zenon_H18f zenon_Had zenon_H102 zenon_H40 zenon_H6f zenon_H26 zenon_H10d zenon_H182 zenon_H14e. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.48/30.60 apply (zenon_L2046_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.48/30.60 apply (zenon_L80_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.48/30.60 apply (zenon_L699_); trivial. % 30.48/30.60 apply (zenon_L137_); trivial. % 30.48/30.60 (* end of lemma zenon_L2047_ *) % 30.48/30.60 assert (zenon_L2048_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H1a2 zenon_H10d zenon_H102 zenon_Had zenon_H18f zenon_H1a5 zenon_H4a zenon_H103 zenon_H23b zenon_H6f zenon_H56 zenon_Hbd zenon_H182 zenon_H17d zenon_H2d zenon_H40 zenon_H113 zenon_H14e zenon_H4c zenon_H15e zenon_H11b zenon_H1b9. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.48/30.60 apply (zenon_L2047_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.48/30.60 apply (zenon_L235_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.48/30.60 exact (zenon_H56 zenon_H25). % 30.48/30.60 apply (zenon_L774_); trivial. % 30.48/30.60 (* end of lemma zenon_L2048_ *) % 30.48/30.60 assert (zenon_L2049_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H42 zenon_H35 zenon_H4e zenon_H19e zenon_H1a2 zenon_H10d zenon_H102 zenon_Had zenon_H18f zenon_H1a5 zenon_H4a zenon_H103 zenon_H23b zenon_H6f zenon_H56 zenon_Hbd zenon_H182 zenon_H17d zenon_H2d zenon_H113 zenon_H14e zenon_H4c zenon_H15e zenon_H11b zenon_H1b9. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.60 apply (zenon_L730_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.60 apply (zenon_L731_); trivial. % 30.48/30.60 apply (zenon_L2048_); trivial. % 30.48/30.60 (* end of lemma zenon_L2049_ *) % 30.48/30.60 assert (zenon_L2050_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H55 zenon_H19e zenon_H103. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.48/30.60 apply (zenon_L763_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.48/30.60 exact (zenon_H18f zenon_Hd2). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.48/30.60 apply (zenon_L787_); trivial. % 30.48/30.60 exact (zenon_H103 zenon_H37). % 30.48/30.60 (* end of lemma zenon_L2050_ *) % 30.48/30.60 assert (zenon_L2051_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H208 zenon_H103 zenon_H19e zenon_H18f zenon_H18c zenon_H4a zenon_H102 zenon_H55 zenon_Hcd zenon_H6f zenon_H1b9 zenon_H156 zenon_H182. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.60 apply (zenon_L2050_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.60 apply (zenon_L212_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.60 apply (zenon_L1138_); trivial. % 30.48/30.60 apply (zenon_L934_); trivial. % 30.48/30.60 (* end of lemma zenon_L2051_ *) % 30.48/30.60 assert (zenon_L2052_ : (((op (e0) (op (e0) (e0))) = (e0))/\(((op (e0) (op (e0) (e1))) = (e1))/\(((op (e0) (op (e0) (e2))) = (e2))/\(((op (e0) (op (e0) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1)))/\(((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2)))/\((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3)))))))))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e1) (e1)) = (e0)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H2ec zenon_H313 zenon_Hc3. % 30.48/30.60 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.48/30.60 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.48/30.60 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.48/30.60 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.48/30.60 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.48/30.60 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H19f | zenon_intro zenon_H68 ]. % 30.48/30.60 exact (zenon_H19f zenon_Hc3). % 30.48/30.60 exact (zenon_H313 zenon_H68). % 30.48/30.60 (* end of lemma zenon_L2052_ *) % 30.48/30.60 assert (zenon_L2053_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H6c zenon_H6b zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.60 exact (zenon_H260 zenon_H142). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.60 apply (zenon_L17_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.60 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.60 apply (zenon_L259_); trivial. % 30.48/30.60 (* end of lemma zenon_L2053_ *) % 30.48/30.60 assert (zenon_L2054_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H6c zenon_H6b zenon_Hd0 zenon_H60 zenon_H155 zenon_H156. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.60 exact (zenon_H260 zenon_H142). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.60 apply (zenon_L17_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.60 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.60 apply (zenon_L179_); trivial. % 30.48/30.60 (* end of lemma zenon_L2054_ *) % 30.48/30.60 assert (zenon_L2055_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H6c zenon_H260 zenon_H1d2 zenon_Hc9 zenon_H20d zenon_H231. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.48/30.60 apply (zenon_L2053_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.48/30.60 apply (zenon_L2054_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.48/30.60 apply (zenon_L627_); trivial. % 30.48/30.60 exact (zenon_H231 zenon_Hf4). % 30.48/30.60 (* end of lemma zenon_L2055_ *) % 30.48/30.60 assert (zenon_L2056_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H1e5 zenon_H108 zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.60 exact (zenon_H260 zenon_H142). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.60 apply (zenon_L1274_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.60 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.60 apply (zenon_L259_); trivial. % 30.48/30.60 (* end of lemma zenon_L2056_ *) % 30.48/30.60 assert (zenon_L2057_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H1e5 zenon_H108 zenon_Hd0 zenon_H60 zenon_H155 zenon_H156. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.60 exact (zenon_H260 zenon_H142). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.60 apply (zenon_L1274_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.60 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.60 apply (zenon_L179_); trivial. % 30.48/30.60 (* end of lemma zenon_L2057_ *) % 30.48/30.60 assert (zenon_L2058_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H1e5 zenon_H260 zenon_H1d2 zenon_Hd6 zenon_H3d zenon_H1af zenon_H231. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.48/30.60 apply (zenon_L2056_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.48/30.60 apply (zenon_L2057_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.48/30.60 apply (zenon_L144_); trivial. % 30.48/30.60 exact (zenon_H231 zenon_Hf4). % 30.48/30.60 (* end of lemma zenon_L2058_ *) % 30.48/30.60 assert (zenon_L2059_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H1e5 zenon_H260 zenon_H1d2 zenon_He1 zenon_H1c5 zenon_H231. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.48/30.60 apply (zenon_L2056_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.48/30.60 apply (zenon_L2057_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.48/30.60 apply (zenon_L221_); trivial. % 30.48/30.60 exact (zenon_H231 zenon_Hf4). % 30.48/30.60 (* end of lemma zenon_L2059_ *) % 30.48/30.60 assert (zenon_L2060_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H1d5 zenon_H1af zenon_Hd6 zenon_H20d zenon_Hc9 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H1e5 zenon_H260 zenon_H1d2 zenon_He1 zenon_H231. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.48/30.60 apply (zenon_L273_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.48/30.60 apply (zenon_L2058_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.48/30.60 apply (zenon_L628_); trivial. % 30.48/30.60 apply (zenon_L2059_); trivial. % 30.48/30.60 (* end of lemma zenon_L2060_ *) % 30.48/30.60 assert (zenon_L2061_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H208 zenon_H6b zenon_H1f zenon_H5e zenon_H3c zenon_He9 zenon_H1d5 zenon_H1af zenon_Hd6 zenon_H20d zenon_Hc9 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_He1 zenon_H231. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.60 apply (zenon_L2055_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.60 apply (zenon_L218_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.60 apply (zenon_L219_); trivial. % 30.48/30.60 apply (zenon_L2060_); trivial. % 30.48/30.60 (* end of lemma zenon_L2061_ *) % 30.48/30.60 assert (zenon_L2062_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H20e zenon_H19a zenon_Hd0 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hc9 zenon_H20d zenon_H231. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.60 exact (zenon_H260 zenon_H142). % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.60 apply (zenon_L225_); trivial. % 30.48/30.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.60 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.60 apply (zenon_L628_); trivial. % 30.48/30.60 (* end of lemma zenon_L2062_ *) % 30.48/30.60 assert (zenon_L2063_ : ((op (e2) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (op (op (e3) (e3)) (e3)))) -> False). % 30.48/30.60 do 0 intro. intros zenon_H1e1 zenon_Hf4 zenon_H249. % 30.48/30.60 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 30.48/30.60 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e0) = (op (op (e3) (e3)) (e3)))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_H249. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H131. % 30.48/30.60 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 30.48/30.60 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H24a]. % 30.48/30.60 congruence. % 30.48/30.60 cut (((op (e2) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_H24a. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H1e1. % 30.48/30.60 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 30.48/30.60 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c4]. % 30.48/30.60 congruence. % 30.48/30.60 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_H131 | zenon_intro zenon_H132 ]. % 30.48/30.60 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_H2c4. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H131. % 30.48/30.60 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 30.48/30.60 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 30.48/30.60 congruence. % 30.48/30.60 apply (zenon_L942_); trivial. % 30.48/30.60 apply zenon_H132. apply refl_equal. % 30.48/30.60 apply zenon_H132. apply refl_equal. % 30.48/30.60 apply zenon_H1d. apply refl_equal. % 30.48/30.60 apply zenon_H132. apply refl_equal. % 30.48/30.60 apply zenon_H132. apply refl_equal. % 30.48/30.60 (* end of lemma zenon_L2063_ *) % 30.48/30.60 assert (zenon_L2064_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 30.48/30.60 do 0 intro. intros zenon_H25 zenon_H1e1 zenon_Hf4. % 30.48/30.60 apply (zenon_notand_s _ _ ax26); [ zenon_intro zenon_H2a5 | zenon_intro zenon_H314 ]. % 30.48/30.60 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 30.48/30.60 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (e3) (e3))))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_H2a5. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H12c. % 30.48/30.60 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 30.48/30.60 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2a6]. % 30.48/30.60 congruence. % 30.48/30.60 cut (((op (e2) (e2)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 30.48/30.60 intro zenon_D_pnotp. % 30.48/30.60 apply zenon_H2a6. % 30.48/30.60 rewrite <- zenon_D_pnotp. % 30.48/30.60 exact zenon_H25. % 30.48/30.60 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 30.48/30.60 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2c6]. % 30.48/30.60 congruence. % 30.48/30.60 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H12c | zenon_intro zenon_H12d ]. % 30.48/30.61 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))))). % 30.48/30.61 intro zenon_D_pnotp. % 30.48/30.61 apply zenon_H2c6. % 30.48/30.61 rewrite <- zenon_D_pnotp. % 30.48/30.61 exact zenon_H12c. % 30.48/30.61 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 30.48/30.61 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 30.48/30.61 congruence. % 30.48/30.61 apply (zenon_L941_); trivial. % 30.48/30.61 apply zenon_H12d. apply refl_equal. % 30.48/30.61 apply zenon_H12d. apply refl_equal. % 30.48/30.61 apply zenon_H22. apply refl_equal. % 30.48/30.61 apply zenon_H12d. apply refl_equal. % 30.48/30.61 apply zenon_H12d. apply refl_equal. % 30.48/30.61 apply (zenon_notand_s _ _ zenon_H314); [ zenon_intro zenon_H249 | zenon_intro zenon_H116 ]. % 30.48/30.61 apply (zenon_L2063_); trivial. % 30.48/30.61 apply zenon_H116. apply sym_equal. exact zenon_Hf4. % 30.48/30.61 (* end of lemma zenon_L2064_ *) % 30.48/30.61 assert (zenon_L2065_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_Hf4 zenon_H1e1 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.61 apply (zenon_L2064_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.61 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.61 apply (zenon_L200_); trivial. % 30.48/30.61 (* end of lemma zenon_L2065_ *) % 30.48/30.61 assert (zenon_L2066_ : (((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) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_Hf9 zenon_Hc9 zenon_H1d8 zenon_He9 zenon_H3f zenon_He1 zenon_H1d2 zenon_H260 zenon_H1e1 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.48/30.61 apply (zenon_L307_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.48/30.61 apply (zenon_L53_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.48/30.61 apply (zenon_L204_); trivial. % 30.48/30.61 apply (zenon_L2065_); trivial. % 30.48/30.61 (* end of lemma zenon_L2066_ *) % 30.48/30.61 assert (zenon_L2067_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (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) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H200 zenon_Hde zenon_Hc3 zenon_H19e zenon_Hf9 zenon_Hc9 zenon_H1d8 zenon_He9 zenon_H3f zenon_He1 zenon_H1d2 zenon_H260 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.61 apply (zenon_L49_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.61 apply (zenon_L347_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_L2066_); trivial. % 30.48/30.61 (* end of lemma zenon_L2067_ *) % 30.48/30.61 assert (zenon_L2068_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.48/30.61 do 0 intro. intros zenon_H14b zenon_Hde zenon_Hda zenon_Hc3 zenon_Hfc zenon_H260 zenon_H2d zenon_Hb6. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.61 apply (zenon_L192_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.61 apply (zenon_L59_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_L304_); trivial. % 30.48/30.61 (* end of lemma zenon_L2068_ *) % 30.48/30.61 assert (zenon_L2069_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H20e zenon_H19a zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.61 apply (zenon_L225_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.61 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.61 apply (zenon_L259_); trivial. % 30.48/30.61 (* end of lemma zenon_L2069_ *) % 30.48/30.61 assert (zenon_L2070_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H225 zenon_H74 zenon_H1dc zenon_He1 zenon_H3f zenon_H1d8 zenon_Hc9 zenon_Hf9 zenon_H19e zenon_H200 zenon_Hb6 zenon_H2d zenon_Hfc zenon_Hc3 zenon_Hde zenon_H14b zenon_H1d2 zenon_H260 zenon_H20e zenon_H19a zenon_Hd0 zenon_H60 zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.61 exact (zenon_H74 zenon_H73). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.61 apply (zenon_L2067_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.61 apply (zenon_L2068_); trivial. % 30.48/30.61 apply (zenon_L2069_); trivial. % 30.48/30.61 (* end of lemma zenon_L2070_ *) % 30.48/30.61 assert (zenon_L2071_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H25c zenon_H6b zenon_H1d2 zenon_H218 zenon_H60 zenon_H156 zenon_H20d zenon_Hc9 zenon_H267 zenon_H19a zenon_H20e zenon_H260 zenon_H225 zenon_Hfc zenon_H2d zenon_H14b zenon_Hde zenon_H19e zenon_Hc3 zenon_Hf9 zenon_H1dc zenon_He1 zenon_H3f zenon_H1d8 zenon_H200 zenon_H74 zenon_H25b. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.48/30.61 apply (zenon_L2062_); trivial. % 30.48/30.61 apply (zenon_L2070_); trivial. % 30.48/30.61 apply (zenon_L552_); trivial. % 30.48/30.61 (* end of lemma zenon_L2071_ *) % 30.48/30.61 assert (zenon_L2072_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H208 zenon_H6b zenon_H1ba zenon_H5e zenon_H1bd zenon_H3c zenon_He9 zenon_H1d5 zenon_H1af zenon_Hd6 zenon_H20d zenon_Hc9 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_He1 zenon_H231. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.61 apply (zenon_L2055_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.61 apply (zenon_L608_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.61 apply (zenon_L219_); trivial. % 30.48/30.61 apply (zenon_L2060_); trivial. % 30.48/30.61 (* end of lemma zenon_L2072_ *) % 30.48/30.61 assert (zenon_L2073_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_Hd6 zenon_Hd5 zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.61 apply (zenon_L46_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.61 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.61 apply (zenon_L259_); trivial. % 30.48/30.61 (* end of lemma zenon_L2073_ *) % 30.48/30.61 assert (zenon_L2074_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H208 zenon_H6b zenon_H98 zenon_H5e zenon_H222 zenon_H3c zenon_He9 zenon_H1d5 zenon_H1af zenon_Hd6 zenon_H20d zenon_Hc9 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_He1 zenon_H231. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.61 apply (zenon_L2055_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.61 apply (zenon_L514_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.61 apply (zenon_L219_); trivial. % 30.48/30.61 apply (zenon_L2060_); trivial. % 30.48/30.61 (* end of lemma zenon_L2074_ *) % 30.48/30.61 assert (zenon_L2075_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H208 zenon_H6b zenon_Hd6 zenon_H27 zenon_H26 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.61 apply (zenon_L2053_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.61 apply (zenon_L2073_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.61 apply (zenon_L3_); trivial. % 30.48/30.61 apply (zenon_L2056_); trivial. % 30.48/30.61 (* end of lemma zenon_L2075_ *) % 30.48/30.61 assert (zenon_L2076_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H9d zenon_H222 zenon_Hd0 zenon_H60 zenon_H155 zenon_H156. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.61 apply (zenon_L256_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.61 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.61 apply (zenon_L179_); trivial. % 30.48/30.61 (* end of lemma zenon_L2076_ *) % 30.48/30.61 assert (zenon_L2077_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H14b zenon_Hde zenon_Hda zenon_Hc3 zenon_Hfc zenon_H1fd zenon_H6f zenon_H1af zenon_H20e zenon_H1d2 zenon_H260 zenon_H9d zenon_H222 zenon_Hd0 zenon_H208 zenon_H6b zenon_Hd6 zenon_H27 zenon_H26 zenon_H108 zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H2d. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.61 apply (zenon_L192_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.61 apply (zenon_L59_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.61 apply (zenon_L598_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.48/30.61 apply (zenon_L2075_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.48/30.61 apply (zenon_L2076_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.48/30.61 apply (zenon_L358_); trivial. % 30.48/30.61 exact (zenon_H231 zenon_Hf4). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.61 apply (zenon_L628_); trivial. % 30.48/30.61 apply (zenon_L304_); trivial. % 30.48/30.61 (* end of lemma zenon_L2077_ *) % 30.48/30.61 assert (zenon_L2078_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.61 do 0 intro. intros zenon_H208 zenon_H218 zenon_H17b zenon_Hd0 zenon_H6b zenon_H260 zenon_H1d2 zenon_H1f zenon_H5e zenon_H3c zenon_He9 zenon_H60 zenon_H156 zenon_H182. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.61 apply (zenon_L2053_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.61 apply (zenon_L218_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.61 apply (zenon_L219_); trivial. % 30.48/30.61 apply (zenon_L934_); trivial. % 30.48/30.61 (* end of lemma zenon_L2078_ *) % 30.48/30.61 assert (zenon_L2079_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1a8 zenon_H313 zenon_H25b zenon_H74 zenon_H200 zenon_H1d8 zenon_H3f zenon_He1 zenon_H1dc zenon_Hf9 zenon_H19e zenon_Hde zenon_H14b zenon_H2d zenon_Hfc zenon_H225 zenon_H20e zenon_H25c zenon_H124 zenon_H33 zenon_H222 zenon_H5e zenon_H3c zenon_H267 zenon_H156 zenon_H6b zenon_Hc9 zenon_H20d zenon_H231 zenon_H208 zenon_H1bd zenon_H13b zenon_H101 zenon_H20 zenon_Hc3 zenon_H218 zenon_H17b zenon_H60 zenon_Hd0 zenon_Hd6 zenon_H260 zenon_H1d2 zenon_H97 zenon_H90. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.61 exact (zenon_H313 zenon_H68). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.61 apply (zenon_L906_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.61 apply (zenon_L2071_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.61 apply (zenon_L2078_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.61 exact (zenon_H13b zenon_Hfd). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.61 apply (zenon_L282_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.61 apply (zenon_L2055_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.61 apply (zenon_L218_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.61 apply (zenon_L256_); trivial. % 30.48/30.61 apply (zenon_L870_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.61 apply (zenon_L906_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.61 apply (zenon_L2073_); trivial. % 30.48/30.61 apply (zenon_L30_); trivial. % 30.48/30.61 (* end of lemma zenon_L2079_ *) % 30.48/30.61 assert (zenon_L2080_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.48/30.61 do 0 intro. intros zenon_H14b zenon_H2d zenon_H117 zenon_Hc3 zenon_Hfc zenon_H1e1 zenon_H108 zenon_Hb5 zenon_H8b. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.61 apply (zenon_L87_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.61 apply (zenon_L59_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.61 apply (zenon_L296_); trivial. % 30.48/30.61 apply (zenon_L297_); trivial. % 30.48/30.61 (* end of lemma zenon_L2080_ *) % 30.48/30.61 assert (zenon_L2081_ : ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (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) (e0)) = (op (e2) (e3)))) -> (((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) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H8b zenon_Hb5 zenon_H108 zenon_Hfc zenon_Hc3 zenon_H14b zenon_H231 zenon_H267 zenon_H218 zenon_H60 zenon_H156 zenon_H19a zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_H20d zenon_Hf9 zenon_Hc9 zenon_H1d8 zenon_He9 zenon_H3f zenon_He1 zenon_H1d2 zenon_H260 zenon_H1e1 zenon_Hd0 zenon_H1dc. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.61 apply (zenon_L2080_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.61 apply (zenon_L235_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.61 apply (zenon_L1803_); trivial. % 30.48/30.61 apply (zenon_L2066_); trivial. % 30.48/30.61 (* end of lemma zenon_L2081_ *) % 30.48/30.61 assert (zenon_L2082_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (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) (e0)) = (op (e2) (e3)))) -> (((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) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H200 zenon_Hde zenon_H19e zenon_H8b zenon_Hb5 zenon_H108 zenon_Hfc zenon_Hc3 zenon_H14b zenon_H231 zenon_H267 zenon_H218 zenon_H60 zenon_H156 zenon_H19a zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_H20d zenon_Hf9 zenon_Hc9 zenon_H1d8 zenon_He9 zenon_H3f zenon_He1 zenon_H1d2 zenon_H260 zenon_Hd0 zenon_H1dc. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.61 apply (zenon_L49_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.61 apply (zenon_L347_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_L2081_); trivial. % 30.48/30.61 (* end of lemma zenon_L2082_ *) % 30.48/30.61 assert (zenon_L2083_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.48/30.61 do 0 intro. intros zenon_H14b zenon_Hde zenon_Hda zenon_Hc3 zenon_Hfc zenon_H260 zenon_Hb5 zenon_H8b. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.61 apply (zenon_L192_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.61 apply (zenon_L59_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_L297_); trivial. % 30.48/30.61 (* end of lemma zenon_L2083_ *) % 30.48/30.61 assert (zenon_L2084_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H1e5 zenon_H108 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.61 apply (zenon_L1274_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.61 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.61 apply (zenon_L200_); trivial. % 30.48/30.61 (* end of lemma zenon_L2084_ *) % 30.48/30.61 assert (zenon_L2085_ : (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (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) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H231 zenon_H267 zenon_H218 zenon_He1 zenon_H60 zenon_H156 zenon_H19a zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_Hc9 zenon_H20d zenon_H3f zenon_He9 zenon_H1d8 zenon_Hf9 zenon_H1d2 zenon_H260 zenon_H1e5 zenon_H108 zenon_Hd0 zenon_H1dc. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.61 apply (zenon_L87_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.61 apply (zenon_L235_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.61 apply (zenon_L1803_); trivial. % 30.48/30.61 apply (zenon_L2084_); trivial. % 30.48/30.61 (* end of lemma zenon_L2085_ *) % 30.48/30.61 assert (zenon_L2086_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H225 zenon_Hcd zenon_H1dc zenon_H108 zenon_Hf9 zenon_H1d8 zenon_H3f zenon_H20d zenon_Hc9 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H156 zenon_He1 zenon_H267 zenon_H231 zenon_H5e zenon_H1f zenon_H3c zenon_Hc8 zenon_H88 zenon_H208 zenon_H8b zenon_Hb5 zenon_Hfc zenon_Hc3 zenon_Hde zenon_H14b zenon_H1d2 zenon_H260 zenon_H20e zenon_H19a zenon_Hd0 zenon_H60 zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.61 apply (zenon_L998_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.61 apply (zenon_L809_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.61 apply (zenon_L218_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.61 apply (zenon_L225_); trivial. % 30.48/30.61 apply (zenon_L2085_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.61 apply (zenon_L2083_); trivial. % 30.48/30.61 apply (zenon_L2069_); trivial. % 30.48/30.61 (* end of lemma zenon_L2086_ *) % 30.48/30.61 assert (zenon_L2087_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H208 zenon_H88 zenon_Hc8 zenon_H3c zenon_H1f zenon_H5e zenon_H9d zenon_H222 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.61 apply (zenon_L809_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.61 apply (zenon_L218_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.61 apply (zenon_L256_); trivial. % 30.48/30.61 apply (zenon_L2056_); trivial. % 30.48/30.61 (* end of lemma zenon_L2087_ *) % 30.48/30.61 assert (zenon_L2088_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (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) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1a8 zenon_H313 zenon_H20 zenon_H20e zenon_H14b zenon_Hde zenon_Hc3 zenon_Hfc zenon_Hb5 zenon_H8b zenon_H231 zenon_H267 zenon_He1 zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_H20d zenon_H3f zenon_H1d8 zenon_Hf9 zenon_H1dc zenon_Hcd zenon_H225 zenon_H101 zenon_H156 zenon_H6b zenon_H13b zenon_H1bd zenon_Hc9 zenon_H208 zenon_H88 zenon_Hc8 zenon_H3c zenon_H1f zenon_H5e zenon_H222 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.61 exact (zenon_H313 zenon_H68). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.61 apply (zenon_L906_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.61 apply (zenon_L2086_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.61 apply (zenon_L2078_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.61 exact (zenon_H13b zenon_Hfd). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.61 apply (zenon_L282_); trivial. % 30.48/30.61 apply (zenon_L2087_); trivial. % 30.48/30.61 (* end of lemma zenon_L2088_ *) % 30.48/30.61 assert (zenon_L2089_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H92 zenon_H108 zenon_H222 zenon_H5e zenon_H1f zenon_H3c zenon_Hc8 zenon_H208 zenon_H1bd zenon_H13b zenon_H101 zenon_H225 zenon_Hcd zenon_H1dc zenon_Hf9 zenon_H1d8 zenon_H3f zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_He1 zenon_Hb5 zenon_Hfc zenon_Hc3 zenon_Hde zenon_H14b zenon_H20e zenon_H1a8 zenon_H1d5 zenon_H1af zenon_Hd6 zenon_H313 zenon_H231 zenon_H20d zenon_Hc9 zenon_H1d2 zenon_H260 zenon_H6b zenon_Hd0 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H8b zenon_H20. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.61 apply (zenon_L998_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.61 apply (zenon_L2061_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.61 apply (zenon_L2083_); trivial. % 30.48/30.61 apply (zenon_L2088_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.61 exact (zenon_H313 zenon_H68). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.61 apply (zenon_L2055_); trivial. % 30.48/30.61 apply (zenon_L27_); trivial. % 30.48/30.61 (* end of lemma zenon_L2089_ *) % 30.48/30.61 assert (zenon_L2090_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H92 zenon_Hd9 zenon_H26 zenon_H313 zenon_H231 zenon_H20d zenon_Hc9 zenon_H1d2 zenon_H260 zenon_H6b zenon_Hd0 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H8b zenon_H20. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.61 apply (zenon_L797_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.61 exact (zenon_H313 zenon_H68). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.61 apply (zenon_L2055_); trivial. % 30.48/30.61 apply (zenon_L27_); trivial. % 30.48/30.61 (* end of lemma zenon_L2090_ *) % 30.48/30.61 assert (zenon_L2091_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H1a0 zenon_H1dc zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.61 apply (zenon_L1834_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.61 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.61 apply (zenon_L259_); trivial. % 30.48/30.61 (* end of lemma zenon_L2091_ *) % 30.48/30.61 assert (zenon_L2092_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1a2 zenon_Hd9 zenon_H88 zenon_H20e zenon_H9d zenon_H222 zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.48/30.61 apply (zenon_L797_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.48/30.61 apply (zenon_L2069_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.48/30.61 apply (zenon_L256_); trivial. % 30.48/30.61 apply (zenon_L2091_); trivial. % 30.48/30.61 (* end of lemma zenon_L2092_ *) % 30.48/30.61 assert (zenon_L2093_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H101 zenon_H3c zenon_H13b zenon_Hd5 zenon_Hcd zenon_H1a2 zenon_Hd9 zenon_H88 zenon_H20e zenon_H222 zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.48/30.61 apply (zenon_L797_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.48/30.61 apply (zenon_L2069_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.48/30.61 apply (zenon_L219_); trivial. % 30.48/30.61 apply (zenon_L2091_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.61 exact (zenon_H13b zenon_Hfd). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.61 apply (zenon_L212_); trivial. % 30.48/30.61 apply (zenon_L2092_); trivial. % 30.48/30.61 (* end of lemma zenon_L2093_ *) % 30.48/30.61 assert (zenon_L2094_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H92 zenon_H33 zenon_H2c1 zenon_H313 zenon_H231 zenon_H20d zenon_Hc9 zenon_H1d2 zenon_H260 zenon_H6b zenon_Hd0 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H8b zenon_H20. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.61 apply (zenon_L940_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.61 exact (zenon_H313 zenon_H68). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.61 apply (zenon_L2055_); trivial. % 30.48/30.61 apply (zenon_L27_); trivial. % 30.48/30.61 (* end of lemma zenon_L2094_ *) % 30.48/30.61 assert (zenon_L2095_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.48/30.61 do 0 intro. intros zenon_Hc0 zenon_H1a2 zenon_H124 zenon_H19e zenon_H5c zenon_H200 zenon_Hd6 zenon_H1af zenon_H1d5 zenon_H1a8 zenon_H20e zenon_H14b zenon_Hde zenon_Hc3 zenon_Hfc zenon_Hb5 zenon_He1 zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_H3f zenon_H1d8 zenon_Hf9 zenon_H1dc zenon_Hcd zenon_H225 zenon_H101 zenon_H13b zenon_H1bd zenon_H208 zenon_Hc8 zenon_H3c zenon_H5e zenon_H222 zenon_H108 zenon_Hd9 zenon_H92 zenon_H2c1 zenon_H313 zenon_H231 zenon_H20d zenon_Hc9 zenon_H1d2 zenon_H260 zenon_H6b zenon_Hd0 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H8b zenon_H20. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.61 apply (zenon_L43_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.61 exact (zenon_H313 zenon_H68). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.61 apply (zenon_L906_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.61 apply (zenon_L2082_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.61 apply (zenon_L2089_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.61 apply (zenon_L906_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.61 apply (zenon_L194_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.61 apply (zenon_L608_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.48/30.61 apply (zenon_L2090_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.48/30.61 apply (zenon_L2081_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.48/30.61 apply (zenon_L46_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.61 apply (zenon_L2080_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.48/30.61 apply (zenon_L2093_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.48/30.61 apply (zenon_L1135_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.48/30.61 apply (zenon_L358_); trivial. % 30.48/30.61 exact (zenon_H231 zenon_Hf4). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.61 apply (zenon_L628_); trivial. % 30.48/30.61 apply (zenon_L540_); trivial. % 30.48/30.61 apply (zenon_L2074_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.61 apply (zenon_L192_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.61 apply (zenon_L2088_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.61 apply (zenon_L906_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.61 apply (zenon_L2093_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.61 apply (zenon_L2074_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.61 exact (zenon_H13b zenon_Hfd). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.61 apply (zenon_L282_); trivial. % 30.48/30.61 apply (zenon_L2092_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.48/30.61 apply (zenon_L2089_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.48/30.61 apply (zenon_L2090_); trivial. % 30.48/30.61 apply (zenon_L2094_); trivial. % 30.48/30.61 (* end of lemma zenon_L2095_ *) % 30.48/30.61 assert (zenon_L2096_ : ((op (e2) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_Hd5 zenon_Hbd zenon_H20 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H260 zenon_H1d2 zenon_Hc9 zenon_H20d zenon_H231 zenon_H313 zenon_H2c1 zenon_H92 zenon_Hd9 zenon_H108 zenon_H222 zenon_H5e zenon_H3c zenon_Hc8 zenon_H208 zenon_H1bd zenon_H13b zenon_H101 zenon_H225 zenon_Hcd zenon_H1dc zenon_Hf9 zenon_H1d8 zenon_H3f zenon_H1fd zenon_H2d zenon_H6f zenon_He1 zenon_Hb5 zenon_Hfc zenon_Hde zenon_H14b zenon_H20e zenon_H1a8 zenon_H1d5 zenon_H1af zenon_Hd6 zenon_H200 zenon_H5c zenon_H19e zenon_H124 zenon_H1a2 zenon_Hc0 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.61 apply (zenon_L49_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.61 apply (zenon_L608_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.61 apply (zenon_L2095_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.61 apply (zenon_L1497_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.61 apply (zenon_L63_); trivial. % 30.48/30.61 apply (zenon_L690_); trivial. % 30.48/30.61 (* end of lemma zenon_L2096_ *) % 30.48/30.61 assert (zenon_L2097_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e2)) = (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.48/30.61 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H260 zenon_H1d2 zenon_Hc9 zenon_H20d zenon_H231 zenon_H313 zenon_H26 zenon_Hd9 zenon_H92 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H1e1. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.61 apply (zenon_L2090_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.61 apply (zenon_L1497_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.61 apply (zenon_L63_); trivial. % 30.48/30.61 apply (zenon_L690_); trivial. % 30.48/30.61 (* end of lemma zenon_L2097_ *) % 30.48/30.61 assert (zenon_L2098_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_H231 zenon_H20d zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_Hf9 zenon_Hc9 zenon_H1d8 zenon_He9 zenon_H3f zenon_He1 zenon_H1d2 zenon_H260 zenon_H1e1 zenon_Hd0 zenon_H1dc. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.61 apply (zenon_L87_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.61 apply (zenon_L235_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.61 apply (zenon_L628_); trivial. % 30.48/30.61 apply (zenon_L2066_); trivial. % 30.48/30.61 (* end of lemma zenon_L2098_ *) % 30.48/30.61 assert (zenon_L2099_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (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))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H200 zenon_Hde zenon_H108 zenon_Hd6 zenon_H1af zenon_H1d5 zenon_H1bd zenon_H5e zenon_H208 zenon_H1a2 zenon_Hf6 zenon_H10d zenon_H100 zenon_Hc3 zenon_H92 zenon_Hd9 zenon_H313 zenon_H6b zenon_H20 zenon_Hbd zenon_He1 zenon_H3f zenon_H1d8 zenon_Hc9 zenon_Hf9 zenon_H267 zenon_H156 zenon_H20d zenon_H231 zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_H3c zenon_He9 zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.61 apply (zenon_L49_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.61 apply (zenon_L2072_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.48/30.61 apply (zenon_L2097_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.48/30.61 apply (zenon_L2098_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.48/30.61 apply (zenon_L219_); trivial. % 30.48/30.61 apply (zenon_L2091_); trivial. % 30.48/30.61 (* end of lemma zenon_L2099_ *) % 30.48/30.61 assert (zenon_L2100_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (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))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1a2 zenon_H1e1 zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_H92 zenon_Hd9 zenon_H313 zenon_H231 zenon_H20d zenon_Hc9 zenon_H6b zenon_H156 zenon_H267 zenon_H20 zenon_Hbd zenon_H20e zenon_H9d zenon_H222 zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.48/30.61 apply (zenon_L2097_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.48/30.61 apply (zenon_L2069_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.48/30.61 apply (zenon_L256_); trivial. % 30.48/30.61 apply (zenon_L2091_); trivial. % 30.48/30.61 (* end of lemma zenon_L2100_ *) % 30.48/30.61 assert (zenon_L2101_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (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))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H101 zenon_H3c zenon_H1fd zenon_H2d zenon_H6f zenon_Hf9 zenon_H1d8 zenon_H3f zenon_He1 zenon_H208 zenon_H5e zenon_H1d5 zenon_H1af zenon_Hd6 zenon_H108 zenon_H13b zenon_H1bd zenon_H200 zenon_Hde zenon_H19e zenon_H1a2 zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_H92 zenon_Hd9 zenon_H313 zenon_H231 zenon_H20d zenon_Hc9 zenon_H6b zenon_H156 zenon_H267 zenon_H20 zenon_Hbd zenon_H20e zenon_H222 zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.61 apply (zenon_L2099_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.61 exact (zenon_H13b zenon_Hfd). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.61 apply (zenon_L282_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.61 apply (zenon_L49_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.61 apply (zenon_L347_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_L2100_); trivial. % 30.48/30.61 (* end of lemma zenon_L2101_ *) % 30.48/30.61 assert (zenon_L2102_ : ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (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))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H90 zenon_H97 zenon_H2c1 zenon_Hc8 zenon_H225 zenon_Hcd zenon_Hb5 zenon_Hfc zenon_H14b zenon_H1a8 zenon_H5c zenon_H124 zenon_Hc0 zenon_H101 zenon_H3c zenon_H1fd zenon_H2d zenon_H6f zenon_Hf9 zenon_H1d8 zenon_H3f zenon_He1 zenon_H208 zenon_H5e zenon_H1d5 zenon_H1af zenon_Hd6 zenon_H108 zenon_H13b zenon_H1bd zenon_H200 zenon_Hde zenon_H19e zenon_H1a2 zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_H92 zenon_Hd9 zenon_H313 zenon_H231 zenon_H20d zenon_Hc9 zenon_H6b zenon_H156 zenon_H267 zenon_H20 zenon_Hbd zenon_H20e zenon_H222 zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hd0 zenon_H60 zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.61 apply (zenon_L43_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.61 apply (zenon_L2061_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.61 apply (zenon_L906_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.61 apply (zenon_L2096_); trivial. % 30.48/30.61 apply (zenon_L30_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.61 apply (zenon_L192_); trivial. % 30.48/30.61 apply (zenon_L2101_); trivial. % 30.48/30.61 (* end of lemma zenon_L2102_ *) % 30.48/30.61 assert (zenon_L2103_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (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))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H97 zenon_H2c1 zenon_Hc8 zenon_H225 zenon_Hcd zenon_Hb5 zenon_Hfc zenon_H14b zenon_H1a8 zenon_H5c zenon_H124 zenon_Hc0 zenon_H101 zenon_H3c zenon_H1fd zenon_H2d zenon_H6f zenon_Hf9 zenon_H1d8 zenon_H3f zenon_He1 zenon_H208 zenon_H5e zenon_H1d5 zenon_H1af zenon_Hd6 zenon_H108 zenon_H13b zenon_H1bd zenon_H200 zenon_Hde zenon_H19e zenon_H1a2 zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_H92 zenon_Hd9 zenon_H313 zenon_H231 zenon_H20d zenon_Hc9 zenon_H6b zenon_H156 zenon_H267 zenon_H20 zenon_Hbd zenon_H20e zenon_H222 zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hd0 zenon_H60 zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.61 apply (zenon_L998_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.61 apply (zenon_L2061_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.61 apply (zenon_L906_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.61 apply (zenon_L2096_); trivial. % 30.48/30.61 apply (zenon_L2074_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.61 apply (zenon_L192_); trivial. % 30.48/30.61 apply (zenon_L2101_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.61 apply (zenon_L43_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.61 apply (zenon_L2061_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.61 apply (zenon_L192_); trivial. % 30.48/30.61 apply (zenon_L2101_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.61 apply (zenon_L797_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.61 exact (zenon_H313 zenon_H68). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.61 apply (zenon_L2055_); trivial. % 30.48/30.61 apply (zenon_L2102_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.61 apply (zenon_L940_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.61 exact (zenon_H313 zenon_H68). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.61 apply (zenon_L2055_); trivial. % 30.48/30.61 apply (zenon_L2102_); trivial. % 30.48/30.61 (* end of lemma zenon_L2103_ *) % 30.48/30.61 assert (zenon_L2104_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.48/30.61 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_Hc3 zenon_H19e zenon_H260 zenon_H218 zenon_H185. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.61 apply (zenon_L49_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.61 apply (zenon_L347_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_L1088_); trivial. % 30.48/30.61 (* end of lemma zenon_L2104_ *) % 30.48/30.61 assert (zenon_L2105_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H6c zenon_H6b zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.61 apply (zenon_L17_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.61 exact (zenon_Hd0 zenon_Hcc). % 30.48/30.61 apply (zenon_L200_); trivial. % 30.48/30.61 (* end of lemma zenon_L2105_ *) % 30.48/30.61 assert (zenon_L2106_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H92 zenon_Hd9 zenon_H26 zenon_H313 zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H6b zenon_H260 zenon_H1d2 zenon_H8b zenon_H20. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.61 apply (zenon_L797_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.61 exact (zenon_H313 zenon_H68). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.61 apply (zenon_L2105_); trivial. % 30.48/30.61 apply (zenon_L27_); trivial. % 30.48/30.61 (* end of lemma zenon_L2106_ *) % 30.48/30.61 assert (zenon_L2107_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H225 zenon_Hc8 zenon_H1dc zenon_Hb6 zenon_He1 zenon_H3f zenon_H1d8 zenon_Hc9 zenon_Hf9 zenon_H19e zenon_Hc3 zenon_H200 zenon_Hde zenon_H10e zenon_H1d2 zenon_H260 zenon_H20e zenon_H19a zenon_Hd0 zenon_H60 zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.61 apply (zenon_L43_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.61 apply (zenon_L2067_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.61 apply (zenon_L192_); trivial. % 30.48/30.61 apply (zenon_L2069_); trivial. % 30.48/30.61 (* end of lemma zenon_L2107_ *) % 30.48/30.61 assert (zenon_L2108_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((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))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H1a2 zenon_H1e1 zenon_Hf6 zenon_H10d zenon_H100 zenon_H92 zenon_Hd9 zenon_H313 zenon_H6b zenon_H20 zenon_Hbd zenon_H20e zenon_H10e zenon_Hde zenon_H200 zenon_Hc3 zenon_H19e zenon_Hf9 zenon_Hc9 zenon_H1d8 zenon_H3f zenon_He1 zenon_Hb6 zenon_Hc8 zenon_H225 zenon_H9d zenon_H222 zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.61 apply (zenon_L2106_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.61 apply (zenon_L1497_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.61 apply (zenon_L63_); trivial. % 30.48/30.61 apply (zenon_L690_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.48/30.61 apply (zenon_L2107_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.48/30.61 apply (zenon_L256_); trivial. % 30.48/30.61 apply (zenon_L2091_); trivial. % 30.48/30.61 (* end of lemma zenon_L2108_ *) % 30.48/30.61 assert (zenon_L2109_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.48/30.61 do 0 intro. intros zenon_H14b zenon_H218 zenon_H17b zenon_H60 zenon_Hd0 zenon_H1dc zenon_H1d2 zenon_H222 zenon_H9d zenon_H225 zenon_Hc8 zenon_He1 zenon_H3f zenon_H1d8 zenon_Hc9 zenon_Hf9 zenon_H19e zenon_H200 zenon_Hde zenon_H20e zenon_Hbd zenon_H20 zenon_H6b zenon_H313 zenon_Hd9 zenon_H92 zenon_H100 zenon_H10d zenon_Hf6 zenon_H1e1 zenon_H1a2 zenon_Hc3 zenon_Hfc zenon_H260 zenon_H2d zenon_Hb6. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.61 apply (zenon_L2108_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.61 apply (zenon_L59_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_L304_); trivial. % 30.48/30.61 (* end of lemma zenon_L2109_ *) % 30.48/30.61 assert (zenon_L2110_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((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))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H101 zenon_H13b zenon_H1bd zenon_H1a2 zenon_Hf6 zenon_H10d zenon_H100 zenon_H92 zenon_Hd9 zenon_H313 zenon_H6b zenon_H20 zenon_Hbd zenon_H20e zenon_H10e zenon_Hde zenon_H200 zenon_Hc3 zenon_H19e zenon_Hf9 zenon_Hc9 zenon_H1d8 zenon_H3f zenon_He1 zenon_Hb6 zenon_Hc8 zenon_H225 zenon_H222 zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hd0 zenon_H60 zenon_H218. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.61 apply (zenon_L43_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.61 apply (zenon_L2067_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.61 apply (zenon_L192_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.61 apply (zenon_L2067_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.61 exact (zenon_H13b zenon_Hfd). % 30.48/30.61 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.61 apply (zenon_L282_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.61 apply (zenon_L49_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.61 apply (zenon_L347_); trivial. % 30.48/30.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.61 exact (zenon_H260 zenon_H142). % 30.48/30.61 apply (zenon_L2108_); trivial. % 30.48/30.61 (* end of lemma zenon_L2110_ *) % 30.48/30.61 assert (zenon_L2111_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.48/30.61 do 0 intro. intros zenon_H25b zenon_H208 zenon_He1 zenon_H1af zenon_Hd6 zenon_H108 zenon_H1d5 zenon_H5e zenon_H3c zenon_H1d2 zenon_H60 zenon_H218 zenon_Hd0 zenon_H6b zenon_H260 zenon_H156 zenon_H20d zenon_Hc9 zenon_H267 zenon_H20 zenon_Hc3 zenon_Hc0 zenon_H2c1 zenon_Hc8 zenon_H92 zenon_H1a8 zenon_H13b zenon_H222 zenon_H101 zenon_H20e zenon_H225 zenon_Hd9 zenon_H1a2 zenon_H5c zenon_H124 zenon_H19e zenon_H1dc zenon_H1d8 zenon_H3f zenon_H10e zenon_H1fd zenon_Hf9 zenon_H6f zenon_H2d zenon_Hfc zenon_Hb5 zenon_H14b zenon_H200 zenon_H313 zenon_H100 zenon_H10d zenon_Hf6 zenon_Hbd zenon_H1bd zenon_Hde zenon_Hcd zenon_H97. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.48/30.62 apply (zenon_L2103_); trivial. % 30.48/30.62 apply (zenon_L2110_); trivial. % 30.48/30.62 (* end of lemma zenon_L2111_ *) % 30.48/30.62 assert (zenon_L2112_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H225 zenon_Hc8 zenon_H1dc zenon_He1 zenon_H3f zenon_H1d8 zenon_Hc9 zenon_Hf9 zenon_H267 zenon_H156 zenon_H20d zenon_H231 zenon_H6f zenon_H2d zenon_H1fd zenon_H19e zenon_Hc3 zenon_H200 zenon_Hde zenon_H10e zenon_H1d2 zenon_H260 zenon_H20e zenon_H19a zenon_Hd0 zenon_H60 zenon_H218. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.62 apply (zenon_L43_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.62 apply (zenon_L49_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.62 apply (zenon_L347_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_L2098_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.62 apply (zenon_L192_); trivial. % 30.48/30.62 apply (zenon_L2069_); trivial. % 30.48/30.62 (* end of lemma zenon_L2112_ *) % 30.48/30.62 assert (zenon_L2113_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H25b zenon_Hc8 zenon_Hc9 zenon_H200 zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_H267 zenon_H20d zenon_H156 zenon_H60 zenon_H218 zenon_Hf9 zenon_Hd0 zenon_H1dc zenon_H1d2 zenon_He1 zenon_H3f zenon_H1d8 zenon_H1fd zenon_H260 zenon_Hc3 zenon_H19e zenon_Hde zenon_H20e zenon_H225. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.48/30.62 apply (zenon_L2112_); trivial. % 30.48/30.62 apply (zenon_L2107_); trivial. % 30.48/30.62 (* end of lemma zenon_L2113_ *) % 30.48/30.62 assert (zenon_L2114_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H20e zenon_H19a zenon_Hc9 zenon_H6b zenon_H1db. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.62 apply (zenon_L225_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.62 apply (zenon_L552_); trivial. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 (* end of lemma zenon_L2114_ *) % 30.48/30.62 assert (zenon_L2115_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H6c zenon_Hc9 zenon_H6b zenon_H1db. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.62 apply (zenon_L17_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.62 apply (zenon_L552_); trivial. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 (* end of lemma zenon_L2115_ *) % 30.48/30.62 assert (zenon_L2116_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_Hd6 zenon_Hd5 zenon_Hc9 zenon_H6b zenon_H1db. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.62 apply (zenon_L46_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.62 apply (zenon_L552_); trivial. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 (* end of lemma zenon_L2116_ *) % 30.48/30.62 assert (zenon_L2117_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.62 do 0 intro. intros zenon_Hf9 zenon_Hde zenon_H8b zenon_He9 zenon_H3f zenon_Hed zenon_H9b zenon_Hb3 zenon_H15e zenon_Hee. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.48/30.62 apply (zenon_L288_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.48/30.62 apply (zenon_L53_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.48/30.62 apply (zenon_L55_); trivial. % 30.48/30.62 apply (zenon_L995_); trivial. % 30.48/30.62 (* end of lemma zenon_L2117_ *) % 30.48/30.62 assert (zenon_L2118_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.48/30.62 do 0 intro. intros zenon_Hbd zenon_Hee zenon_H15e zenon_Hb3 zenon_H9b zenon_Hed zenon_H3f zenon_He9 zenon_Hde zenon_Hf9 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H1e1. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.62 apply (zenon_L2117_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.62 apply (zenon_L1497_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.62 apply (zenon_L63_); trivial. % 30.48/30.62 apply (zenon_L690_); trivial. % 30.48/30.62 (* end of lemma zenon_L2118_ *) % 30.48/30.62 assert (zenon_L2119_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> False). % 30.48/30.62 do 0 intro. intros zenon_Hf9 zenon_Hde zenon_H8b zenon_He9 zenon_H3f zenon_Hb6 zenon_He1 zenon_H25 zenon_H1e1. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.48/30.62 apply (zenon_L288_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.48/30.62 apply (zenon_L53_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.48/30.62 apply (zenon_L204_); trivial. % 30.48/30.62 apply (zenon_L2064_); trivial. % 30.48/30.62 (* end of lemma zenon_L2119_ *) % 30.48/30.62 assert (zenon_L2120_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 30.48/30.62 do 0 intro. intros zenon_Hbd zenon_H1e1 zenon_H25 zenon_He1 zenon_H3f zenon_He9 zenon_Hde zenon_Hf9 zenon_Hc3 zenon_H100 zenon_H2d zenon_Hb5 zenon_Hb3 zenon_Hb6. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.62 apply (zenon_L2119_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.62 apply (zenon_L1497_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.62 apply (zenon_L304_); trivial. % 30.48/30.62 apply (zenon_L37_); trivial. % 30.48/30.62 (* end of lemma zenon_L2120_ *) % 30.48/30.62 assert (zenon_L2121_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1fd zenon_Hf6 zenon_H10d zenon_H10e zenon_Hed zenon_H9b zenon_Hee zenon_H1db zenon_Hbd zenon_H1e1 zenon_H25 zenon_He1 zenon_H3f zenon_He9 zenon_Hde zenon_Hf9 zenon_Hc3 zenon_H100 zenon_H2d zenon_Hb5 zenon_Hb3. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.62 apply (zenon_L87_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.62 apply (zenon_L2118_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 apply (zenon_L2120_); trivial. % 30.48/30.62 (* end of lemma zenon_L2121_ *) % 30.48/30.62 assert (zenon_L2122_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H208 zenon_H6b zenon_Hc9 zenon_Hd6 zenon_H260 zenon_H1d2 zenon_Hb3 zenon_Hb5 zenon_H2d zenon_H100 zenon_Hc3 zenon_Hf9 zenon_Hde zenon_He9 zenon_H3f zenon_He1 zenon_H1e1 zenon_Hbd zenon_H1db zenon_Hee zenon_H9b zenon_Hed zenon_H10e zenon_H10d zenon_Hf6 zenon_H1fd zenon_H156 zenon_H182. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.62 apply (zenon_L2115_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.62 apply (zenon_L2116_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.62 apply (zenon_L2121_); trivial. % 30.48/30.62 apply (zenon_L934_); trivial. % 30.48/30.62 (* end of lemma zenon_L2122_ *) % 30.48/30.62 assert (zenon_L2123_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.62 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_H90 zenon_H9c zenon_H97 zenon_Hee zenon_Hed zenon_H9b zenon_Hb3 zenon_H117 zenon_H10d. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.48/30.62 apply (zenon_L386_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.48/30.62 apply (zenon_L31_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.48/30.62 apply (zenon_L55_); trivial. % 30.48/30.62 apply (zenon_L68_); trivial. % 30.48/30.62 (* end of lemma zenon_L2123_ *) % 30.48/30.62 assert (zenon_L2124_ : (((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) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.62 do 0 intro. intros zenon_Hf9 zenon_Hc9 zenon_H1d8 zenon_H9c zenon_H97 zenon_Hed zenon_H9b zenon_Hb3 zenon_H15e zenon_Hee. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.48/30.62 apply (zenon_L307_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.48/30.62 apply (zenon_L31_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.48/30.62 apply (zenon_L55_); trivial. % 30.48/30.62 apply (zenon_L995_); trivial. % 30.48/30.62 (* end of lemma zenon_L2124_ *) % 30.48/30.62 assert (zenon_L2125_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H200 zenon_H19e zenon_H14b zenon_Hf6 zenon_Hfc zenon_H208 zenon_H6b zenon_Hd6 zenon_H260 zenon_H1d2 zenon_Hb3 zenon_Hb5 zenon_H2d zenon_H100 zenon_Hc3 zenon_Hf9 zenon_Hde zenon_He9 zenon_H3f zenon_He1 zenon_Hbd zenon_H1db zenon_Hc9 zenon_H1d8 zenon_H97 zenon_Hed zenon_H9b zenon_Hee zenon_Hcd zenon_H90 zenon_H10d zenon_H1fd zenon_H156 zenon_H182. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.62 apply (zenon_L49_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.62 apply (zenon_L347_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.62 apply (zenon_L2122_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.62 apply (zenon_L59_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.62 apply (zenon_L2115_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.62 apply (zenon_L2116_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.62 apply (zenon_L2123_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.62 apply (zenon_L2124_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 apply (zenon_L2120_); trivial. % 30.48/30.62 apply (zenon_L934_); trivial. % 30.48/30.62 (* end of lemma zenon_L2125_ *) % 30.48/30.62 assert (zenon_L2126_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H200 zenon_H19e zenon_H208 zenon_H6b zenon_Hc9 zenon_Hd6 zenon_H260 zenon_H1d2 zenon_Hb3 zenon_Hb5 zenon_H2d zenon_H100 zenon_Hc3 zenon_Hf9 zenon_Hde zenon_He9 zenon_H3f zenon_He1 zenon_Hbd zenon_H1db zenon_Hee zenon_H9b zenon_Hed zenon_H10e zenon_H10d zenon_Hf6 zenon_H1fd zenon_H156 zenon_H182. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.62 apply (zenon_L49_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.62 apply (zenon_L347_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_L2122_); trivial. % 30.48/30.62 (* end of lemma zenon_L2126_ *) % 30.48/30.62 assert (zenon_L2127_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H173 zenon_H18c zenon_H35 zenon_H156 zenon_H1fd zenon_Hf6 zenon_H10d zenon_H10e zenon_H9b zenon_Hee zenon_H1db zenon_Hbd zenon_He1 zenon_H3f zenon_He9 zenon_Hde zenon_Hf9 zenon_Hc3 zenon_H100 zenon_H2d zenon_Hb5 zenon_Hb3 zenon_H1d2 zenon_H260 zenon_Hd6 zenon_Hc9 zenon_H6b zenon_H208 zenon_H19e zenon_H200 zenon_H182 zenon_Hcd. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.62 apply (zenon_L142_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.62 apply (zenon_L95_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.62 apply (zenon_L2126_); trivial. % 30.48/30.62 apply (zenon_L1135_); trivial. % 30.48/30.62 (* end of lemma zenon_L2127_ *) % 30.48/30.62 assert (zenon_L2128_ : ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H9b zenon_Hb6 zenon_H17b zenon_Ha4. % 30.48/30.62 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.48/30.62 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 30.48/30.62 intro zenon_D_pnotp. % 30.48/30.62 apply zenon_Ha4. % 30.48/30.62 rewrite <- zenon_D_pnotp. % 30.48/30.62 exact zenon_Ha5. % 30.48/30.62 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.48/30.62 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 30.48/30.62 congruence. % 30.48/30.62 cut (((op (e3) (op (e3) (e2))) = (e2)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 30.48/30.62 intro zenon_D_pnotp. % 30.48/30.62 apply zenon_Ha7. % 30.48/30.62 rewrite <- zenon_D_pnotp. % 30.48/30.62 exact zenon_H9b. % 30.48/30.62 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 30.48/30.62 cut (((op (e3) (op (e3) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H315]. % 30.48/30.62 congruence. % 30.48/30.62 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 30.48/30.62 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (op (e3) (e2))) = (op (e3) (e3)))). % 30.48/30.62 intro zenon_D_pnotp. % 30.48/30.62 apply zenon_H315. % 30.48/30.62 rewrite <- zenon_D_pnotp. % 30.48/30.62 exact zenon_Ha5. % 30.48/30.62 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 30.48/30.62 cut (((op (e3) (e3)) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H316]. % 30.48/30.62 congruence. % 30.48/30.62 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 30.48/30.62 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.48/30.62 congruence. % 30.48/30.62 apply zenon_H2f. apply refl_equal. % 30.48/30.62 apply zenon_Hb7. apply sym_equal. exact zenon_Hb6. % 30.48/30.62 apply zenon_Ha6. apply refl_equal. % 30.48/30.62 apply zenon_Ha6. apply refl_equal. % 30.48/30.62 apply zenon_H223. apply sym_equal. exact zenon_H17b. % 30.48/30.62 apply zenon_Ha6. apply refl_equal. % 30.48/30.62 apply zenon_Ha6. apply refl_equal. % 30.48/30.62 (* end of lemma zenon_L2128_ *) % 30.48/30.62 assert (zenon_L2129_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.48/30.62 do 0 intro. intros zenon_Hb8 zenon_Had zenon_H6e zenon_H9d zenon_He1 zenon_Ha4 zenon_H17b zenon_H9b zenon_Hb9. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.48/30.62 apply (zenon_L34_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.48/30.62 apply (zenon_L1354_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.48/30.62 apply (zenon_L2128_); trivial. % 30.48/30.62 exact (zenon_Hb9 zenon_Hbc). % 30.48/30.62 (* end of lemma zenon_L2129_ *) % 30.48/30.62 assert (zenon_L2130_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H173 zenon_H18c zenon_Hb9 zenon_H9b zenon_H17b zenon_Ha4 zenon_He1 zenon_H6e zenon_Had zenon_Hb8 zenon_Hc9 zenon_H1bd zenon_Hfc zenon_H200 zenon_H19e zenon_H260 zenon_H1fd zenon_H2d zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_Hf9 zenon_Hde zenon_H3f zenon_Hb3 zenon_Hee zenon_Hbd zenon_H1db zenon_H101 zenon_H182 zenon_Hcd. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.62 apply (zenon_L142_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.62 apply (zenon_L782_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.62 apply (zenon_L49_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.62 apply (zenon_L347_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.62 apply (zenon_L87_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.62 apply (zenon_L2118_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 apply (zenon_L2128_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.62 apply (zenon_L58_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.62 apply (zenon_L282_); trivial. % 30.48/30.62 apply (zenon_L2129_); trivial. % 30.48/30.62 apply (zenon_L1135_); trivial. % 30.48/30.62 (* end of lemma zenon_L2130_ *) % 30.48/30.62 assert (zenon_L2131_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H23b zenon_H20 zenon_H8b zenon_H1f zenon_H25 zenon_H1dc zenon_Hb3 zenon_H2c zenon_H3f. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.48/30.62 apply (zenon_L27_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.48/30.62 apply (zenon_L336_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.48/30.62 apply (zenon_L1834_); trivial. % 30.48/30.62 apply (zenon_L720_); trivial. % 30.48/30.62 (* end of lemma zenon_L2131_ *) % 30.48/30.62 assert (zenon_L2132_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.48/30.62 do 0 intro. intros zenon_Hbd zenon_H3f zenon_H2c zenon_Hb3 zenon_H1dc zenon_H25 zenon_H1f zenon_H20 zenon_H23b zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H1e1. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.62 apply (zenon_L2131_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.62 apply (zenon_L1497_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.62 apply (zenon_L63_); trivial. % 30.48/30.62 apply (zenon_L690_); trivial. % 30.48/30.62 (* end of lemma zenon_L2132_ *) % 30.48/30.62 assert (zenon_L2133_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H200 zenon_Hde zenon_H19e zenon_H208 zenon_H1db zenon_H6b zenon_Hc9 zenon_Hd6 zenon_H260 zenon_H1d2 zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_H23b zenon_H20 zenon_H1f zenon_H1dc zenon_Hb3 zenon_H2c zenon_H3f zenon_Hbd zenon_H156 zenon_H182. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.62 apply (zenon_L49_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.62 apply (zenon_L347_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.62 apply (zenon_L2115_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.62 apply (zenon_L2116_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.62 apply (zenon_L2132_); trivial. % 30.48/30.62 apply (zenon_L934_); trivial. % 30.48/30.62 (* end of lemma zenon_L2133_ *) % 30.48/30.62 assert (zenon_L2134_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H23b zenon_H88 zenon_He7 zenon_H1f zenon_H3f zenon_H25 zenon_H1dc zenon_Hb3 zenon_H3d zenon_H222. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.48/30.62 apply (zenon_L1053_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.48/30.62 apply (zenon_L336_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.48/30.62 apply (zenon_L1834_); trivial. % 30.48/30.62 apply (zenon_L722_); trivial. % 30.48/30.62 (* end of lemma zenon_L2134_ *) % 30.48/30.62 assert (zenon_L2135_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H208 zenon_Hc8 zenon_H1db zenon_H6b zenon_Hc9 zenon_Hd6 zenon_H260 zenon_H1d2 zenon_H222 zenon_H3d zenon_Hb3 zenon_H1dc zenon_H3f zenon_H1f zenon_He7 zenon_H88 zenon_H23b zenon_H156 zenon_H182. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.62 apply (zenon_L809_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.62 apply (zenon_L2116_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.62 apply (zenon_L2134_); trivial. % 30.48/30.62 apply (zenon_L934_); trivial. % 30.48/30.62 (* end of lemma zenon_L2135_ *) % 30.48/30.62 assert (zenon_L2136_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H42 zenon_Hbd zenon_H20 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H19e zenon_Hde zenon_H200 zenon_H2d zenon_Hc3 zenon_H182 zenon_H156 zenon_H23b zenon_H88 zenon_He7 zenon_H1f zenon_H3f zenon_H1dc zenon_Hb3 zenon_H222 zenon_H1d2 zenon_H260 zenon_Hd6 zenon_Hc9 zenon_H6b zenon_H1db zenon_Hc8 zenon_H208 zenon_He1 zenon_H9d. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.62 apply (zenon_L2133_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.62 apply (zenon_L364_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.62 apply (zenon_L2135_); trivial. % 30.48/30.62 apply (zenon_L1354_); trivial. % 30.48/30.62 (* end of lemma zenon_L2136_ *) % 30.48/30.62 assert (zenon_L2137_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H8d zenon_H85 zenon_Hcd zenon_H182 zenon_H101 zenon_H1db zenon_Hbd zenon_Hee zenon_Hb3 zenon_H3f zenon_Hde zenon_Hf9 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H2d zenon_H1fd zenon_H260 zenon_H19e zenon_H200 zenon_Hfc zenon_H1bd zenon_Hb8 zenon_Had zenon_Ha4 zenon_H17b zenon_H9b zenon_Hb9 zenon_H18c zenon_H173 zenon_He1 zenon_Hc9 zenon_H6f zenon_H90. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.62 exact (zenon_H85 zenon_H89). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.62 apply (zenon_L2130_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.62 apply (zenon_L273_); trivial. % 30.48/30.62 apply (zenon_L39_); trivial. % 30.48/30.62 (* end of lemma zenon_L2137_ *) % 30.48/30.62 assert (zenon_L2138_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H92 zenon_H97 zenon_Haa zenon_H42 zenon_H20 zenon_H23b zenon_He7 zenon_H1f zenon_H1dc zenon_H222 zenon_H313 zenon_H225 zenon_Hc8 zenon_H208 zenon_H6b zenon_Hd6 zenon_H1d2 zenon_Hb5 zenon_H156 zenon_H35 zenon_H8d zenon_H85 zenon_Hcd zenon_H182 zenon_H101 zenon_H1db zenon_Hbd zenon_Hee zenon_Hb3 zenon_H3f zenon_Hde zenon_Hf9 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H2d zenon_H1fd zenon_H260 zenon_H19e zenon_H200 zenon_Hfc zenon_H1bd zenon_Hb8 zenon_Had zenon_Ha4 zenon_H9b zenon_Hb9 zenon_H18c zenon_H173 zenon_He1 zenon_Hc9 zenon_H6f. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.62 apply (zenon_L998_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.62 apply (zenon_L2127_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.62 apply (zenon_L192_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.62 exact (zenon_H85 zenon_H89). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.62 apply (zenon_L2130_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.62 apply (zenon_L273_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.62 apply (zenon_L142_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.62 apply (zenon_L782_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.62 apply (zenon_L2126_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.62 apply (zenon_L58_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.62 apply (zenon_L1515_); trivial. % 30.48/30.62 apply (zenon_L2136_); trivial. % 30.48/30.62 apply (zenon_L1135_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.62 exact (zenon_H313 zenon_H68). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.62 apply (zenon_L2115_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.62 apply (zenon_L43_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.62 apply (zenon_L2127_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.62 apply (zenon_L192_); trivial. % 30.48/30.62 apply (zenon_L2137_); trivial. % 30.48/30.62 (* end of lemma zenon_L2138_ *) % 30.48/30.62 assert (zenon_L2139_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H124 zenon_Hcd zenon_H182 zenon_H1d8 zenon_H14b zenon_H6f zenon_He1 zenon_H173 zenon_H18c zenon_Hb9 zenon_Ha4 zenon_Had zenon_Hb8 zenon_H1bd zenon_H200 zenon_H19e zenon_H1fd zenon_H2d zenon_Hf6 zenon_H10d zenon_H100 zenon_Hf9 zenon_Hde zenon_H3f zenon_Hb3 zenon_Hee zenon_Hbd zenon_H101 zenon_H85 zenon_H8d zenon_H35 zenon_H156 zenon_Hb5 zenon_H208 zenon_Hc8 zenon_H225 zenon_H313 zenon_H222 zenon_H1dc zenon_He7 zenon_H23b zenon_H42 zenon_Haa zenon_H92 zenon_Hfc zenon_H9b zenon_H20 zenon_Hc3 zenon_H1db zenon_H6b zenon_Hc9 zenon_Hd6 zenon_H260 zenon_H1d2 zenon_H97 zenon_H90. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.62 apply (zenon_L142_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.62 apply (zenon_L782_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.62 apply (zenon_L2125_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.62 apply (zenon_L58_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.62 apply (zenon_L282_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.62 apply (zenon_L2138_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.62 apply (zenon_L59_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_L31_); trivial. % 30.48/30.62 apply (zenon_L1135_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.62 apply (zenon_L906_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.62 apply (zenon_L2116_); trivial. % 30.48/30.62 apply (zenon_L30_); trivial. % 30.48/30.62 (* end of lemma zenon_L2139_ *) % 30.48/30.62 assert (zenon_L2140_ : ((op (e0) (e0)) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H64 zenon_H124 zenon_Hcd zenon_H182 zenon_H1d8 zenon_H14b zenon_H6f zenon_He1 zenon_H173 zenon_H18c zenon_Hb9 zenon_Ha4 zenon_Had zenon_Hb8 zenon_H1bd zenon_H200 zenon_H19e zenon_H1fd zenon_H2d zenon_Hf6 zenon_H10d zenon_H100 zenon_Hf9 zenon_Hde zenon_H3f zenon_Hb3 zenon_Hee zenon_Hbd zenon_H101 zenon_H85 zenon_H8d zenon_H35 zenon_H156 zenon_Hb5 zenon_H208 zenon_Hc8 zenon_H225 zenon_H313 zenon_H222 zenon_H1dc zenon_He7 zenon_H23b zenon_H42 zenon_Haa zenon_H92 zenon_Hfc zenon_H9b zenon_H20 zenon_Hc3 zenon_H1db zenon_H6b zenon_Hc9 zenon_Hd6 zenon_H260 zenon_H1d2 zenon_H97. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.62 apply (zenon_L912_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.62 exact (zenon_H313 zenon_H68). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.62 apply (zenon_L2115_); trivial. % 30.48/30.62 apply (zenon_L2139_); trivial. % 30.48/30.62 (* end of lemma zenon_L2140_ *) % 30.48/30.62 assert (zenon_L2141_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H225 zenon_H208 zenon_H88 zenon_Hc8 zenon_H6b zenon_Hd6 zenon_H1d2 zenon_Hbd zenon_H100 zenon_H10d zenon_Hf6 zenon_H156 zenon_H35 zenon_H10e zenon_H8d zenon_H85 zenon_Hcd zenon_H182 zenon_H101 zenon_H1db zenon_Hf9 zenon_Hde zenon_H3f zenon_Hb3 zenon_Hee zenon_H14b zenon_Hc3 zenon_H108 zenon_Hb5 zenon_H1fd zenon_H260 zenon_H19e zenon_H200 zenon_Hfc zenon_H1bd zenon_Hb8 zenon_Had zenon_Ha4 zenon_H9b zenon_Hb9 zenon_H18c zenon_H173 zenon_He1 zenon_Hc9 zenon_H2d zenon_H8b. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.48/30.62 apply (zenon_L998_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.62 apply (zenon_L142_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.62 apply (zenon_L95_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.62 apply (zenon_L49_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.62 apply (zenon_L347_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.62 apply (zenon_L809_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.62 apply (zenon_L2116_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.62 apply (zenon_L2080_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.62 apply (zenon_L2118_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 apply (zenon_L2119_); trivial. % 30.48/30.62 apply (zenon_L934_); trivial. % 30.48/30.62 apply (zenon_L1135_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.48/30.62 apply (zenon_L192_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.62 exact (zenon_H85 zenon_H89). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.62 apply (zenon_L142_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.62 apply (zenon_L782_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.62 apply (zenon_L49_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.62 apply (zenon_L347_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.62 apply (zenon_L2080_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.62 apply (zenon_L2117_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 apply (zenon_L2128_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.62 apply (zenon_L58_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.62 apply (zenon_L282_); trivial. % 30.48/30.62 apply (zenon_L2129_); trivial. % 30.48/30.62 apply (zenon_L1135_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.62 apply (zenon_L273_); trivial. % 30.48/30.62 apply (zenon_L25_); trivial. % 30.48/30.62 (* end of lemma zenon_L2141_ *) % 30.48/30.62 assert (zenon_L2142_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.48/30.62 do 0 intro. intros zenon_Hf6 zenon_H97 zenon_H9b zenon_H100 zenon_Hc3 zenon_H225 zenon_H208 zenon_H88 zenon_Hc8 zenon_H6b zenon_Hd6 zenon_H1d2 zenon_Hbd zenon_H10d zenon_H156 zenon_H35 zenon_H10e zenon_H8d zenon_H85 zenon_H101 zenon_H1db zenon_Hf9 zenon_Hde zenon_H3f zenon_Hb3 zenon_Hee zenon_H14b zenon_H108 zenon_Hb5 zenon_H1fd zenon_H260 zenon_H19e zenon_H200 zenon_Hfc zenon_H1bd zenon_Hb8 zenon_Had zenon_Ha4 zenon_Hb9 zenon_H18c zenon_H173 zenon_He1 zenon_Hc9 zenon_H2d zenon_H182 zenon_Hcd. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.62 apply (zenon_L142_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.62 apply (zenon_L782_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.62 apply (zenon_L2126_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.62 apply (zenon_L58_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.62 apply (zenon_L282_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.62 apply (zenon_L49_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.62 apply (zenon_L347_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.62 apply (zenon_L2141_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.62 apply (zenon_L1497_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.62 apply (zenon_L31_); trivial. % 30.48/30.62 apply (zenon_L690_); trivial. % 30.48/30.62 apply (zenon_L1135_); trivial. % 30.48/30.62 (* end of lemma zenon_L2142_ *) % 30.48/30.62 assert (zenon_L2143_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1a8 zenon_H20e zenon_H92 zenon_H97 zenon_Haa zenon_H42 zenon_H20 zenon_H23b zenon_He7 zenon_H1f zenon_H1dc zenon_H222 zenon_H313 zenon_H225 zenon_Hc8 zenon_H208 zenon_H6b zenon_Hd6 zenon_H1d2 zenon_Hb5 zenon_H156 zenon_H35 zenon_H8d zenon_H85 zenon_Hcd zenon_H101 zenon_H1db zenon_Hbd zenon_Hee zenon_Hb3 zenon_H3f zenon_Hde zenon_Hf9 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H2d zenon_H1fd zenon_H260 zenon_H19e zenon_H200 zenon_Hfc zenon_H1bd zenon_Hb8 zenon_Had zenon_Ha4 zenon_H9b zenon_Hb9 zenon_H18c zenon_H173 zenon_He1 zenon_Hc9 zenon_H6f. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.62 exact (zenon_H313 zenon_H68). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.62 apply (zenon_L906_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.62 apply (zenon_L2114_); trivial. % 30.48/30.62 apply (zenon_L2138_); trivial. % 30.48/30.62 (* end of lemma zenon_L2143_ *) % 30.48/30.62 assert (zenon_L2144_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H92 zenon_Hd9 zenon_H26 zenon_H313 zenon_H1db zenon_H6b zenon_Hc9 zenon_H260 zenon_H1d2 zenon_H8b zenon_H20. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.62 apply (zenon_L797_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.62 exact (zenon_H313 zenon_H68). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.62 apply (zenon_L2115_); trivial. % 30.48/30.62 apply (zenon_L27_); trivial. % 30.48/30.62 (* end of lemma zenon_L2144_ *) % 30.48/30.62 assert (zenon_L2145_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e2)) = (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.48/30.62 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H1d2 zenon_H260 zenon_Hc9 zenon_H6b zenon_H1db zenon_H313 zenon_H26 zenon_Hd9 zenon_H92 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H1e1. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.62 apply (zenon_L2144_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.62 apply (zenon_L1497_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.62 apply (zenon_L63_); trivial. % 30.48/30.62 apply (zenon_L690_); trivial. % 30.48/30.62 (* end of lemma zenon_L2145_ *) % 30.48/30.62 assert (zenon_L2146_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e2)) = (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H200 zenon_Hde zenon_H19e zenon_Hbd zenon_H20 zenon_H1d2 zenon_H260 zenon_Hc9 zenon_H6b zenon_H1db zenon_H313 zenon_H26 zenon_Hd9 zenon_H92 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.62 apply (zenon_L49_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.62 apply (zenon_L347_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_L2145_); trivial. % 30.48/30.62 (* end of lemma zenon_L2146_ *) % 30.48/30.62 assert (zenon_L2147_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1a8 zenon_H313 zenon_H20 zenon_H20e zenon_H173 zenon_H18c zenon_H35 zenon_H156 zenon_H1fd zenon_Hf6 zenon_H10d zenon_H10e zenon_H9b zenon_Hee zenon_H1db zenon_Hbd zenon_He1 zenon_H3f zenon_He9 zenon_Hde zenon_Hf9 zenon_Hc3 zenon_H100 zenon_H2d zenon_Hb5 zenon_Hb3 zenon_H1d2 zenon_H260 zenon_Hd6 zenon_Hc9 zenon_H6b zenon_H208 zenon_H19e zenon_H200 zenon_Hcd. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.62 exact (zenon_H313 zenon_H68). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.62 apply (zenon_L906_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.62 apply (zenon_L2114_); trivial. % 30.48/30.62 apply (zenon_L2127_); trivial. % 30.48/30.62 (* end of lemma zenon_L2147_ *) % 30.48/30.62 assert (zenon_L2148_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1a8 zenon_H313 zenon_H20 zenon_H6b zenon_H20e zenon_H1d2 zenon_H173 zenon_H18c zenon_Hb9 zenon_H9b zenon_H17b zenon_Ha4 zenon_He1 zenon_H6e zenon_Had zenon_Hb8 zenon_Hc9 zenon_H1bd zenon_Hfc zenon_H200 zenon_H19e zenon_H260 zenon_H1fd zenon_H2d zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_Hf9 zenon_Hde zenon_H3f zenon_Hb3 zenon_Hee zenon_Hbd zenon_H1db zenon_H101 zenon_Hcd. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.62 exact (zenon_H313 zenon_H68). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.62 apply (zenon_L906_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.62 apply (zenon_L2114_); trivial. % 30.48/30.62 apply (zenon_L2130_); trivial. % 30.48/30.62 (* end of lemma zenon_L2148_ *) % 30.48/30.62 assert (zenon_L2149_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_H1db zenon_H110 zenon_Hbc. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.62 apply (zenon_L87_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.62 apply (zenon_L235_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 apply (zenon_L1303_); trivial. % 30.48/30.62 (* end of lemma zenon_L2149_ *) % 30.48/30.62 assert (zenon_L2150_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H1a0 zenon_H1dc zenon_Hc9 zenon_H6b zenon_H1db. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.62 apply (zenon_L1834_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.62 apply (zenon_L552_); trivial. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 (* end of lemma zenon_L2150_ *) % 30.48/30.62 assert (zenon_L2151_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (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) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1a2 zenon_H1e1 zenon_Hf6 zenon_H10d zenon_H100 zenon_Hc3 zenon_H92 zenon_Hd9 zenon_H313 zenon_H20 zenon_Hbd zenon_Hbc zenon_H110 zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_Hd6 zenon_Hd5 zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hc9 zenon_H6b zenon_H1db. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.48/30.62 apply (zenon_L2145_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.48/30.62 apply (zenon_L2149_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.48/30.62 apply (zenon_L46_); trivial. % 30.48/30.62 apply (zenon_L2150_); trivial. % 30.48/30.62 (* end of lemma zenon_L2151_ *) % 30.48/30.62 assert (zenon_L2152_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H208 zenon_H1db zenon_H6b zenon_Hc9 zenon_H260 zenon_H1d2 zenon_Hd6 zenon_H1fd zenon_H2d zenon_H6f zenon_H110 zenon_Hbc zenon_H313 zenon_Hd9 zenon_H92 zenon_H1a2 zenon_H1e1 zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_H23b zenon_H20 zenon_H1f zenon_H1dc zenon_Hb3 zenon_H2c zenon_H3f zenon_Hbd zenon_H156 zenon_H182. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.62 apply (zenon_L2115_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.62 apply (zenon_L2151_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.62 apply (zenon_L2132_); trivial. % 30.48/30.62 apply (zenon_L934_); trivial. % 30.48/30.62 (* end of lemma zenon_L2152_ *) % 30.48/30.62 assert (zenon_L2153_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 30.48/30.62 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H1e1 zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_Hf9 zenon_Hde zenon_He9 zenon_H3f zenon_Hed zenon_H9b zenon_Hb3 zenon_Hee zenon_Hbd zenon_H1db zenon_H110 zenon_Hbc. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.62 apply (zenon_L87_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.62 apply (zenon_L2118_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.62 exact (zenon_H1db zenon_H1b9). % 30.48/30.62 apply (zenon_L1303_); trivial. % 30.48/30.62 (* end of lemma zenon_L2153_ *) % 30.48/30.62 assert (zenon_L2154_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.62 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_H19e zenon_H14b zenon_Hbc zenon_H110 zenon_H1db zenon_Hbd zenon_H3f zenon_He9 zenon_Hde zenon_H100 zenon_Hf6 zenon_H2d zenon_H1fd zenon_Hc3 zenon_Hfc zenon_H260 zenon_Hf9 zenon_Hcd zenon_H90 zenon_H97 zenon_Hee zenon_Hed zenon_H9b zenon_Hb3 zenon_H117 zenon_H10d. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.62 apply (zenon_L49_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.62 apply (zenon_L347_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.62 apply (zenon_L2153_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.62 apply (zenon_L59_); trivial. % 30.48/30.62 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.62 exact (zenon_H260 zenon_H142). % 30.48/30.62 apply (zenon_L2123_); trivial. % 30.48/30.62 (* end of lemma zenon_L2154_ *) % 30.48/30.63 assert (zenon_L2155_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H200 zenon_Hde zenon_H19e zenon_H208 zenon_H1db zenon_H6b zenon_Hc9 zenon_H260 zenon_H1d2 zenon_Hd6 zenon_H1fd zenon_H2d zenon_H6f zenon_H110 zenon_Hbc zenon_H313 zenon_Hd9 zenon_H92 zenon_H1a2 zenon_Hf6 zenon_H10d zenon_H10e zenon_H100 zenon_Hc3 zenon_H23b zenon_H20 zenon_H1f zenon_H1dc zenon_Hb3 zenon_H2c zenon_H3f zenon_Hbd zenon_H156 zenon_H182. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.63 apply (zenon_L49_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.63 apply (zenon_L347_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_L2152_); trivial. % 30.48/30.63 (* end of lemma zenon_L2155_ *) % 30.48/30.63 assert (zenon_L2156_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((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))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.48/30.63 do 0 intro. intros zenon_H174 zenon_H85 zenon_H182 zenon_H156 zenon_Hbd zenon_H3f zenon_H1dc zenon_H1f zenon_H20 zenon_H23b zenon_Hc3 zenon_H100 zenon_H10d zenon_Hf6 zenon_H1a2 zenon_H92 zenon_Hd9 zenon_H313 zenon_H110 zenon_H6f zenon_H1fd zenon_Hd6 zenon_H1d2 zenon_H260 zenon_Hc9 zenon_H6b zenon_H1db zenon_H208 zenon_H19e zenon_Hde zenon_H200 zenon_H2d zenon_H10e zenon_Hb3 zenon_Hbc zenon_Ha4. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.48/30.63 exact (zenon_H85 zenon_H89). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.48/30.63 apply (zenon_L2155_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.48/30.63 apply (zenon_L87_); trivial. % 30.48/30.63 apply (zenon_L1309_); trivial. % 30.48/30.63 (* end of lemma zenon_L2156_ *) % 30.48/30.63 assert (zenon_L2157_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H14b zenon_Ha4 zenon_Hbc zenon_Hb3 zenon_H2d zenon_H200 zenon_Hde zenon_H19e zenon_H208 zenon_H1db zenon_H6b zenon_Hc9 zenon_H1d2 zenon_Hd6 zenon_H1fd zenon_H6f zenon_H110 zenon_H313 zenon_Hd9 zenon_H92 zenon_H1a2 zenon_Hf6 zenon_H10d zenon_H100 zenon_H23b zenon_H20 zenon_H1f zenon_H1dc zenon_H3f zenon_Hbd zenon_H156 zenon_H182 zenon_H85 zenon_H174 zenon_Hc3 zenon_Hfc zenon_H260 zenon_H97 zenon_H9b zenon_H9d. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.63 apply (zenon_L2156_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.63 apply (zenon_L59_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_L31_); trivial. % 30.48/30.63 (* end of lemma zenon_L2157_ *) % 30.48/30.63 assert (zenon_L2158_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H124 zenon_Hcd zenon_H182 zenon_H101 zenon_Hf9 zenon_H1d8 zenon_Hee zenon_H2c zenon_H1bd zenon_H14b zenon_Ha4 zenon_Hbc zenon_Hb3 zenon_H2d zenon_H200 zenon_Hde zenon_H19e zenon_H208 zenon_H1fd zenon_H6f zenon_H110 zenon_H313 zenon_Hd9 zenon_H92 zenon_H1a2 zenon_Hf6 zenon_H10d zenon_H100 zenon_H23b zenon_H1dc zenon_H3f zenon_Hbd zenon_H156 zenon_H85 zenon_H174 zenon_Hfc zenon_H9b zenon_H18c zenon_H173 zenon_H20 zenon_Hc3 zenon_H1db zenon_H6b zenon_Hc9 zenon_Hd6 zenon_H260 zenon_H1d2 zenon_H97 zenon_H90. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.63 apply (zenon_L142_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.63 apply (zenon_L782_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.63 apply (zenon_L49_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.63 apply (zenon_L347_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.63 apply (zenon_L2152_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.63 apply (zenon_L59_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.48/30.63 apply (zenon_L2154_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.48/30.63 apply (zenon_L2124_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.48/30.63 exact (zenon_H1db zenon_H1b9). % 30.48/30.63 apply (zenon_L304_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.63 apply (zenon_L58_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.63 apply (zenon_L282_); trivial. % 30.48/30.63 apply (zenon_L2157_); trivial. % 30.48/30.63 apply (zenon_L1135_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.63 apply (zenon_L906_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.63 apply (zenon_L2116_); trivial. % 30.48/30.63 apply (zenon_L30_); trivial. % 30.48/30.63 (* end of lemma zenon_L2158_ *) % 30.48/30.63 assert (zenon_L2159_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H124 zenon_Hcd zenon_H182 zenon_H101 zenon_H117 zenon_Hee zenon_Hf9 zenon_H1bd zenon_H14b zenon_Ha4 zenon_Hbc zenon_Hb3 zenon_H2d zenon_H200 zenon_Hde zenon_H19e zenon_H208 zenon_H1fd zenon_H6f zenon_H110 zenon_H313 zenon_Hd9 zenon_H92 zenon_H1a2 zenon_Hf6 zenon_H10d zenon_H100 zenon_H23b zenon_H1dc zenon_H3f zenon_Hbd zenon_H156 zenon_H85 zenon_H174 zenon_Hfc zenon_H9b zenon_H18c zenon_H173 zenon_H20 zenon_Hc3 zenon_H1db zenon_H6b zenon_Hc9 zenon_Hd6 zenon_H260 zenon_H1d2 zenon_H97 zenon_H90. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.63 apply (zenon_L142_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.63 apply (zenon_L782_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.63 apply (zenon_L2154_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.63 apply (zenon_L58_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.63 apply (zenon_L282_); trivial. % 30.48/30.63 apply (zenon_L2157_); trivial. % 30.48/30.63 apply (zenon_L1135_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.48/30.63 apply (zenon_L906_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.48/30.63 apply (zenon_L2116_); trivial. % 30.48/30.63 apply (zenon_L30_); trivial. % 30.48/30.63 (* end of lemma zenon_L2159_ *) % 30.48/30.63 assert (zenon_L2160_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((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))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 30.48/30.63 do 0 intro. intros zenon_H1d8 zenon_H90 zenon_H97 zenon_H1d2 zenon_H260 zenon_Hd6 zenon_Hc9 zenon_H6b zenon_H1db zenon_Hc3 zenon_H20 zenon_H173 zenon_H18c zenon_H9b zenon_Hfc zenon_H174 zenon_H85 zenon_H156 zenon_Hbd zenon_H3f zenon_H1dc zenon_H23b zenon_H100 zenon_H10d zenon_Hf6 zenon_H1a2 zenon_H92 zenon_Hd9 zenon_H313 zenon_H110 zenon_H6f zenon_H1fd zenon_H208 zenon_H19e zenon_Hde zenon_H200 zenon_H2d zenon_H14b zenon_H1bd zenon_Hf9 zenon_Hee zenon_H101 zenon_H182 zenon_Hcd zenon_H124 zenon_Hb3 zenon_Hbc zenon_Ha4. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.48/30.63 exact (zenon_H85 zenon_H89). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.48/30.63 apply (zenon_L2158_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.48/30.63 apply (zenon_L2159_); trivial. % 30.48/30.63 apply (zenon_L1309_); trivial. % 30.48/30.63 (* end of lemma zenon_L2160_ *) % 30.48/30.63 assert (zenon_L2161_ : ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 30.48/30.63 do 0 intro. intros zenon_H9b zenon_Heb zenon_H9d zenon_H30b. % 30.48/30.63 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 30.48/30.63 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e1)) = (op (e3) (e2)))). % 30.48/30.63 intro zenon_D_pnotp. % 30.48/30.63 apply zenon_H30b. % 30.48/30.63 rewrite <- zenon_D_pnotp. % 30.48/30.63 exact zenon_Hef. % 30.48/30.63 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 30.48/30.63 cut (((op (e3) (e2)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H30c]. % 30.48/30.63 congruence. % 30.48/30.63 cut (((op (e3) (op (e3) (e2))) = (e2)) = ((op (e3) (e2)) = (op (e3) (e1)))). % 30.48/30.63 intro zenon_D_pnotp. % 30.48/30.63 apply zenon_H30c. % 30.48/30.63 rewrite <- zenon_D_pnotp. % 30.48/30.63 exact zenon_H9b. % 30.48/30.63 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 30.48/30.63 cut (((op (e3) (op (e3) (e2))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 30.48/30.63 congruence. % 30.48/30.63 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 30.48/30.63 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (op (e3) (e2))) = (op (e3) (e2)))). % 30.48/30.63 intro zenon_D_pnotp. % 30.48/30.63 apply zenon_Hf3. % 30.48/30.63 rewrite <- zenon_D_pnotp. % 30.48/30.63 exact zenon_Hef. % 30.48/30.63 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 30.48/30.63 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 30.48/30.63 congruence. % 30.48/30.63 apply (zenon_L54_); trivial. % 30.48/30.63 apply zenon_Hf0. apply refl_equal. % 30.48/30.63 apply zenon_Hf0. apply refl_equal. % 30.48/30.63 apply zenon_H9e. apply sym_equal. exact zenon_H9d. % 30.48/30.63 apply zenon_Hf0. apply refl_equal. % 30.48/30.63 apply zenon_Hf0. apply refl_equal. % 30.48/30.63 (* end of lemma zenon_L2161_ *) % 30.48/30.63 assert (zenon_L2162_ : (((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 (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H2b7 zenon_H8b zenon_Hb5 zenon_H1db zenon_H6b zenon_Hc9 zenon_H1dc zenon_H260 zenon_H1d2 zenon_H30b zenon_H9d zenon_H9b zenon_H110 zenon_Hbc. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.48/30.63 apply (zenon_L297_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.48/30.63 apply (zenon_L2150_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.48/30.63 apply (zenon_L2161_); trivial. % 30.48/30.63 apply (zenon_L1303_); trivial. % 30.48/30.63 (* end of lemma zenon_L2162_ *) % 30.48/30.63 assert (zenon_L2163_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> False). % 30.48/30.63 do 0 intro. intros zenon_Hbd zenon_Hbc zenon_H110 zenon_H9b zenon_H9d zenon_H30b zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hc9 zenon_H6b zenon_H1db zenon_Hb5 zenon_H2b7 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6 zenon_H1e1. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.48/30.63 apply (zenon_L2162_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.48/30.63 apply (zenon_L1497_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.48/30.63 apply (zenon_L63_); trivial. % 30.48/30.63 apply (zenon_L690_); trivial. % 30.48/30.63 (* end of lemma zenon_L2163_ *) % 30.48/30.63 assert (zenon_L2164_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 30.48/30.63 do 0 intro. intros zenon_H200 zenon_Hde zenon_H19e zenon_Hbd zenon_Hbc zenon_H110 zenon_H9b zenon_H9d zenon_H30b zenon_H1d2 zenon_H260 zenon_H1dc zenon_Hc9 zenon_H6b zenon_H1db zenon_Hb5 zenon_H2b7 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_Hf6. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.63 apply (zenon_L49_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.63 apply (zenon_L347_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_L2163_); trivial. % 30.48/30.63 (* end of lemma zenon_L2164_ *) % 30.48/30.63 assert (zenon_L2165_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.48/30.63 do 0 intro. intros zenon_H301 zenon_Ha4 zenon_H124 zenon_H14b zenon_H208 zenon_H6f zenon_H313 zenon_Hd9 zenon_H92 zenon_H1a2 zenon_H23b zenon_H156 zenon_H85 zenon_H174 zenon_Hfc zenon_H20 zenon_Hd6 zenon_H97 zenon_H1d8 zenon_H35 zenon_Hcd zenon_H182 zenon_H101 zenon_Hee zenon_Hb3 zenon_H3f zenon_Hf9 zenon_H2d zenon_H1fd zenon_H1bd zenon_Hbd zenon_Hbc zenon_H110 zenon_H9b zenon_H30b zenon_H1d2 zenon_H1dc zenon_H6b zenon_H1db zenon_Hb5 zenon_H2b7 zenon_H100 zenon_H10d zenon_Hf6 zenon_H18c zenon_H173 zenon_H200 zenon_Hc9 zenon_Hde zenon_Hc3 zenon_H19e zenon_H260 zenon_H218. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.48/30.63 apply (zenon_L912_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.48/30.63 exact (zenon_H313 zenon_H68). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.48/30.63 apply (zenon_L2115_); trivial. % 30.48/30.63 apply (zenon_L2160_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.48/30.63 apply (zenon_L42_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.63 apply (zenon_L142_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.63 apply (zenon_L782_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.63 apply (zenon_L49_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.63 apply (zenon_L347_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_L2153_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.63 apply (zenon_L782_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.63 apply (zenon_L282_); trivial. % 30.48/30.63 apply (zenon_L2164_); trivial. % 30.48/30.63 apply (zenon_L1135_); trivial. % 30.48/30.63 apply (zenon_L2104_); trivial. % 30.48/30.63 (* end of lemma zenon_L2165_ *) % 30.48/30.63 assert (zenon_L2166_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_H1e zenon_H3c zenon_H260 zenon_Hf6 zenon_Hb1. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.63 apply (zenon_L49_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.63 apply (zenon_L207_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_L690_); trivial. % 30.48/30.63 (* end of lemma zenon_L2166_ *) % 30.48/30.63 assert (zenon_L2167_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_Hc3 zenon_H19e zenon_H260 zenon_Hf6 zenon_Hb1. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.48/30.63 apply (zenon_L49_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.48/30.63 apply (zenon_L347_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_L690_); trivial. % 30.48/30.63 (* end of lemma zenon_L2167_ *) % 30.48/30.63 assert (zenon_L2168_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_Hb1 zenon_H1a0. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.63 exact (zenon_H56 zenon_H25). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.63 apply (zenon_L552_); trivial. % 30.48/30.63 apply (zenon_L751_); trivial. % 30.48/30.63 (* end of lemma zenon_L2168_ *) % 30.48/30.63 assert (zenon_L2169_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H1a2 zenon_H1a5 zenon_Hfd zenon_H4a zenon_H6f zenon_H15e zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_Hb1. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.48/30.63 apply (zenon_L748_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.48/30.63 apply (zenon_L235_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.48/30.63 exact (zenon_H56 zenon_H25). % 30.48/30.63 apply (zenon_L2168_); trivial. % 30.48/30.63 (* end of lemma zenon_L2169_ *) % 30.48/30.63 assert (zenon_L2170_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.48/30.63 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_Hb6 zenon_H1dc. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.63 exact (zenon_H56 zenon_H25). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.63 apply (zenon_L552_); trivial. % 30.48/30.63 apply (zenon_L200_); trivial. % 30.48/30.63 (* end of lemma zenon_L2170_ *) % 30.48/30.63 assert (zenon_L2171_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.48/30.63 do 0 intro. intros zenon_Hb8 zenon_H2fb zenon_H222 zenon_H3d zenon_H1dc zenon_H6b zenon_Hc9 zenon_H56 zenon_H260 zenon_H1d2 zenon_Hb1 zenon_H2d. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.48/30.63 exact (zenon_H2fb zenon_H8a). % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.48/30.63 apply (zenon_L775_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.48/30.63 apply (zenon_L2170_); trivial. % 30.48/30.63 apply (zenon_L107_); trivial. % 30.48/30.63 (* end of lemma zenon_L2171_ *) % 30.48/30.63 assert (zenon_L2172_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H2d zenon_Hb1 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H1dc zenon_H222 zenon_H2fb zenon_Hb8 zenon_Hfd zenon_H1ba zenon_H156 zenon_H4e zenon_H16c. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.48/30.63 apply (zenon_L332_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.48/30.63 apply (zenon_L2171_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.48/30.63 apply (zenon_L777_); trivial. % 30.48/30.63 apply (zenon_L779_); trivial. % 30.48/30.63 (* end of lemma zenon_L2172_ *) % 30.48/30.63 assert (zenon_L2173_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H16f zenon_H48 zenon_H14e zenon_He1 zenon_H6f zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H2d zenon_Hb1 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H1dc zenon_H222 zenon_H2fb zenon_Hb8 zenon_Hfd zenon_H1ba zenon_H156 zenon_H4e. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.63 apply (zenon_L770_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.63 apply (zenon_L158_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.63 apply (zenon_L2169_); trivial. % 30.48/30.63 apply (zenon_L2172_); trivial. % 30.48/30.63 (* end of lemma zenon_L2173_ *) % 30.48/30.63 assert (zenon_L2174_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.48/30.63 do 0 intro. intros zenon_H2fc zenon_H17d zenon_Hb1 zenon_H89 zenon_Hf4 zenon_Hc9 zenon_H1d8 zenon_H2fb. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H8b | zenon_intro zenon_H2fd ]. % 30.48/30.63 apply (zenon_L772_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H90 | zenon_intro zenon_H2fe ]. % 30.48/30.63 apply (zenon_L538_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_He2 | zenon_intro zenon_H8a ]. % 30.48/30.63 apply (zenon_L307_); trivial. % 30.48/30.63 exact (zenon_H2fb zenon_H8a). % 30.48/30.63 (* end of lemma zenon_L2174_ *) % 30.48/30.63 assert (zenon_L2175_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.48/30.63 do 0 intro. intros zenon_Hf9 zenon_He9 zenon_H3f zenon_Hed zenon_H4c zenon_Hee zenon_H2fc zenon_H17d zenon_Hb1 zenon_H89 zenon_Hc9 zenon_H1d8 zenon_H2fb. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.48/30.63 apply (zenon_L307_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.48/30.63 apply (zenon_L53_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.48/30.63 apply (zenon_L1207_); trivial. % 30.48/30.63 apply (zenon_L2174_); trivial. % 30.48/30.63 (* end of lemma zenon_L2175_ *) % 30.48/30.63 assert (zenon_L2176_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H101 zenon_H2fb zenon_H1d8 zenon_H89 zenon_Hb1 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hed zenon_Hfc zenon_H1bd zenon_Hc9 zenon_He1 zenon_H40. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.63 apply (zenon_L2175_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.63 apply (zenon_L58_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.63 apply (zenon_L282_); trivial. % 30.48/30.63 apply (zenon_L1354_); trivial. % 30.48/30.63 (* end of lemma zenon_L2176_ *) % 30.48/30.63 assert (zenon_L2177_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e2)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e zenon_H155. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.48/30.63 exact (zenon_H260 zenon_H142). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.48/30.63 exact (zenon_H56 zenon_H25). % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.48/30.63 apply (zenon_L552_); trivial. % 30.48/30.63 apply (zenon_L829_); trivial. % 30.48/30.63 (* end of lemma zenon_L2177_ *) % 30.48/30.63 assert (zenon_L2178_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H173 zenon_H18c zenon_H1a5 zenon_H26 zenon_H4a zenon_H40 zenon_He1 zenon_H1bd zenon_Hfc zenon_Hf9 zenon_H3f zenon_H4c zenon_Hee zenon_H2fc zenon_H17d zenon_Hb1 zenon_H89 zenon_H1d8 zenon_H2fb zenon_H101 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.63 apply (zenon_L142_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.63 apply (zenon_L748_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.63 apply (zenon_L2176_); trivial. % 30.48/30.63 apply (zenon_L2177_); trivial. % 30.48/30.63 (* end of lemma zenon_L2178_ *) % 30.48/30.63 assert (zenon_L2179_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.48/30.63 do 0 intro. intros zenon_Hb8 zenon_H4e zenon_H20e zenon_H6b zenon_Hc9 zenon_H56 zenon_H260 zenon_H1d2 zenon_H101 zenon_H2fb zenon_H1d8 zenon_H89 zenon_H17d zenon_H2fc zenon_H4c zenon_H3f zenon_Hf9 zenon_Hfc zenon_H1bd zenon_He1 zenon_H4a zenon_H26 zenon_H1a5 zenon_H18c zenon_H173 zenon_Hee zenon_H15e zenon_Hb1 zenon_H2d. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.48/30.63 exact (zenon_H2fb zenon_H8a). % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.48/30.63 apply (zenon_L2178_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.48/30.63 apply (zenon_L490_); trivial. % 30.48/30.63 apply (zenon_L107_); trivial. % 30.48/30.63 (* end of lemma zenon_L2179_ *) % 30.48/30.63 assert (zenon_L2180_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H101 zenon_H2fb zenon_H1d8 zenon_Hc9 zenon_H89 zenon_Hb1 zenon_H17d zenon_H2fc zenon_Hee zenon_H3f zenon_Hf9 zenon_Hed zenon_Hfc zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.63 apply (zenon_L2175_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.63 apply (zenon_L58_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.63 apply (zenon_L824_); trivial. % 30.48/30.63 apply (zenon_L1184_); trivial. % 30.48/30.63 (* end of lemma zenon_L2180_ *) % 30.48/30.63 assert (zenon_L2181_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H173 zenon_H18c zenon_H156 zenon_H1ba zenon_Hb8 zenon_H222 zenon_H1dc zenon_H2d zenon_Hc8 zenon_H1d5 zenon_H6f zenon_H2c zenon_H35 zenon_H14e zenon_H48 zenon_H16f zenon_H19a zenon_H4c zenon_H100 zenon_H19e zenon_Hfc zenon_Hf9 zenon_H3f zenon_Hee zenon_H2fc zenon_H17d zenon_Hb1 zenon_H89 zenon_H1d8 zenon_H2fb zenon_H101 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.63 apply (zenon_L142_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.63 apply (zenon_L770_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.63 apply (zenon_L1002_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.63 apply (zenon_L235_); trivial. % 30.48/30.63 apply (zenon_L2172_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.63 apply (zenon_L2180_); trivial. % 30.48/30.63 apply (zenon_L2177_); trivial. % 30.48/30.63 (* end of lemma zenon_L2181_ *) % 30.48/30.63 assert (zenon_L2182_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H1a2 zenon_H15e zenon_H1a5 zenon_H4a zenon_He1 zenon_H1bd zenon_H4e zenon_H20e zenon_H101 zenon_H2fb zenon_H1d8 zenon_H89 zenon_H17d zenon_H2fc zenon_Hee zenon_H3f zenon_Hf9 zenon_Hfc zenon_H19e zenon_H100 zenon_H4c zenon_H16f zenon_H48 zenon_H14e zenon_H35 zenon_H2c zenon_H6f zenon_H1d5 zenon_Hc8 zenon_H2d zenon_H1dc zenon_H222 zenon_Hb8 zenon_H1ba zenon_H156 zenon_H18c zenon_H173 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_Hb1. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.48/30.63 apply (zenon_L2179_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.48/30.63 apply (zenon_L2181_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.48/30.63 exact (zenon_H56 zenon_H25). % 30.48/30.63 apply (zenon_L2168_); trivial. % 30.48/30.63 (* end of lemma zenon_L2182_ *) % 30.48/30.63 assert (zenon_L2183_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.48/30.63 do 0 intro. intros zenon_Hb8 zenon_H2fb zenon_H9d zenon_He1 zenon_H1dc zenon_H1b9 zenon_Hb1 zenon_H2d. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.48/30.63 exact (zenon_H2fb zenon_H8a). % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.48/30.63 apply (zenon_L1354_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.48/30.63 apply (zenon_L200_); trivial. % 30.48/30.63 apply (zenon_L107_); trivial. % 30.48/30.63 (* end of lemma zenon_L2183_ *) % 30.48/30.63 assert (zenon_L2184_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.48/30.63 do 0 intro. intros zenon_H1d5 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H222 zenon_H2d zenon_Hb1 zenon_H1dc zenon_He1 zenon_H9d zenon_H2fb zenon_Hb8 zenon_H156 zenon_H4e zenon_H16c. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.48/30.63 apply (zenon_L273_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.48/30.63 apply (zenon_L2171_); trivial. % 30.48/30.63 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.48/30.63 apply (zenon_L2183_); trivial. % 30.48/30.63 apply (zenon_L779_); trivial. % 30.48/30.63 (* end of lemma zenon_L2184_ *) % 30.48/30.63 assert (zenon_L2185_ : ((op (e1) (e2)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.48/30.64 do 0 intro. intros zenon_Hed zenon_H173 zenon_H18c zenon_H1ba zenon_Hc8 zenon_H6f zenon_H2c zenon_H35 zenon_H14e zenon_H48 zenon_H16f zenon_H4c zenon_H100 zenon_H19e zenon_Hfc zenon_Hf9 zenon_H3f zenon_Hee zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H101 zenon_H20e zenon_H1bd zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H1d5 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H222 zenon_H2d zenon_Hb1 zenon_H1dc zenon_He1 zenon_H2fb zenon_Hb8 zenon_H156 zenon_H4e. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.64 apply (zenon_L2175_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.64 apply (zenon_L58_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.64 apply (zenon_L282_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.64 apply (zenon_L770_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.64 apply (zenon_L320_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.64 apply (zenon_L2182_); trivial. % 30.48/30.64 apply (zenon_L2184_); trivial. % 30.48/30.64 (* end of lemma zenon_L2185_ *) % 30.48/30.64 assert (zenon_L2186_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H8d zenon_H113 zenon_Hb1 zenon_Hcd zenon_H156 zenon_Hb8 zenon_H1dc zenon_H2d zenon_H222 zenon_H1d5 zenon_H1a2 zenon_H1a5 zenon_H4a zenon_H1bd zenon_H101 zenon_H1d8 zenon_H17d zenon_H2fc zenon_Hee zenon_H3f zenon_Hf9 zenon_Hfc zenon_H19e zenon_H100 zenon_H4c zenon_H16f zenon_H48 zenon_H14e zenon_H35 zenon_H2c zenon_Hc8 zenon_H18c zenon_H173 zenon_H1d2 zenon_H260 zenon_H56 zenon_H6b zenon_H20e zenon_H4e zenon_H200 zenon_Hde zenon_Hf6 zenon_H3c zenon_H296 zenon_H6f zenon_H68 zenon_He1 zenon_Hc9 zenon_H2fb. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.64 apply (zenon_L2166_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.64 apply (zenon_L2167_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.64 apply (zenon_L48_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.64 apply (zenon_L2173_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.64 apply (zenon_L2185_); trivial. % 30.48/30.64 apply (zenon_L2177_); trivial. % 30.48/30.64 apply (zenon_L798_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.64 apply (zenon_L18_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.64 apply (zenon_L273_); trivial. % 30.48/30.64 exact (zenon_H2fb zenon_H8a). % 30.48/30.64 (* end of lemma zenon_L2186_ *) % 30.48/30.64 assert (zenon_L2187_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H14b zenon_H2d zenon_H117 zenon_Hc9 zenon_H4c zenon_H18c zenon_H260 zenon_Hb1 zenon_H110. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.48/30.64 apply (zenon_L87_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.48/30.64 apply (zenon_L784_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.48/30.64 exact (zenon_H260 zenon_H142). % 30.48/30.64 apply (zenon_L65_); trivial. % 30.48/30.64 (* end of lemma zenon_L2187_ *) % 30.48/30.64 assert (zenon_L2188_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.48/30.64 do 0 intro. intros zenon_H173 zenon_H18c zenon_H156 zenon_H1ba zenon_Hb8 zenon_H222 zenon_H1dc zenon_H2d zenon_Hc8 zenon_H1d5 zenon_H1a2 zenon_H1a5 zenon_H4a zenon_H6f zenon_He1 zenon_H14e zenon_H48 zenon_H16f zenon_H19a zenon_H4c zenon_H100 zenon_H19e zenon_Hfc zenon_Hf9 zenon_H3f zenon_Hee zenon_H2fc zenon_H17d zenon_Hb1 zenon_H89 zenon_H1d8 zenon_H2fb zenon_H101 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.64 apply (zenon_L142_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.64 apply (zenon_L2173_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.64 apply (zenon_L2180_); trivial. % 30.48/30.64 apply (zenon_L2177_); trivial. % 30.48/30.64 (* end of lemma zenon_L2188_ *) % 30.48/30.64 assert (zenon_L2189_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H16f zenon_Hd1 zenon_H4e zenon_He1 zenon_Hb1 zenon_H6b zenon_Hc9 zenon_H56 zenon_H260 zenon_H1d2 zenon_H4a zenon_Hfd zenon_H1a5 zenon_H1a2 zenon_H182 zenon_H6f. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.64 apply (zenon_L729_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.64 apply (zenon_L158_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.64 apply (zenon_L2169_); trivial. % 30.48/30.64 apply (zenon_L758_); trivial. % 30.48/30.64 (* end of lemma zenon_L2189_ *) % 30.48/30.64 assert (zenon_L2190_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.48/30.64 do 0 intro. intros zenon_H42 zenon_H35 zenon_Hb1 zenon_H182 zenon_H4e zenon_H19e zenon_He1 zenon_H9d. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.64 apply (zenon_L730_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.64 apply (zenon_L320_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.64 apply (zenon_L731_); trivial. % 30.48/30.64 apply (zenon_L1354_); trivial. % 30.48/30.64 (* end of lemma zenon_L2190_ *) % 30.48/30.64 assert (zenon_L2191_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H101 zenon_H2fb zenon_H1d8 zenon_H89 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hed zenon_Hfc zenon_H1bd zenon_Hc9 zenon_H42 zenon_H35 zenon_Hb1 zenon_H182 zenon_H4e zenon_H19e zenon_He1. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.64 apply (zenon_L2175_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.64 apply (zenon_L58_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.64 apply (zenon_L282_); trivial. % 30.48/30.64 apply (zenon_L2190_); trivial. % 30.48/30.64 (* end of lemma zenon_L2191_ *) % 30.48/30.64 assert (zenon_L2192_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.48/30.64 do 0 intro. intros zenon_H173 zenon_H18c zenon_H6f zenon_H1a2 zenon_H1a5 zenon_H4a zenon_Hd1 zenon_H16f zenon_He1 zenon_H19e zenon_H182 zenon_Hb1 zenon_H35 zenon_H42 zenon_H1bd zenon_Hfc zenon_Hf9 zenon_H3f zenon_H4c zenon_Hee zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H101 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.64 apply (zenon_L142_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.64 apply (zenon_L2189_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.64 apply (zenon_L2191_); trivial. % 30.48/30.64 apply (zenon_L2177_); trivial. % 30.48/30.64 (* end of lemma zenon_L2192_ *) % 30.48/30.64 assert (zenon_L2193_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.48/30.64 do 0 intro. intros zenon_H1a8 zenon_H6c zenon_H18f zenon_H100 zenon_H48 zenon_H14e zenon_H1d5 zenon_Hc8 zenon_H2d zenon_H1dc zenon_H222 zenon_Hb8 zenon_H1ba zenon_H156 zenon_H173 zenon_H18c zenon_H6f zenon_H1a2 zenon_H1a5 zenon_H4a zenon_Hd1 zenon_H16f zenon_He1 zenon_H19e zenon_Hb1 zenon_H35 zenon_H42 zenon_H1bd zenon_Hfc zenon_Hf9 zenon_H3f zenon_H4c zenon_Hee zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H101 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.64 apply (zenon_L120_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.64 exact (zenon_H18f zenon_Hd2). % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.64 apply (zenon_L2188_); trivial. % 30.48/30.64 apply (zenon_L2192_); trivial. % 30.48/30.64 (* end of lemma zenon_L2193_ *) % 30.48/30.64 assert (zenon_L2194_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H8d zenon_H113 zenon_H1a8 zenon_H6c zenon_H18f zenon_H100 zenon_H1d5 zenon_Hc8 zenon_H2d zenon_H1dc zenon_H222 zenon_Hb8 zenon_H156 zenon_H173 zenon_H18c zenon_H6f zenon_H1a2 zenon_H1a5 zenon_H4a zenon_Hd1 zenon_H16f zenon_H19e zenon_H35 zenon_H42 zenon_H1bd zenon_Hfc zenon_Hf9 zenon_H3f zenon_H4c zenon_Hee zenon_H2fc zenon_H17d zenon_H1d8 zenon_H101 zenon_H1d2 zenon_H260 zenon_H56 zenon_H6b zenon_H20e zenon_H4e zenon_H200 zenon_Hde zenon_Hf6 zenon_H2c zenon_H296 zenon_Hb1 zenon_H48 zenon_H14e zenon_He1 zenon_Hc9 zenon_H2fb. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.64 apply (zenon_L4_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.64 apply (zenon_L2167_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.64 apply (zenon_L2193_); trivial. % 30.48/30.64 apply (zenon_L798_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.64 apply (zenon_L770_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.64 apply (zenon_L273_); trivial. % 30.48/30.64 exact (zenon_H2fb zenon_H8a). % 30.48/30.64 (* end of lemma zenon_L2194_ *) % 30.48/30.64 assert (zenon_L2195_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H16f zenon_H68 zenon_He1 zenon_Hb1 zenon_H6b zenon_Hc9 zenon_H56 zenon_H260 zenon_H1d2 zenon_H6f zenon_H4a zenon_Hfd zenon_H1a5 zenon_H1a2 zenon_H4e zenon_H16b zenon_H16a. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.64 apply (zenon_L18_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.64 apply (zenon_L158_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.64 apply (zenon_L2169_); trivial. % 30.48/30.64 apply (zenon_L859_); trivial. % 30.48/30.64 (* end of lemma zenon_L2195_ *) % 30.48/30.64 assert (zenon_L2196_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.48/30.64 do 0 intro. intros zenon_H173 zenon_Hcd zenon_H16b zenon_H1a2 zenon_H1a5 zenon_H6f zenon_Hb1 zenon_He1 zenon_H68 zenon_H16f zenon_H16a zenon_H33 zenon_H4a zenon_Hfc zenon_H18f zenon_H19e zenon_H1ba zenon_H102 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.64 apply (zenon_L48_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.64 apply (zenon_L2195_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.64 apply (zenon_L1716_); trivial. % 30.48/30.64 apply (zenon_L2177_); trivial. % 30.48/30.64 (* end of lemma zenon_L2196_ *) % 30.48/30.64 assert (zenon_L2197_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.48/30.64 do 0 intro. intros zenon_H173 zenon_H18c zenon_H6f zenon_H1a2 zenon_H1a5 zenon_H4a zenon_Hd1 zenon_H16f zenon_He1 zenon_H19e zenon_H182 zenon_Hb1 zenon_H35 zenon_H42 zenon_Hcd zenon_Hd5 zenon_Hfc zenon_Hf9 zenon_H3f zenon_H4c zenon_Hee zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H101 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.64 apply (zenon_L142_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.64 apply (zenon_L2189_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.64 apply (zenon_L2175_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.64 apply (zenon_L58_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.64 apply (zenon_L212_); trivial. % 30.48/30.64 apply (zenon_L2190_); trivial. % 30.48/30.64 apply (zenon_L2177_); trivial. % 30.48/30.64 (* end of lemma zenon_L2197_ *) % 30.48/30.64 assert (zenon_L2198_ : (((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 (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H256 zenon_Hb1 zenon_H14e zenon_H1e5 zenon_H156 zenon_H20e zenon_H6b zenon_Hc9 zenon_H56 zenon_H260 zenon_H1d2 zenon_H4e zenon_H16b zenon_H16a. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 30.48/30.64 apply (zenon_L84_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 30.48/30.64 apply (zenon_L934_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 30.48/30.64 apply (zenon_L2177_); trivial. % 30.48/30.64 apply (zenon_L859_); trivial. % 30.48/30.64 (* end of lemma zenon_L2198_ *) % 30.48/30.64 assert (zenon_L2199_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H2b1 zenon_H102 zenon_H1ba zenon_H18f zenon_H68 zenon_H101 zenon_H2fb zenon_H1d8 zenon_H89 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hfc zenon_Hd5 zenon_Hcd zenon_H42 zenon_H35 zenon_H19e zenon_He1 zenon_H16f zenon_Hd1 zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H6f zenon_H18c zenon_H173 zenon_H16a zenon_H16b zenon_H4e zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H156 zenon_H14e zenon_Hb1 zenon_H256 zenon_H1ab. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.48/30.64 apply (zenon_L2196_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.48/30.64 apply (zenon_L2197_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.48/30.64 apply (zenon_L2198_); trivial. % 30.48/30.64 exact (zenon_H1ab zenon_H112). % 30.48/30.64 (* end of lemma zenon_L2199_ *) % 30.48/30.64 assert (zenon_L2200_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H8d zenon_H4e zenon_H20e zenon_H6b zenon_H56 zenon_H260 zenon_H1d2 zenon_H101 zenon_H1d8 zenon_Hb1 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hfc zenon_H1bd zenon_H40 zenon_H16f zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H16b zenon_H16a zenon_Hcd zenon_H173 zenon_H6f zenon_H68 zenon_He1 zenon_Hc9 zenon_H2fb. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.64 apply (zenon_L48_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.64 apply (zenon_L2195_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.64 apply (zenon_L2176_); trivial. % 30.48/30.64 apply (zenon_L2177_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.64 apply (zenon_L18_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.64 apply (zenon_L273_); trivial. % 30.48/30.64 exact (zenon_H2fb zenon_H8a). % 30.48/30.64 (* end of lemma zenon_L2200_ *) % 30.48/30.64 assert (zenon_L2201_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H113 zenon_Hb1 zenon_H156 zenon_Hb8 zenon_H1dc zenon_H2d zenon_H222 zenon_H1d5 zenon_H14e zenon_H256 zenon_H2b1 zenon_H102 zenon_H18f zenon_H42 zenon_H35 zenon_H19e zenon_Hd1 zenon_H18c zenon_H1ab zenon_H1a8 zenon_H100 zenon_Hc8 zenon_H200 zenon_Hde zenon_Hf6 zenon_H296 zenon_H48 zenon_H208 zenon_H8d zenon_H101 zenon_H1d8 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hfc zenon_H1bd zenon_H16f zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H16b zenon_H16a zenon_Hcd zenon_H173 zenon_H1d2 zenon_H260 zenon_H56 zenon_H6b zenon_H20e zenon_H4e zenon_H3c zenon_H6f zenon_H68 zenon_He1 zenon_Hc9 zenon_H2fb. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.64 apply (zenon_L2166_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.64 apply (zenon_L2167_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.64 apply (zenon_L142_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.64 apply (zenon_L2173_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.48/30.64 apply (zenon_L2175_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.48/30.64 apply (zenon_L58_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.48/30.64 apply (zenon_L282_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.64 apply (zenon_L770_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.64 apply (zenon_L320_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.48/30.64 apply (zenon_L2194_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.48/30.64 apply (zenon_L2199_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.48/30.64 exact (zenon_H56 zenon_H25). % 30.48/30.64 apply (zenon_L2198_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.48/30.64 apply (zenon_L203_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.48/30.64 apply (zenon_L2171_); trivial. % 30.48/30.64 apply (zenon_L2200_); trivial. % 30.48/30.64 apply (zenon_L2184_); trivial. % 30.48/30.64 apply (zenon_L2177_); trivial. % 30.48/30.64 apply (zenon_L798_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.64 apply (zenon_L18_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.64 apply (zenon_L273_); trivial. % 30.48/30.64 exact (zenon_H2fb zenon_H8a). % 30.48/30.64 (* end of lemma zenon_L2201_ *) % 30.48/30.64 assert (zenon_L2202_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H16f zenon_Hb1 zenon_H48 zenon_H14e zenon_He1 zenon_Hfd zenon_H6f zenon_H19a zenon_H4e zenon_H16b zenon_H16a. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.48/30.64 apply (zenon_L770_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.48/30.64 apply (zenon_L158_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.48/30.64 apply (zenon_L235_); trivial. % 30.48/30.64 apply (zenon_L859_); trivial. % 30.48/30.64 (* end of lemma zenon_L2202_ *) % 30.48/30.64 assert (zenon_L2203_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.48/30.64 do 0 intro. intros zenon_H173 zenon_H18c zenon_H16a zenon_H16b zenon_H6f zenon_He1 zenon_H14e zenon_H48 zenon_H16f zenon_H19a zenon_H4c zenon_H100 zenon_H19e zenon_Hfc zenon_Hf9 zenon_H3f zenon_Hee zenon_H2fc zenon_H17d zenon_Hb1 zenon_H89 zenon_H1d8 zenon_H2fb zenon_H101 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.48/30.64 apply (zenon_L142_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.48/30.64 apply (zenon_L2202_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.48/30.64 apply (zenon_L2180_); trivial. % 30.48/30.64 apply (zenon_L2177_); trivial. % 30.48/30.64 (* end of lemma zenon_L2203_ *) % 30.48/30.64 assert (zenon_L2204_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H174 zenon_H3c zenon_H296 zenon_Hf6 zenon_Hde zenon_H200 zenon_H156 zenon_Hb8 zenon_H222 zenon_H1dc zenon_Hc8 zenon_H1d5 zenon_H113 zenon_H110 zenon_H2d zenon_H14b zenon_H8d zenon_H4e zenon_H20e zenon_H6b zenon_H56 zenon_H260 zenon_H1d2 zenon_H101 zenon_H1d8 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hfc zenon_H1bd zenon_H42 zenon_H35 zenon_H19e zenon_H16f zenon_Hd1 zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H6f zenon_H18c zenon_H173 zenon_H16a zenon_H100 zenon_H18f zenon_H6c zenon_H1a8 zenon_Hb1 zenon_H48 zenon_H14e zenon_He1 zenon_Hc9 zenon_H2fb. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.64 apply (zenon_L2166_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.64 apply (zenon_L763_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.64 apply (zenon_L2193_); trivial. % 30.48/30.64 apply (zenon_L798_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.48/30.64 apply (zenon_L2194_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.48/30.64 apply (zenon_L2187_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.64 apply (zenon_L120_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.64 exact (zenon_H18f zenon_Hd2). % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.64 apply (zenon_L2203_); trivial. % 30.48/30.64 apply (zenon_L2192_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.64 apply (zenon_L770_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.64 apply (zenon_L273_); trivial. % 30.48/30.64 exact (zenon_H2fb zenon_H8a). % 30.48/30.64 (* end of lemma zenon_L2204_ *) % 30.48/30.64 assert (zenon_L2205_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H296 zenon_H3c zenon_Hf6 zenon_Hde zenon_H200 zenon_H4e zenon_H20e zenon_H6b zenon_Hc9 zenon_H56 zenon_H260 zenon_H1d2 zenon_H101 zenon_H2fb zenon_H1d8 zenon_H89 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hfc zenon_H1bd zenon_H42 zenon_H35 zenon_H19e zenon_He1 zenon_H16f zenon_Hd1 zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H6f zenon_H18c zenon_H173 zenon_H156 zenon_Hb8 zenon_H222 zenon_H1dc zenon_H2d zenon_Hc8 zenon_H1d5 zenon_H14e zenon_H48 zenon_H100 zenon_H18f zenon_Had zenon_H90 zenon_H1a8 zenon_Hb1 zenon_H113. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.64 apply (zenon_L2166_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.64 apply (zenon_L2167_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.64 apply (zenon_L639_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.64 exact (zenon_H18f zenon_Hd2). % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.64 apply (zenon_L2188_); trivial. % 30.48/30.64 apply (zenon_L2192_); trivial. % 30.48/30.64 apply (zenon_L798_); trivial. % 30.48/30.64 (* end of lemma zenon_L2205_ *) % 30.48/30.64 assert (zenon_L2206_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H8d zenon_H113 zenon_H1a8 zenon_H90 zenon_Had zenon_H18f zenon_H20e zenon_H6b zenon_H56 zenon_H260 zenon_H1d2 zenon_H101 zenon_H1d8 zenon_H17d zenon_H2fc zenon_Hee zenon_H3f zenon_Hf9 zenon_Hfc zenon_H19e zenon_H100 zenon_H4c zenon_H16f zenon_H6f zenon_H1d5 zenon_Hc8 zenon_H2d zenon_H1dc zenon_H222 zenon_Hb8 zenon_H156 zenon_H18c zenon_H173 zenon_H4e zenon_H2c zenon_H35 zenon_H4a zenon_H200 zenon_Hde zenon_H3c zenon_Hf6 zenon_H296 zenon_Hb1 zenon_H48 zenon_H14e zenon_He1 zenon_Hc9 zenon_H2fb. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.48/30.64 apply (zenon_L2166_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.48/30.64 apply (zenon_L769_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.64 apply (zenon_L639_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.64 exact (zenon_H18f zenon_Hd2). % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.64 apply (zenon_L2181_); trivial. % 30.48/30.64 apply (zenon_L730_); trivial. % 30.48/30.64 apply (zenon_L798_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.64 apply (zenon_L770_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.64 apply (zenon_L273_); trivial. % 30.48/30.64 exact (zenon_H2fb zenon_H8a). % 30.48/30.64 (* end of lemma zenon_L2206_ *) % 30.48/30.64 assert (zenon_L2207_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.48/30.64 do 0 intro. intros zenon_H8d zenon_H4e zenon_H20e zenon_H6b zenon_H56 zenon_H260 zenon_H1d2 zenon_H101 zenon_H1d8 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hfc zenon_H1bd zenon_H42 zenon_H35 zenon_H19e zenon_H16f zenon_Hd1 zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H6f zenon_H18c zenon_H173 zenon_H16a zenon_H16b zenon_H100 zenon_H18f zenon_Had zenon_H90 zenon_H1a8 zenon_Hb1 zenon_H48 zenon_H14e zenon_He1 zenon_Hc9 zenon_H2fb. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.48/30.64 apply (zenon_L639_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.48/30.64 exact (zenon_H18f zenon_Hd2). % 30.48/30.64 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.48/30.64 apply (zenon_L2203_); trivial. % 30.48/30.64 apply (zenon_L2192_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.48/30.64 apply (zenon_L770_); trivial. % 30.48/30.64 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.48/30.64 apply (zenon_L273_); trivial. % 30.48/30.64 exact (zenon_H2fb zenon_H8a). % 30.48/30.64 (* end of lemma zenon_L2207_ *) % 30.48/30.64 assert (zenon_L2208_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H174 zenon_H296 zenon_Hf6 zenon_H3c zenon_Hde zenon_H200 zenon_H156 zenon_Hb8 zenon_H222 zenon_H1dc zenon_Hc8 zenon_H1d5 zenon_H113 zenon_H110 zenon_H2d zenon_H14b zenon_H8d zenon_H4e zenon_H20e zenon_H6b zenon_H56 zenon_H260 zenon_H1d2 zenon_H101 zenon_H1d8 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hfc zenon_H1bd zenon_H42 zenon_H35 zenon_H19e zenon_H16f zenon_Hd1 zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H6f zenon_H18c zenon_H173 zenon_H16a zenon_H100 zenon_H18f zenon_Had zenon_H90 zenon_H1a8 zenon_Hb1 zenon_H48 zenon_H14e zenon_He1 zenon_Hc9 zenon_H2fb. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.65 apply (zenon_L2205_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.65 apply (zenon_L2206_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.65 apply (zenon_L2187_); trivial. % 30.58/30.65 apply (zenon_L2207_); trivial. % 30.58/30.65 (* end of lemma zenon_L2208_ *) % 30.58/30.65 assert (zenon_L2209_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.58/30.65 do 0 intro. intros zenon_H173 zenon_H18c zenon_H156 zenon_H1ba zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H1a2 zenon_H1a5 zenon_H4a zenon_H6f zenon_H14e zenon_H48 zenon_H16f zenon_H40 zenon_He1 zenon_H1bd zenon_Hfc zenon_Hf9 zenon_H3f zenon_H4c zenon_Hee zenon_H2fc zenon_H17d zenon_Hb1 zenon_H89 zenon_H1d8 zenon_H2fb zenon_H101 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.58/30.65 apply (zenon_L142_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.58/30.65 apply (zenon_L770_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.58/30.65 apply (zenon_L158_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.58/30.65 apply (zenon_L2169_); trivial. % 30.58/30.65 apply (zenon_L780_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.58/30.65 apply (zenon_L2176_); trivial. % 30.58/30.65 apply (zenon_L2177_); trivial. % 30.58/30.65 (* end of lemma zenon_L2209_ *) % 30.58/30.65 assert (zenon_L2210_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.58/30.65 do 0 intro. intros zenon_H296 zenon_H3c zenon_Hf6 zenon_H19e zenon_Hde zenon_H200 zenon_H4e zenon_H20e zenon_H6b zenon_Hc9 zenon_H56 zenon_H260 zenon_H1d2 zenon_H101 zenon_H2fb zenon_H1d8 zenon_H89 zenon_Hb1 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hfc zenon_H1bd zenon_He1 zenon_H16f zenon_H48 zenon_H14e zenon_H6f zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H1d5 zenon_Hc8 zenon_H222 zenon_H156 zenon_H18c zenon_H173 zenon_H2d zenon_H40. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.58/30.65 apply (zenon_L2166_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.58/30.65 apply (zenon_L2167_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.58/30.65 apply (zenon_L2209_); trivial. % 30.58/30.65 apply (zenon_L766_); trivial. % 30.58/30.65 (* end of lemma zenon_L2210_ *) % 30.58/30.65 assert (zenon_L2211_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.58/30.65 do 0 intro. intros zenon_H173 zenon_H18c zenon_H6f zenon_H182 zenon_H1a2 zenon_H1a5 zenon_H4a zenon_Hd1 zenon_H16f zenon_H40 zenon_He1 zenon_H1bd zenon_Hfc zenon_Hf9 zenon_H3f zenon_H4c zenon_Hee zenon_H2fc zenon_H17d zenon_Hb1 zenon_H89 zenon_H1d8 zenon_H2fb zenon_H101 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hc9 zenon_H6b zenon_H20e zenon_H4e. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.58/30.65 apply (zenon_L142_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.58/30.65 apply (zenon_L2189_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.58/30.65 apply (zenon_L2176_); trivial. % 30.58/30.65 apply (zenon_L2177_); trivial. % 30.58/30.65 (* end of lemma zenon_L2211_ *) % 30.58/30.65 assert (zenon_L2212_ : ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H4e zenon_H20e zenon_H6b zenon_H56 zenon_H260 zenon_H1d2 zenon_H101 zenon_H1d8 zenon_H17d zenon_H2fc zenon_Hee zenon_H4c zenon_H3f zenon_Hf9 zenon_Hfc zenon_H1bd zenon_H40 zenon_H16f zenon_Hd1 zenon_H4a zenon_H1a5 zenon_H1a2 zenon_H6f zenon_H18c zenon_H173 zenon_H16a zenon_H16b zenon_H18f zenon_H8d zenon_Hcd zenon_H1a8 zenon_Hb1 zenon_H48 zenon_H14e zenon_He1 zenon_Hc9 zenon_H2fb. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.58/30.65 apply (zenon_L2200_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.58/30.65 exact (zenon_H18f zenon_Hd2). % 30.58/30.65 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.58/30.65 apply (zenon_L142_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.58/30.65 apply (zenon_L2202_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.58/30.65 apply (zenon_L2176_); trivial. % 30.58/30.65 apply (zenon_L2177_); trivial. % 30.58/30.65 apply (zenon_L2211_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.58/30.65 apply (zenon_L770_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.58/30.65 apply (zenon_L273_); trivial. % 30.58/30.65 exact (zenon_H2fb zenon_H8a). % 30.58/30.65 (* end of lemma zenon_L2212_ *) % 30.58/30.65 assert (zenon_L2213_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 30.58/30.65 do 0 intro. intros zenon_H256 zenon_H15a zenon_H89 zenon_Hd2 zenon_H4a zenon_H159 zenon_H20e zenon_H6b zenon_Hc9 zenon_H56 zenon_H260 zenon_H1d2 zenon_H156 zenon_H4e zenon_H1c5. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 30.58/30.65 apply (zenon_L744_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 30.58/30.65 apply (zenon_L872_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 30.58/30.65 apply (zenon_L2177_); trivial. % 30.58/30.65 apply (zenon_L779_); trivial. % 30.58/30.65 (* end of lemma zenon_L2213_ *) % 30.58/30.65 assert (zenon_L2214_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.65 do 0 intro. intros zenon_H200 zenon_Hde zenon_H231 zenon_He1 zenon_H1d2 zenon_H108 zenon_Hd0 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_Hc9 zenon_H20d zenon_Hd6 zenon_H1af zenon_H1d5 zenon_He9 zenon_H3c zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.65 apply (zenon_L49_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.65 apply (zenon_L2072_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.65 exact (zenon_H260 zenon_H142). % 30.58/30.65 apply (zenon_L690_); trivial. % 30.58/30.65 (* end of lemma zenon_L2214_ *) % 30.58/30.65 assert (zenon_L2215_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.58/30.65 do 0 intro. intros zenon_Hf9 zenon_H25 zenon_H60 zenon_H222 zenon_Hb6 zenon_He1 zenon_H2fc zenon_H17d zenon_Hb1 zenon_H89 zenon_Hc9 zenon_H1d8 zenon_H2fb. % 30.58/30.65 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.58/30.65 apply (zenon_L307_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.58/30.65 apply (zenon_L256_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.58/30.65 apply (zenon_L204_); trivial. % 30.58/30.65 apply (zenon_L2174_); trivial. % 30.58/30.65 (* end of lemma zenon_L2215_ *) % 30.58/30.65 assert (zenon_L2216_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H208 zenon_H6b zenon_H1ba zenon_H5e zenon_H1bd zenon_H2fb zenon_H1d8 zenon_Hc9 zenon_H89 zenon_Hb1 zenon_H17d zenon_H2fc zenon_He1 zenon_H222 zenon_H60 zenon_Hf9 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.65 apply (zenon_L2105_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.65 apply (zenon_L608_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.65 apply (zenon_L2215_); trivial. % 30.58/30.65 apply (zenon_L2084_); trivial. % 30.58/30.65 (* end of lemma zenon_L2216_ *) % 30.58/30.65 assert (zenon_L2217_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.65 do 0 intro. intros zenon_H200 zenon_Hde zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_H60 zenon_H222 zenon_He1 zenon_H2fc zenon_H17d zenon_H89 zenon_Hc9 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.65 apply (zenon_L49_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.65 apply (zenon_L2216_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.65 exact (zenon_H260 zenon_H142). % 30.58/30.65 apply (zenon_L690_); trivial. % 30.58/30.65 (* end of lemma zenon_L2217_ *) % 30.58/30.65 assert (zenon_L2218_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.58/30.65 do 0 intro. intros zenon_Hb8 zenon_H3d zenon_Hf6 zenon_H260 zenon_H208 zenon_H6b zenon_H5e zenon_H1bd zenon_H2fb zenon_H1d8 zenon_Hc9 zenon_H89 zenon_H17d zenon_H2fc zenon_He1 zenon_H222 zenon_H60 zenon_Hf9 zenon_H1d2 zenon_H108 zenon_Hd0 zenon_H1dc zenon_Hde zenon_H200 zenon_Hb1 zenon_H2d. % 30.58/30.65 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.58/30.65 exact (zenon_H2fb zenon_H8a). % 30.58/30.65 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.58/30.65 apply (zenon_L775_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.58/30.65 apply (zenon_L2217_); trivial. % 30.58/30.65 apply (zenon_L107_); trivial. % 30.58/30.65 (* end of lemma zenon_L2218_ *) % 30.58/30.65 assert (zenon_L2219_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H1d5 zenon_Hc8 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_H222 zenon_He1 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb8 zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H218 zenon_H267 zenon_H1af zenon_H16c zenon_H156. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.58/30.65 apply (zenon_L332_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.58/30.65 apply (zenon_L2218_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.58/30.65 apply (zenon_L628_); trivial. % 30.58/30.65 apply (zenon_L290_); trivial. % 30.58/30.65 (* end of lemma zenon_L2219_ *) % 30.58/30.65 assert (zenon_L2220_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H16f zenon_H6f zenon_H68 zenon_H9d zenon_Hfc zenon_H1e zenon_H42 zenon_H1d5 zenon_Hc8 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_H222 zenon_He1 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb8 zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H218 zenon_H267 zenon_H1af zenon_H156. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.58/30.65 apply (zenon_L18_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.58/30.65 apply (zenon_L320_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.65 apply (zenon_L4_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.65 apply (zenon_L203_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.65 apply (zenon_L2218_); trivial. % 30.58/30.65 apply (zenon_L1354_); trivial. % 30.58/30.65 apply (zenon_L2219_); trivial. % 30.58/30.65 (* end of lemma zenon_L2220_ *) % 30.58/30.65 assert (zenon_L2221_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H101 zenon_H3c zenon_Hd6 zenon_H13b zenon_H16f zenon_H6f zenon_H68 zenon_Hfc zenon_H1e zenon_H42 zenon_H1d5 zenon_Hc8 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_H222 zenon_He1 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb8 zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H218 zenon_H267 zenon_H1af zenon_H156. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.65 apply (zenon_L2214_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.65 exact (zenon_H13b zenon_Hfd). % 30.58/30.65 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.65 apply (zenon_L282_); trivial. % 30.58/30.65 apply (zenon_L2220_); trivial. % 30.58/30.65 (* end of lemma zenon_L2221_ *) % 30.58/30.65 assert (zenon_L2222_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H6c zenon_H260 zenon_H1d2 zenon_H20e zenon_H15e zenon_H1af zenon_H231. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.58/30.65 apply (zenon_L2053_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.58/30.65 apply (zenon_L2054_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.58/30.65 apply (zenon_L358_); trivial. % 30.58/30.65 exact (zenon_H231 zenon_Hf4). % 30.58/30.65 (* end of lemma zenon_L2222_ *) % 30.58/30.65 assert (zenon_L2223_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H101 zenon_H3c zenon_H13b zenon_H16f zenon_H6f zenon_H68 zenon_Hd6 zenon_H1ba zenon_H20e zenon_H1d5 zenon_Hc8 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_H222 zenon_He1 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb8 zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H218 zenon_H267 zenon_H1af zenon_H156. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.65 apply (zenon_L2214_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.65 exact (zenon_H13b zenon_Hfd). % 30.58/30.65 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.65 apply (zenon_L282_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.58/30.65 apply (zenon_L18_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.58/30.65 apply (zenon_L320_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.65 apply (zenon_L2222_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.65 apply (zenon_L608_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.65 apply (zenon_L256_); trivial. % 30.58/30.65 apply (zenon_L2060_); trivial. % 30.58/30.65 apply (zenon_L2219_); trivial. % 30.58/30.65 (* end of lemma zenon_L2223_ *) % 30.58/30.65 assert (zenon_L2224_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H8d zenon_H113 zenon_Hb1 zenon_H101 zenon_H3c zenon_H13b zenon_H16f zenon_Hd6 zenon_H20e zenon_H1d5 zenon_Hc8 zenon_H2d zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_H222 zenon_H2fc zenon_H17d zenon_H1d8 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb8 zenon_H231 zenon_H20d zenon_H60 zenon_H218 zenon_H267 zenon_H1af zenon_H156 zenon_H19e zenon_Hfc zenon_H42 zenon_H296 zenon_H6f zenon_H68 zenon_He1 zenon_Hc9 zenon_H2fb. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.58/30.65 apply (zenon_L2221_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.58/30.65 apply (zenon_L2167_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.58/30.65 apply (zenon_L2223_); trivial. % 30.58/30.65 apply (zenon_L798_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.58/30.65 apply (zenon_L18_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.58/30.65 apply (zenon_L273_); trivial. % 30.58/30.65 exact (zenon_H2fb zenon_H8a). % 30.58/30.65 (* end of lemma zenon_L2224_ *) % 30.58/30.65 assert (zenon_L2225_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.65 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_Hd5 zenon_H5e zenon_H1bd zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.65 apply (zenon_L49_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.65 apply (zenon_L608_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.65 exact (zenon_H260 zenon_H142). % 30.58/30.65 apply (zenon_L690_); trivial. % 30.58/30.65 (* end of lemma zenon_L2225_ *) % 30.58/30.65 assert (zenon_L2226_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H208 zenon_H6b zenon_Hf6 zenon_H1bd zenon_H5e zenon_Hde zenon_H200 zenon_H3f zenon_H2c zenon_H222 zenon_H97 zenon_H90 zenon_Hb1 zenon_H113 zenon_Haa zenon_H1d5 zenon_H1af zenon_Hd6 zenon_H20d zenon_Hc9 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_He1 zenon_H231. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.65 apply (zenon_L2055_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.65 apply (zenon_L2225_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.65 apply (zenon_L1866_); trivial. % 30.58/30.65 apply (zenon_L2060_); trivial. % 30.58/30.65 (* end of lemma zenon_L2226_ *) % 30.58/30.65 assert (zenon_L2227_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H208 zenon_H20d zenon_Hc9 zenon_H6b zenon_H1ba zenon_H5e zenon_H1bd zenon_H9d zenon_H222 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_Hd6 zenon_H3d zenon_H1af zenon_H231. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.65 apply (zenon_L2055_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.65 apply (zenon_L608_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.65 apply (zenon_L256_); trivial. % 30.58/30.65 apply (zenon_L2058_); trivial. % 30.58/30.65 (* end of lemma zenon_L2227_ *) % 30.58/30.65 assert (zenon_L2228_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.65 do 0 intro. intros zenon_H200 zenon_H27 zenon_H117 zenon_Hde zenon_H135 zenon_H231 zenon_H1af zenon_H3d zenon_Hd6 zenon_H1d2 zenon_H108 zenon_Hd0 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H222 zenon_H9d zenon_H1bd zenon_H5e zenon_H6b zenon_Hc9 zenon_H20d zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.65 apply (zenon_L444_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.65 apply (zenon_L2227_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.65 exact (zenon_H260 zenon_H142). % 30.58/30.65 apply (zenon_L690_); trivial. % 30.58/30.65 (* end of lemma zenon_L2228_ *) % 30.58/30.65 assert (zenon_L2229_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H25 zenon_H108 zenon_Hd6 zenon_H3d zenon_H1af zenon_H16b zenon_H218. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.58/30.65 apply (zenon_L690_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.58/30.65 apply (zenon_L1274_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.58/30.65 apply (zenon_L144_); trivial. % 30.58/30.65 apply (zenon_L245_); trivial. % 30.58/30.65 (* end of lemma zenon_L2229_ *) % 30.58/30.65 assert (zenon_L2230_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.65 do 0 intro. intros zenon_H200 zenon_Hde zenon_H231 zenon_H1af zenon_H3d zenon_Hd6 zenon_H1d2 zenon_H108 zenon_Hd0 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H1e6 zenon_H16b zenon_H1bd zenon_H5e zenon_H6b zenon_Hc9 zenon_H20d zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.65 apply (zenon_L49_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.65 apply (zenon_L2055_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.65 apply (zenon_L608_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.65 apply (zenon_L2229_); trivial. % 30.58/30.65 apply (zenon_L2058_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.65 exact (zenon_H260 zenon_H142). % 30.58/30.65 apply (zenon_L690_); trivial. % 30.58/30.65 (* end of lemma zenon_L2230_ *) % 30.58/30.65 assert (zenon_L2231_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H174 zenon_Hb8 zenon_H2fb zenon_H1d8 zenon_H17d zenon_H2fc zenon_Hf9 zenon_H1dc zenon_H2d zenon_H27 zenon_H135 zenon_H101 zenon_H3c zenon_H13b zenon_H42 zenon_H1d5 zenon_Haa zenon_H113 zenon_H90 zenon_H97 zenon_H222 zenon_H3f zenon_Hb1 zenon_Hf6 zenon_H260 zenon_H208 zenon_H20d zenon_Hc9 zenon_H6b zenon_H5e zenon_H1bd zenon_H1e6 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hd6 zenon_H1af zenon_H231 zenon_Hde zenon_H200 zenon_He1. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.65 apply (zenon_L2214_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.65 exact (zenon_H13b zenon_Hfd). % 30.58/30.65 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.65 apply (zenon_L282_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.65 apply (zenon_L2226_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.65 apply (zenon_L320_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.65 apply (zenon_L2218_); trivial. % 30.58/30.65 apply (zenon_L1354_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.65 apply (zenon_L2226_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.65 apply (zenon_L2214_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.65 exact (zenon_H13b zenon_Hfd). % 30.58/30.65 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.65 apply (zenon_L282_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.65 apply (zenon_L2226_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.65 apply (zenon_L320_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.65 apply (zenon_L2228_); trivial. % 30.58/30.65 apply (zenon_L1354_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.65 apply (zenon_L2214_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.65 exact (zenon_H13b zenon_Hfd). % 30.58/30.65 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.65 apply (zenon_L282_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.65 apply (zenon_L2226_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.65 apply (zenon_L320_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.65 apply (zenon_L2230_); trivial. % 30.58/30.65 apply (zenon_L1354_); trivial. % 30.58/30.65 (* end of lemma zenon_L2231_ *) % 30.58/30.65 assert (zenon_L2232_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.58/30.65 do 0 intro. intros zenon_H8d zenon_H156 zenon_H1af zenon_H267 zenon_H218 zenon_H60 zenon_H20d zenon_H231 zenon_Hb8 zenon_Hf6 zenon_H260 zenon_H208 zenon_H6b zenon_H5e zenon_H1bd zenon_H1d8 zenon_H17d zenon_H2fc zenon_H222 zenon_Hf9 zenon_H1d2 zenon_H108 zenon_Hd0 zenon_H1dc zenon_Hde zenon_H200 zenon_Hb1 zenon_H2d zenon_Hc8 zenon_H1d5 zenon_H42 zenon_H1e zenon_Hfc zenon_Hd6 zenon_H135 zenon_H117 zenon_H27 zenon_H16f zenon_H13b zenon_H3c zenon_H101 zenon_H6f zenon_H68 zenon_He1 zenon_Hc9 zenon_H2fb. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.65 apply (zenon_L2214_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.65 exact (zenon_H13b zenon_Hfd). % 30.58/30.65 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.65 apply (zenon_L282_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.58/30.65 apply (zenon_L18_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.58/30.65 apply (zenon_L320_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.65 apply (zenon_L4_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.65 apply (zenon_L203_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.65 apply (zenon_L2228_); trivial. % 30.58/30.65 apply (zenon_L1354_); trivial. % 30.58/30.65 apply (zenon_L2219_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.58/30.65 apply (zenon_L18_); trivial. % 30.58/30.65 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.58/30.65 apply (zenon_L273_); trivial. % 30.58/30.65 exact (zenon_H2fb zenon_H8a). % 30.58/30.65 (* end of lemma zenon_L2232_ *) % 30.58/30.65 assert (zenon_L2233_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H174 zenon_H27 zenon_H135 zenon_H8d zenon_H156 zenon_H1af zenon_H267 zenon_H218 zenon_H60 zenon_H20d zenon_H231 zenon_Hb8 zenon_Hf6 zenon_H260 zenon_H208 zenon_H6b zenon_H5e zenon_H1bd zenon_H1d8 zenon_H17d zenon_H2fc zenon_H222 zenon_Hf9 zenon_H1d2 zenon_H108 zenon_Hd0 zenon_H1dc zenon_Hde zenon_H200 zenon_Hb1 zenon_H2d zenon_Hc8 zenon_H1d5 zenon_H42 zenon_H1e zenon_Hfc zenon_Hd6 zenon_H1e6 zenon_H20e zenon_H16f zenon_H13b zenon_H3c zenon_H101 zenon_H6f zenon_H68 zenon_He1 zenon_Hc9 zenon_H2fb. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.66 apply (zenon_L2221_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.66 apply (zenon_L4_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.66 apply (zenon_L2232_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.66 apply (zenon_L2214_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.66 exact (zenon_H13b zenon_Hfd). % 30.58/30.66 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.66 apply (zenon_L282_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.58/30.66 apply (zenon_L18_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.58/30.66 apply (zenon_L320_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.66 apply (zenon_L4_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.66 apply (zenon_L203_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.66 apply (zenon_L2230_); trivial. % 30.58/30.66 apply (zenon_L1338_); trivial. % 30.58/30.66 apply (zenon_L2219_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.58/30.66 apply (zenon_L18_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.58/30.66 apply (zenon_L273_); trivial. % 30.58/30.66 exact (zenon_H2fb zenon_H8a). % 30.58/30.66 (* end of lemma zenon_L2233_ *) % 30.58/30.66 assert (zenon_L2234_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H92 zenon_H6f zenon_H16f zenon_H20e zenon_Hfc zenon_H1e zenon_Hc8 zenon_H8d zenon_H174 zenon_Hb8 zenon_H2fb zenon_H1d8 zenon_H17d zenon_H2fc zenon_Hf9 zenon_H1dc zenon_H2d zenon_H27 zenon_H135 zenon_H101 zenon_H3c zenon_H13b zenon_H42 zenon_H1d5 zenon_Haa zenon_H113 zenon_H97 zenon_H222 zenon_H3f zenon_Hb1 zenon_Hf6 zenon_H260 zenon_H208 zenon_H20d zenon_Hc9 zenon_H6b zenon_H5e zenon_H1bd zenon_H1e6 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hd6 zenon_H1af zenon_H231 zenon_Hde zenon_H200 zenon_He1. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.66 apply (zenon_L734_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.66 apply (zenon_L4_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.66 apply (zenon_L2214_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.66 exact (zenon_H13b zenon_Hfd). % 30.58/30.66 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.66 apply (zenon_L282_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.66 apply (zenon_L4_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.66 apply (zenon_L320_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.66 apply (zenon_L2228_); trivial. % 30.58/30.66 apply (zenon_L1354_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.66 apply (zenon_L2214_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.66 exact (zenon_H13b zenon_Hfd). % 30.58/30.66 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.66 apply (zenon_L282_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.66 apply (zenon_L4_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.66 apply (zenon_L320_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.66 apply (zenon_L2230_); trivial. % 30.58/30.66 apply (zenon_L1354_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.58/30.66 apply (zenon_L2233_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.58/30.66 apply (zenon_L2055_); trivial. % 30.58/30.66 apply (zenon_L2231_); trivial. % 30.58/30.66 (* end of lemma zenon_L2234_ *) % 30.58/30.66 assert (zenon_L2235_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H8d zenon_H113 zenon_Hb1 zenon_H208 zenon_H6b zenon_H5e zenon_H1bd zenon_H1d8 zenon_H17d zenon_H2fc zenon_H222 zenon_H60 zenon_Hf9 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_Hb6 zenon_H1dc zenon_H200 zenon_Hde zenon_H19e zenon_Hf6 zenon_H2c zenon_H2d zenon_H296 zenon_H6f zenon_H68 zenon_He1 zenon_Hc9 zenon_H2fb. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.58/30.66 apply (zenon_L4_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.58/30.66 apply (zenon_L2167_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.58/30.66 apply (zenon_L2216_); trivial. % 30.58/30.66 apply (zenon_L798_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.58/30.66 apply (zenon_L18_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.58/30.66 apply (zenon_L273_); trivial. % 30.58/30.66 exact (zenon_H2fb zenon_H8a). % 30.58/30.66 (* end of lemma zenon_L2235_ *) % 30.58/30.66 assert (zenon_L2236_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H108 zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H6f zenon_H25 zenon_H1af zenon_H16b zenon_H218. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.58/30.66 apply (zenon_L273_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.58/30.66 apply (zenon_L2229_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.58/30.66 apply (zenon_L1138_); trivial. % 30.58/30.66 apply (zenon_L245_); trivial. % 30.58/30.66 (* end of lemma zenon_L2236_ *) % 30.58/30.66 assert (zenon_L2237_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H208 zenon_H6b zenon_H1ba zenon_H5e zenon_H1bd zenon_H218 zenon_H16b zenon_H1af zenon_H6f zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_Hd6 zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.66 apply (zenon_L2105_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.66 apply (zenon_L608_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.66 apply (zenon_L2236_); trivial. % 30.58/30.66 apply (zenon_L2084_); trivial. % 30.58/30.66 (* end of lemma zenon_L2237_ *) % 30.58/30.66 assert (zenon_L2238_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.66 do 0 intro. intros zenon_H200 zenon_Hde zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H16b zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.66 apply (zenon_L49_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.66 apply (zenon_L2237_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.66 exact (zenon_H260 zenon_H142). % 30.58/30.66 apply (zenon_L690_); trivial. % 30.58/30.66 (* end of lemma zenon_L2238_ *) % 30.58/30.66 assert (zenon_L2239_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.66 do 0 intro. intros zenon_H174 zenon_H2fb zenon_H68 zenon_H296 zenon_H19e zenon_Hf9 zenon_H60 zenon_H222 zenon_H2fc zenon_H17d zenon_H1d8 zenon_H113 zenon_H8d zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.66 apply (zenon_L2217_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.66 apply (zenon_L2235_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.66 apply (zenon_L87_); trivial. % 30.58/30.66 apply (zenon_L2238_); trivial. % 30.58/30.66 (* end of lemma zenon_L2239_ *) % 30.58/30.66 assert (zenon_L2240_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H208 zenon_H6b zenon_H1ba zenon_H5e zenon_H1bd zenon_H89 zenon_H90 zenon_He1 zenon_H222 zenon_H60 zenon_Hcd zenon_Hf9 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.66 apply (zenon_L2105_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.66 apply (zenon_L608_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.66 apply (zenon_L2012_); trivial. % 30.58/30.66 apply (zenon_L2084_); trivial. % 30.58/30.66 (* end of lemma zenon_L2240_ *) % 30.58/30.66 assert (zenon_L2241_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.66 do 0 intro. intros zenon_H200 zenon_Hc9 zenon_Hde zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_Hcd zenon_H60 zenon_H222 zenon_He1 zenon_H90 zenon_H89 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.66 apply (zenon_L49_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.66 apply (zenon_L2240_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.66 exact (zenon_H260 zenon_H142). % 30.58/30.66 apply (zenon_L690_); trivial. % 30.58/30.66 (* end of lemma zenon_L2241_ *) % 30.58/30.66 assert (zenon_L2242_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H208 zenon_H6b zenon_H1ba zenon_H5e zenon_H1bd zenon_H3f zenon_H2c zenon_H222 zenon_H60 zenon_H97 zenon_H90 zenon_Hb1 zenon_H113 zenon_Haa zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.66 apply (zenon_L2105_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.66 apply (zenon_L608_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.66 apply (zenon_L1866_); trivial. % 30.58/30.66 apply (zenon_L2084_); trivial. % 30.58/30.66 (* end of lemma zenon_L2242_ *) % 30.58/30.66 assert (zenon_L2243_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H296 zenon_H2d zenon_Hf6 zenon_H19e zenon_Hde zenon_Hc9 zenon_H200 zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_Haa zenon_H90 zenon_H97 zenon_H60 zenon_H222 zenon_H2c zenon_H3f zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_Hb1 zenon_H113. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.58/30.66 apply (zenon_L4_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.58/30.66 apply (zenon_L2167_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.58/30.66 apply (zenon_L2242_); trivial. % 30.58/30.66 apply (zenon_L798_); trivial. % 30.58/30.66 (* end of lemma zenon_L2243_ *) % 30.58/30.66 assert (zenon_L2244_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.66 do 0 intro. intros zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_H90 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.66 apply (zenon_L2241_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.66 apply (zenon_L2243_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.66 apply (zenon_L87_); trivial. % 30.58/30.66 apply (zenon_L2238_); trivial. % 30.58/30.66 (* end of lemma zenon_L2244_ *) % 30.58/30.66 assert (zenon_L2245_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.66 do 0 intro. intros zenon_H92 zenon_Hd9 zenon_H26 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.58/30.66 apply (zenon_L797_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.58/30.66 apply (zenon_L2239_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.58/30.66 apply (zenon_L2105_); trivial. % 30.58/30.66 apply (zenon_L2244_); trivial. % 30.58/30.66 (* end of lemma zenon_L2245_ *) % 30.58/30.66 assert (zenon_L2246_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.66 do 0 intro. intros zenon_H1fd zenon_H20e zenon_H6c zenon_H231 zenon_H20d zenon_H156 zenon_H267 zenon_H92 zenon_Hd9 zenon_H26 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.66 apply (zenon_L87_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.66 apply (zenon_L2222_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.66 apply (zenon_L628_); trivial. % 30.58/30.66 apply (zenon_L2245_); trivial. % 30.58/30.66 (* end of lemma zenon_L2246_ *) % 30.58/30.66 assert (zenon_L2247_ : (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (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) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H231 zenon_H267 zenon_H218 zenon_He1 zenon_H60 zenon_H156 zenon_H19a zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_Hc9 zenon_H20d zenon_H3f zenon_He9 zenon_H1d8 zenon_Hf9 zenon_H1d2 zenon_H260 zenon_H6c zenon_H6b zenon_Hd0 zenon_H1dc. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.66 apply (zenon_L87_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.66 apply (zenon_L235_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.66 apply (zenon_L1803_); trivial. % 30.58/30.66 apply (zenon_L2105_); trivial. % 30.58/30.66 (* end of lemma zenon_L2247_ *) % 30.58/30.66 assert (zenon_L2248_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (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) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H208 zenon_H6b zenon_H1ba zenon_H5e zenon_H1bd zenon_H20e zenon_H231 zenon_H267 zenon_H218 zenon_He1 zenon_H60 zenon_H156 zenon_H19a zenon_H6f zenon_H10e zenon_H2d zenon_H1fd zenon_Hc9 zenon_H20d zenon_H3f zenon_He9 zenon_H1d8 zenon_Hf9 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H1dc. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.66 apply (zenon_L2247_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.66 apply (zenon_L608_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.66 apply (zenon_L225_); trivial. % 30.58/30.66 apply (zenon_L2085_); trivial. % 30.58/30.66 (* end of lemma zenon_L2248_ *) % 30.58/30.66 assert (zenon_L2249_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H1a2 zenon_Hb1 zenon_Hf6 zenon_H1e6 zenon_Hd6 zenon_H1d5 zenon_Hde zenon_H200 zenon_H296 zenon_H19e zenon_Haa zenon_H97 zenon_H222 zenon_H113 zenon_Hcd zenon_H174 zenon_H2fb zenon_H2fc zenon_H17d zenon_H8d zenon_Hd9 zenon_H92 zenon_H108 zenon_Hf9 zenon_H1d8 zenon_He9 zenon_H3f zenon_He1 zenon_H1bd zenon_H5e zenon_H1ba zenon_H208 zenon_H1fd zenon_H2d zenon_H10e zenon_H1af zenon_H20e zenon_H1d2 zenon_H260 zenon_H6c zenon_H6b zenon_Hd0 zenon_H1dc zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H6f. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.58/30.66 apply (zenon_L2246_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.58/30.66 apply (zenon_L2248_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.58/30.66 apply (zenon_L17_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.66 apply (zenon_L87_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.58/30.66 apply (zenon_L2091_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.58/30.66 apply (zenon_L2054_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.58/30.66 apply (zenon_L358_); trivial. % 30.58/30.66 exact (zenon_H231 zenon_Hf4). % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.66 apply (zenon_L628_); trivial. % 30.58/30.66 apply (zenon_L540_); trivial. % 30.58/30.66 (* end of lemma zenon_L2249_ *) % 30.58/30.66 assert (zenon_L2250_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H225 zenon_Hc8 zenon_Hb1 zenon_Hf6 zenon_H1a2 zenon_H1e6 zenon_Hd6 zenon_H1d5 zenon_H200 zenon_H296 zenon_H19e zenon_Haa zenon_H97 zenon_H222 zenon_H113 zenon_Hcd zenon_H174 zenon_H2fb zenon_H2fc zenon_H17d zenon_H8d zenon_Hd9 zenon_H92 zenon_H108 zenon_Hf9 zenon_H1d8 zenon_H3f zenon_He1 zenon_H1bd zenon_H5e zenon_H208 zenon_H1fd zenon_H2d zenon_H1af zenon_H20e zenon_H1dc zenon_H231 zenon_H20d zenon_Hc9 zenon_H156 zenon_H267 zenon_H6f zenon_Hde zenon_H10e zenon_H1d2 zenon_H260 zenon_H6c zenon_H6b zenon_Hd0 zenon_H60 zenon_H218. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.58/30.66 apply (zenon_L43_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.66 apply (zenon_L49_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.66 apply (zenon_L2249_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.66 exact (zenon_H260 zenon_H142). % 30.58/30.66 apply (zenon_L690_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.58/30.66 apply (zenon_L192_); trivial. % 30.58/30.66 apply (zenon_L2053_); trivial. % 30.58/30.66 (* end of lemma zenon_L2250_ *) % 30.58/30.66 assert (zenon_L2251_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H1d5 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_Hf9 zenon_H222 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_Hf6 zenon_Hb8 zenon_H20d zenon_Hc9 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H1e5 zenon_H260 zenon_H1d2 zenon_He1 zenon_H231. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.58/30.66 apply (zenon_L273_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.58/30.66 apply (zenon_L2218_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.58/30.66 apply (zenon_L628_); trivial. % 30.58/30.66 apply (zenon_L2059_); trivial. % 30.58/30.66 (* end of lemma zenon_L2251_ *) % 30.58/30.66 assert (zenon_L2252_ : (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H6f zenon_H20e zenon_H1af zenon_H10e zenon_H1fd zenon_H3f zenon_H92 zenon_Hd9 zenon_H8d zenon_H174 zenon_Hcd zenon_H113 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_Hd6 zenon_H1e6 zenon_H1a2 zenon_H1ba zenon_H3c zenon_He9 zenon_H1d5 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_Hf9 zenon_H222 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_Hf6 zenon_Hb8 zenon_H20d zenon_Hc9 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_He1 zenon_H231. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.66 apply (zenon_L2249_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.66 apply (zenon_L608_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.66 apply (zenon_L219_); trivial. % 30.58/30.66 apply (zenon_L2251_); trivial. % 30.58/30.66 (* end of lemma zenon_L2252_ *) % 30.58/30.66 assert (zenon_L2253_ : (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.66 do 0 intro. intros zenon_H231 zenon_He1 zenon_H1d2 zenon_H108 zenon_Hd0 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_Hc9 zenon_H20d zenon_Hb8 zenon_H208 zenon_H6b zenon_H5e zenon_H1bd zenon_H2fb zenon_H1d8 zenon_H89 zenon_H17d zenon_H2fc zenon_H222 zenon_Hf9 zenon_H1dc zenon_Hde zenon_H200 zenon_H2d zenon_H1d5 zenon_He9 zenon_H3c zenon_H1a2 zenon_H1e6 zenon_Hd6 zenon_H296 zenon_H19e zenon_Haa zenon_H97 zenon_H113 zenon_Hcd zenon_H174 zenon_H8d zenon_Hd9 zenon_H92 zenon_H3f zenon_H1fd zenon_H10e zenon_H1af zenon_H20e zenon_H6f zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.66 apply (zenon_L49_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.66 apply (zenon_L2252_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.66 exact (zenon_H260 zenon_H142). % 30.58/30.66 apply (zenon_L690_); trivial. % 30.58/30.66 (* end of lemma zenon_L2253_ *) % 30.58/30.66 assert (zenon_L2254_ : ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.66 do 0 intro. intros zenon_H1af zenon_H15e zenon_H20e zenon_H3c zenon_He9 zenon_H1d5 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_Hf9 zenon_H222 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_Hf6 zenon_Hb8 zenon_H20d zenon_Hc9 zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_He1 zenon_H231. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.66 apply (zenon_L2222_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.66 apply (zenon_L2225_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.66 apply (zenon_L219_); trivial. % 30.58/30.66 apply (zenon_L2251_); trivial. % 30.58/30.66 (* end of lemma zenon_L2254_ *) % 30.58/30.66 assert (zenon_L2255_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.66 do 0 intro. intros zenon_H92 zenon_H33 zenon_H2c1 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.58/30.66 apply (zenon_L940_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.58/30.66 apply (zenon_L2239_); trivial. % 30.58/30.66 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.58/30.66 apply (zenon_L2105_); trivial. % 30.58/30.66 apply (zenon_L2244_); trivial. % 30.58/30.66 (* end of lemma zenon_L2255_ *) % 30.58/30.66 assert (zenon_L2256_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H208 zenon_H1dc zenon_Hb6 zenon_H6b zenon_H1ba zenon_H5e zenon_H1bd zenon_H3f zenon_H2c zenon_H222 zenon_H97 zenon_H90 zenon_Hb1 zenon_H113 zenon_Haa zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.67 apply (zenon_L2105_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.67 apply (zenon_L608_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.67 apply (zenon_L1866_); trivial. % 30.58/30.67 apply (zenon_L2056_); trivial. % 30.58/30.67 (* end of lemma zenon_L2256_ *) % 30.58/30.67 assert (zenon_L2257_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H208 zenon_H6b zenon_H1bd zenon_H5e zenon_Hde zenon_Hc9 zenon_H200 zenon_H1c7 zenon_H3d zenon_H1af zenon_H17b zenon_H218 zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.67 apply (zenon_L2105_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.67 apply (zenon_L2225_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.67 apply (zenon_L1345_); trivial. % 30.58/30.67 apply (zenon_L2084_); trivial. % 30.58/30.67 (* end of lemma zenon_L2257_ *) % 30.58/30.67 assert (zenon_L2258_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H42 zenon_H60 zenon_Haa zenon_H113 zenon_H90 zenon_H97 zenon_H222 zenon_H3f zenon_H1ba zenon_Hd2 zenon_H6f zenon_H1dc zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H218 zenon_H17b zenon_H1af zenon_H1c7 zenon_H200 zenon_Hc9 zenon_Hde zenon_H5e zenon_H1bd zenon_H6b zenon_H208 zenon_Hb6 zenon_H30b. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.67 apply (zenon_L2256_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.67 apply (zenon_L125_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.67 apply (zenon_L2257_); trivial. % 30.58/30.67 apply (zenon_L1806_); trivial. % 30.58/30.67 (* end of lemma zenon_L2258_ *) % 30.58/30.67 assert (zenon_L2259_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H102 zenon_H19e zenon_H2fb zenon_H1d8 zenon_Hc9 zenon_H42 zenon_H60 zenon_Haa zenon_H113 zenon_H97 zenon_H222 zenon_H3f zenon_H1ba zenon_H6f zenon_H1dc zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H218 zenon_H17b zenon_H1af zenon_H1c7 zenon_H200 zenon_Hde zenon_H5e zenon_H1bd zenon_H6b zenon_H208 zenon_Hb6 zenon_H30b zenon_H17d zenon_H2fc zenon_H13b zenon_H2c zenon_H35. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.58/30.67 apply (zenon_L347_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H8b | zenon_intro zenon_H2fd ]. % 30.58/30.67 apply (zenon_L772_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H90 | zenon_intro zenon_H2fe ]. % 30.58/30.67 apply (zenon_L2258_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_He2 | zenon_intro zenon_H8a ]. % 30.58/30.67 apply (zenon_L307_); trivial. % 30.58/30.67 exact (zenon_H2fb zenon_H8a). % 30.58/30.67 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.58/30.67 exact (zenon_H13b zenon_Hfd). % 30.58/30.67 apply (zenon_L1002_); trivial. % 30.58/30.67 (* end of lemma zenon_L2259_ *) % 30.58/30.67 assert (zenon_L2260_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H2bd zenon_Ha4 zenon_H88 zenon_H2c1 zenon_H35 zenon_H2c zenon_H13b zenon_H2fc zenon_H17d zenon_H30b zenon_Hb6 zenon_H208 zenon_H6b zenon_H1bd zenon_H5e zenon_Hde zenon_H200 zenon_H1c7 zenon_Hf6 zenon_Hb1 zenon_H1e6 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H1dc zenon_H6f zenon_H1ba zenon_H3f zenon_H222 zenon_H97 zenon_H113 zenon_Haa zenon_H60 zenon_H42 zenon_Hc9 zenon_H1d8 zenon_H2fb zenon_H19e zenon_H102 zenon_H1af zenon_H1c5 zenon_H218. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H185 | zenon_intro zenon_H2be ]. % 30.58/30.67 apply (zenon_L869_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H33 | zenon_intro zenon_H2bf ]. % 30.58/30.67 apply (zenon_L940_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H17b | zenon_intro zenon_H16b ]. % 30.58/30.67 apply (zenon_L2259_); trivial. % 30.58/30.67 apply (zenon_L245_); trivial. % 30.58/30.67 (* end of lemma zenon_L2260_ *) % 30.58/30.67 assert (zenon_L2261_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.58/30.67 do 0 intro. intros zenon_H30d zenon_Hd6 zenon_He1 zenon_H1d5 zenon_H182 zenon_H218 zenon_H1af zenon_H102 zenon_H19e zenon_H2fb zenon_H1d8 zenon_Hc9 zenon_H42 zenon_H60 zenon_Haa zenon_H113 zenon_H97 zenon_H222 zenon_H3f zenon_H1ba zenon_H6f zenon_H1dc zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_H1e6 zenon_Hb1 zenon_Hf6 zenon_H1c7 zenon_H200 zenon_Hde zenon_H5e zenon_H1bd zenon_H6b zenon_H208 zenon_H30b zenon_H17d zenon_H2fc zenon_H13b zenon_H2c zenon_H35 zenon_H2c1 zenon_H88 zenon_Ha4 zenon_H2bd zenon_H110 zenon_Hb6. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H30d); [ zenon_intro zenon_H16b | zenon_intro zenon_H30e ]. % 30.58/30.67 apply (zenon_L2238_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H16c | zenon_intro zenon_H30f ]. % 30.58/30.67 apply (zenon_L758_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H1c5 | zenon_intro zenon_Hbc ]. % 30.58/30.67 apply (zenon_L2260_); trivial. % 30.58/30.67 apply (zenon_L1303_); trivial. % 30.58/30.67 (* end of lemma zenon_L2261_ *) % 30.58/30.67 assert (zenon_L2262_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H2fc zenon_Hb1 zenon_H112 zenon_H17d zenon_Hc9 zenon_H1d8 zenon_H2fb. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H8b | zenon_intro zenon_H2fd ]. % 30.58/30.67 apply (zenon_L772_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H90 | zenon_intro zenon_H2fe ]. % 30.58/30.67 apply (zenon_L139_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2fe); [ zenon_intro zenon_He2 | zenon_intro zenon_H8a ]. % 30.58/30.67 apply (zenon_L307_); trivial. % 30.58/30.67 exact (zenon_H2fb zenon_H8a). % 30.58/30.67 (* end of lemma zenon_L2262_ *) % 30.58/30.67 assert (zenon_L2263_ : (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H2fb zenon_H1d8 zenon_Hc9 zenon_H17d zenon_H2fc zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_Hb6 zenon_H1dc zenon_H30d zenon_Hd6 zenon_He1 zenon_H1d5 zenon_H218 zenon_H1af zenon_H102 zenon_H19e zenon_H42 zenon_H60 zenon_Haa zenon_H97 zenon_H222 zenon_H3f zenon_H6f zenon_H1e6 zenon_Hf6 zenon_H1c7 zenon_H200 zenon_Hde zenon_H5e zenon_H1bd zenon_H6b zenon_H208 zenon_H30b zenon_H13b zenon_H2c zenon_H35 zenon_H2c1 zenon_H88 zenon_Ha4 zenon_H2bd zenon_H110 zenon_H92 zenon_H8d zenon_H174 zenon_Hcd zenon_Hf9 zenon_H296 zenon_H2d zenon_H10e zenon_H2b1 zenon_Hb1 zenon_H113. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.58/30.67 apply (zenon_L4_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.58/30.67 apply (zenon_L2167_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.58/30.67 apply (zenon_L2255_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.58/30.67 apply (zenon_L2261_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.58/30.67 apply (zenon_L2084_); trivial. % 30.58/30.67 apply (zenon_L2262_); trivial. % 30.58/30.67 apply (zenon_L798_); trivial. % 30.58/30.67 (* end of lemma zenon_L2263_ *) % 30.58/30.67 assert (zenon_L2264_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H23b zenon_H2c zenon_H222 zenon_H60 zenon_H97 zenon_H113 zenon_Haa zenon_H1f zenon_H3f zenon_H25 zenon_H1dc zenon_H2fc zenon_Hb1 zenon_H17d zenon_Hc9 zenon_H1d8 zenon_H2fb. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.58/30.67 apply (zenon_L1866_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.58/30.67 apply (zenon_L336_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.58/30.67 apply (zenon_L1834_); trivial. % 30.58/30.67 apply (zenon_L2262_); trivial. % 30.58/30.67 (* end of lemma zenon_L2264_ *) % 30.58/30.67 assert (zenon_L2265_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H208 zenon_H6b zenon_Hf6 zenon_H1bd zenon_H5e zenon_Hde zenon_H200 zenon_H2fb zenon_H1d8 zenon_Hc9 zenon_H17d zenon_Hb1 zenon_H2fc zenon_H3f zenon_H1f zenon_Haa zenon_H113 zenon_H97 zenon_H60 zenon_H222 zenon_H2c zenon_H23b zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.67 apply (zenon_L2105_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.67 apply (zenon_L2225_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.67 apply (zenon_L2264_); trivial. % 30.58/30.67 apply (zenon_L2084_); trivial. % 30.58/30.67 (* end of lemma zenon_L2265_ *) % 30.58/30.67 assert (zenon_L2266_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.67 do 0 intro. intros zenon_Hc0 zenon_H30d zenon_H102 zenon_H42 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_Ha4 zenon_H2bd zenon_H110 zenon_H2b1 zenon_H23b zenon_Hd9 zenon_H92 zenon_H2c1 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.67 apply (zenon_L734_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.67 apply (zenon_L2263_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.67 apply (zenon_L87_); trivial. % 30.58/30.67 apply (zenon_L2238_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.67 apply (zenon_L734_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.67 apply (zenon_L2265_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.67 apply (zenon_L87_); trivial. % 30.58/30.67 apply (zenon_L2238_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.58/30.67 apply (zenon_L2239_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.58/30.67 apply (zenon_L2105_); trivial. % 30.58/30.67 apply (zenon_L2244_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.58/30.67 apply (zenon_L2245_); trivial. % 30.58/30.67 apply (zenon_L2255_); trivial. % 30.58/30.67 (* end of lemma zenon_L2266_ *) % 30.58/30.67 assert (zenon_L2267_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.58/30.67 do 0 intro. intros zenon_Hb8 zenon_H16b zenon_H15e zenon_H20e zenon_Hf6 zenon_H260 zenon_H208 zenon_H6b zenon_H5e zenon_H1bd zenon_H218 zenon_H1af zenon_H6f zenon_H1e6 zenon_Hd6 zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H1d2 zenon_H108 zenon_Hd0 zenon_H1dc zenon_Hde zenon_H200 zenon_H10e zenon_H296 zenon_H19e zenon_Haa zenon_H97 zenon_H60 zenon_H222 zenon_H3f zenon_H113 zenon_Hf9 zenon_Hcd zenon_H174 zenon_H2fb zenon_H2fc zenon_H17d zenon_H1d8 zenon_H8d zenon_H2c1 zenon_H92 zenon_Hd9 zenon_H23b zenon_H2b1 zenon_H110 zenon_H2bd zenon_Ha4 zenon_H35 zenon_H13b zenon_H30b zenon_H1c7 zenon_H42 zenon_H102 zenon_H30d zenon_Hc0 zenon_Hb1 zenon_H2d. % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.58/30.67 exact (zenon_H2fb zenon_H8a). % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.58/30.67 apply (zenon_L1338_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.58/30.67 apply (zenon_L2266_); trivial. % 30.58/30.67 apply (zenon_L107_); trivial. % 30.58/30.67 (* end of lemma zenon_L2267_ *) % 30.58/30.67 assert (zenon_L2268_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e2)) -> False). % 30.58/30.67 do 0 intro. intros zenon_H1fd zenon_H2d zenon_Hb1 zenon_Hc0 zenon_H30d zenon_H102 zenon_H42 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_Ha4 zenon_H2bd zenon_H110 zenon_H2b1 zenon_H23b zenon_Hd9 zenon_H92 zenon_H2c1 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_H20e zenon_H16b zenon_Hb8 zenon_H218 zenon_H17b zenon_H60 zenon_He1 zenon_Heb. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.67 apply (zenon_L87_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.67 apply (zenon_L2267_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.67 apply (zenon_L259_); trivial. % 30.58/30.67 apply (zenon_L204_); trivial. % 30.58/30.67 (* end of lemma zenon_L2268_ *) % 30.58/30.67 assert (zenon_L2269_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H267 zenon_Heb zenon_He1 zenon_H218 zenon_Hb8 zenon_H16b zenon_H20e zenon_Hf6 zenon_H260 zenon_H208 zenon_H6b zenon_H5e zenon_H1bd zenon_H1af zenon_H6f zenon_H1e6 zenon_Hd6 zenon_H1d5 zenon_H1d2 zenon_H108 zenon_Hd0 zenon_H1dc zenon_Hde zenon_H200 zenon_H10e zenon_H296 zenon_H19e zenon_Haa zenon_H97 zenon_H222 zenon_H3f zenon_H113 zenon_Hf9 zenon_Hcd zenon_H174 zenon_H2fb zenon_H2fc zenon_H17d zenon_H1d8 zenon_H8d zenon_H2c1 zenon_H92 zenon_Hd9 zenon_H23b zenon_H2b1 zenon_H110 zenon_H2bd zenon_Ha4 zenon_H35 zenon_H13b zenon_H30b zenon_H1c7 zenon_H42 zenon_H102 zenon_H30d zenon_Hc0 zenon_Hb1 zenon_H2d zenon_H1fd zenon_H156 zenon_H1b9 zenon_H60 zenon_Hc9 zenon_H20d zenon_H231. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.58/30.67 apply (zenon_L2268_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.58/30.67 apply (zenon_L179_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.58/30.67 apply (zenon_L627_); trivial. % 30.58/30.67 exact (zenon_H231 zenon_Hf4). % 30.58/30.67 (* end of lemma zenon_L2269_ *) % 30.58/30.67 assert (zenon_L2270_ : (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.67 do 0 intro. intros zenon_H231 zenon_H267 zenon_Hb8 zenon_H16b zenon_H20e zenon_H1fd zenon_H156 zenon_H20d zenon_He9 zenon_Hc0 zenon_H30d zenon_H102 zenon_H42 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_Ha4 zenon_H2bd zenon_H110 zenon_H2b1 zenon_H23b zenon_Hd9 zenon_H92 zenon_H2c1 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.67 apply (zenon_L87_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.67 apply (zenon_L2267_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.58/30.67 apply (zenon_L307_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.58/30.67 apply (zenon_L53_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.58/30.67 apply (zenon_L2269_); trivial. % 30.58/30.67 exact (zenon_H231 zenon_Hf4). % 30.58/30.67 apply (zenon_L2266_); trivial. % 30.58/30.67 (* end of lemma zenon_L2270_ *) % 30.58/30.67 assert (zenon_L2271_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H208 zenon_H6b zenon_Hb1 zenon_Hf6 zenon_H1bd zenon_H5e zenon_Hde zenon_Hc9 zenon_H200 zenon_H3c zenon_He9 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.67 apply (zenon_L2053_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.67 apply (zenon_L2225_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.67 apply (zenon_L219_); trivial. % 30.58/30.67 apply (zenon_L2056_); trivial. % 30.58/30.67 (* end of lemma zenon_L2271_ *) % 30.58/30.67 assert (zenon_L2272_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H296 zenon_H2d zenon_H35 zenon_H2c zenon_H13b zenon_H2fc zenon_H17d zenon_H30b zenon_Hb6 zenon_H208 zenon_H6b zenon_H1bd zenon_H5e zenon_Hde zenon_H200 zenon_H1c7 zenon_H1af zenon_H17b zenon_H218 zenon_Hf6 zenon_H1e6 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H1dc zenon_H6f zenon_H3f zenon_H222 zenon_H97 zenon_Haa zenon_H60 zenon_H42 zenon_Hc9 zenon_H1d8 zenon_H2fb zenon_H19e zenon_H102 zenon_Hb1 zenon_H113. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.58/30.67 apply (zenon_L4_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.58/30.67 apply (zenon_L2167_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.58/30.67 apply (zenon_L2259_); trivial. % 30.58/30.67 apply (zenon_L798_); trivial. % 30.58/30.67 (* end of lemma zenon_L2272_ *) % 30.58/30.67 assert (zenon_L2273_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.58/30.67 do 0 intro. intros zenon_Hb8 zenon_H113 zenon_H102 zenon_H19e zenon_H2fb zenon_H1d8 zenon_Hc9 zenon_H42 zenon_H60 zenon_Haa zenon_H97 zenon_H222 zenon_H3f zenon_H6f zenon_H1dc zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_H1e6 zenon_Hf6 zenon_H218 zenon_H17b zenon_H1af zenon_H1c7 zenon_H200 zenon_Hde zenon_H5e zenon_H1bd zenon_H6b zenon_H208 zenon_H30b zenon_H17d zenon_H2fc zenon_H13b zenon_H2c zenon_H35 zenon_H296 zenon_Hb1 zenon_H2d. % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.58/30.67 exact (zenon_H2fb zenon_H8a). % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.58/30.67 apply (zenon_L746_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.58/30.67 apply (zenon_L2272_); trivial. % 30.58/30.67 apply (zenon_L107_); trivial. % 30.58/30.67 (* end of lemma zenon_L2273_ *) % 30.58/30.67 assert (zenon_L2274_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 30.58/30.67 do 0 intro. intros zenon_H101 zenon_H3c zenon_H296 zenon_H35 zenon_H13b zenon_H30b zenon_H1c7 zenon_H1af zenon_H17b zenon_H218 zenon_H1e6 zenon_H6f zenon_H3f zenon_H97 zenon_Haa zenon_H42 zenon_H19e zenon_H102 zenon_H113 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_H60 zenon_H222 zenon_H2fc zenon_H17d zenon_H89 zenon_Hc9 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb8 zenon_He1. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.67 apply (zenon_L2271_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.67 exact (zenon_H13b zenon_Hfd). % 30.58/30.67 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.67 apply (zenon_L282_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.67 apply (zenon_L2273_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.67 apply (zenon_L320_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.67 apply (zenon_L2218_); trivial. % 30.58/30.67 apply (zenon_L1354_); trivial. % 30.58/30.67 (* end of lemma zenon_L2274_ *) % 30.58/30.67 assert (zenon_L2275_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.67 do 0 intro. intros zenon_H3c zenon_H101 zenon_H1fd zenon_H20e zenon_Hb8 zenon_H17b zenon_Hc0 zenon_H30d zenon_H102 zenon_H42 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_Ha4 zenon_H2bd zenon_H110 zenon_H2b1 zenon_H23b zenon_Hd9 zenon_H92 zenon_H2c1 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.67 apply (zenon_L2274_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.67 apply (zenon_L2273_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.67 apply (zenon_L87_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.67 apply (zenon_L87_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.67 apply (zenon_L2267_); trivial. % 30.58/30.67 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.67 apply (zenon_L259_); trivial. % 30.58/30.67 apply (zenon_L2266_); trivial. % 30.58/30.67 (* end of lemma zenon_L2275_ *) % 30.58/30.67 assert (zenon_L2276_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.68 do 0 intro. intros zenon_H225 zenon_H20d zenon_H156 zenon_H267 zenon_H231 zenon_Hc8 zenon_H16f zenon_H68 zenon_H1a2 zenon_H3c zenon_H101 zenon_H1fd zenon_H20e zenon_Hb8 zenon_Hc0 zenon_H30d zenon_H102 zenon_H42 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_Ha4 zenon_H2bd zenon_H110 zenon_H2b1 zenon_H23b zenon_Hd9 zenon_H92 zenon_H2c1 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.58/30.68 apply (zenon_L43_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.68 apply (zenon_L2253_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.58/30.68 apply (zenon_L18_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.58/30.68 apply (zenon_L1002_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.58/30.68 apply (zenon_L2254_); trivial. % 30.58/30.68 apply (zenon_L2219_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.58/30.68 apply (zenon_L18_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.58/30.68 apply (zenon_L273_); trivial. % 30.58/30.68 exact (zenon_H2fb zenon_H8a). % 30.58/30.68 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.68 apply (zenon_L87_); trivial. % 30.58/30.68 apply (zenon_L2270_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.58/30.68 apply (zenon_L192_); trivial. % 30.58/30.68 apply (zenon_L2275_); trivial. % 30.58/30.68 (* end of lemma zenon_L2276_ *) % 30.58/30.68 assert (zenon_L2277_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.68 do 0 intro. intros zenon_H208 zenon_H6b zenon_Hf6 zenon_H1bd zenon_H5e zenon_Hde zenon_Hc9 zenon_H200 zenon_H3f zenon_H2c zenon_H222 zenon_H97 zenon_H90 zenon_Hb1 zenon_H113 zenon_Haa zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H60 zenon_H155 zenon_H156. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.68 apply (zenon_L2054_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.68 apply (zenon_L2225_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.68 apply (zenon_L1866_); trivial. % 30.58/30.68 apply (zenon_L2057_); trivial. % 30.58/30.68 (* end of lemma zenon_L2277_ *) % 30.58/30.68 assert (zenon_L2278_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.68 do 0 intro. intros zenon_H267 zenon_H2d zenon_H296 zenon_H35 zenon_H13b zenon_H2fc zenon_H17d zenon_H30b zenon_H1c7 zenon_H218 zenon_H1e6 zenon_H1dc zenon_H6f zenon_H42 zenon_H1d8 zenon_H2fb zenon_H19e zenon_H102 zenon_Hb8 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_Haa zenon_H113 zenon_Hb1 zenon_H90 zenon_H97 zenon_H222 zenon_H2c zenon_H3f zenon_H200 zenon_Hc9 zenon_Hde zenon_H5e zenon_H1bd zenon_Hf6 zenon_H6b zenon_H208 zenon_H20e zenon_H15e zenon_H1af zenon_H231. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.58/30.68 apply (zenon_L2273_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.58/30.68 apply (zenon_L2277_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.58/30.68 apply (zenon_L358_); trivial. % 30.58/30.68 exact (zenon_H231 zenon_Hf4). % 30.58/30.68 (* end of lemma zenon_L2278_ *) % 30.58/30.68 assert (zenon_L2279_ : (~((op (e3) (e3)) = (e2))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 30.58/30.68 do 0 intro. intros zenon_H231 zenon_H15e zenon_H20e zenon_H1d2 zenon_H260 zenon_H6b zenon_Hd0 zenon_H156 zenon_H101 zenon_H296 zenon_H35 zenon_H13b zenon_H30b zenon_H1c7 zenon_H218 zenon_H1e6 zenon_H6f zenon_H3f zenon_H97 zenon_Haa zenon_H42 zenon_H19e zenon_H102 zenon_H113 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_H108 zenon_Hf9 zenon_H2fc zenon_H17d zenon_H89 zenon_Hc9 zenon_H1d8 zenon_H2fb zenon_H208 zenon_Hf6 zenon_Hb8 zenon_He1 zenon_H267 zenon_H1ba zenon_H5e zenon_H1bd zenon_H3c zenon_He9 zenon_H60 zenon_H222 zenon_H1af zenon_H40. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.58/30.68 apply (zenon_L2274_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.58/30.68 apply (zenon_L2054_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.58/30.68 apply (zenon_L358_); trivial. % 30.58/30.68 exact (zenon_H231 zenon_Hf4). % 30.58/30.68 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.68 apply (zenon_L608_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.68 apply (zenon_L219_); trivial. % 30.58/30.68 apply (zenon_L1337_); trivial. % 30.58/30.68 (* end of lemma zenon_L2279_ *) % 30.58/30.68 assert (zenon_L2280_ : ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> False). % 30.58/30.68 do 0 intro. intros zenon_H90 zenon_Hfc zenon_H231 zenon_H15e zenon_H20e zenon_H1d2 zenon_H260 zenon_H6b zenon_Hd0 zenon_H156 zenon_H101 zenon_H296 zenon_H35 zenon_H13b zenon_H30b zenon_H1c7 zenon_H218 zenon_H1e6 zenon_H6f zenon_H3f zenon_H97 zenon_Haa zenon_H42 zenon_H19e zenon_H102 zenon_H113 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_H108 zenon_Hf9 zenon_H2fc zenon_H17d zenon_H89 zenon_Hc9 zenon_H1d8 zenon_H2fb zenon_H208 zenon_Hf6 zenon_Hb8 zenon_He1 zenon_H267 zenon_H1ba zenon_H5e zenon_H1bd zenon_H3c zenon_He9 zenon_H60 zenon_H222 zenon_H1af. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.68 apply (zenon_L2278_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.68 apply (zenon_L203_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.68 apply (zenon_L2218_); trivial. % 30.58/30.68 apply (zenon_L2279_); trivial. % 30.58/30.68 (* end of lemma zenon_L2280_ *) % 30.58/30.68 assert (zenon_L2281_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e1)) = (e0)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.68 do 0 intro. intros zenon_H1fd zenon_H10e zenon_H1af zenon_H222 zenon_He9 zenon_H3c zenon_H1bd zenon_H5e zenon_H1ba zenon_He1 zenon_Hb8 zenon_Hf6 zenon_H208 zenon_H2fb zenon_H1d8 zenon_H89 zenon_H17d zenon_H2fc zenon_Hf9 zenon_H108 zenon_Hde zenon_H200 zenon_Hb1 zenon_H2d zenon_H113 zenon_H102 zenon_H19e zenon_H42 zenon_Haa zenon_H97 zenon_H3f zenon_H6f zenon_H1e6 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_H296 zenon_H101 zenon_H20e zenon_Hfc zenon_H90 zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H1d2 zenon_H260 zenon_H6c zenon_H6b zenon_Hd0 zenon_H1dc. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.68 apply (zenon_L87_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.68 apply (zenon_L2280_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.68 apply (zenon_L628_); trivial. % 30.58/30.68 apply (zenon_L2105_); trivial. % 30.58/30.68 (* end of lemma zenon_L2281_ *) % 30.58/30.68 assert (zenon_L2282_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 30.58/30.68 do 0 intro. intros zenon_H1dc zenon_Hd0 zenon_H6b zenon_H260 zenon_H1d2 zenon_H267 zenon_H218 zenon_H156 zenon_Hc9 zenon_H20d zenon_H231 zenon_H90 zenon_Hfc zenon_H20e zenon_H101 zenon_H296 zenon_H35 zenon_H13b zenon_H30b zenon_H1c7 zenon_H1e6 zenon_H6f zenon_H3f zenon_H97 zenon_Haa zenon_H42 zenon_H19e zenon_H102 zenon_H113 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H108 zenon_Hf9 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H208 zenon_Hf6 zenon_Hb8 zenon_He1 zenon_H10e zenon_H1fd zenon_H1ba zenon_H5e zenon_H1bd zenon_H3c zenon_He9 zenon_H60 zenon_H222 zenon_H1af zenon_H40. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.68 apply (zenon_L2281_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.68 apply (zenon_L608_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.68 apply (zenon_L219_); trivial. % 30.58/30.68 apply (zenon_L1337_); trivial. % 30.58/30.68 (* end of lemma zenon_L2282_ *) % 30.58/30.68 assert (zenon_L2283_ : ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.68 do 0 intro. intros zenon_H1e zenon_Hd2 zenon_H1af zenon_H222 zenon_H60 zenon_He9 zenon_H3c zenon_H1bd zenon_H5e zenon_H1fd zenon_H10e zenon_He1 zenon_Hb8 zenon_H208 zenon_H2fb zenon_H1d8 zenon_H89 zenon_H17d zenon_H2fc zenon_Hf9 zenon_H108 zenon_Hde zenon_H200 zenon_H2d zenon_H113 zenon_H102 zenon_H19e zenon_H42 zenon_Haa zenon_H97 zenon_H3f zenon_H6f zenon_H1e6 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_H296 zenon_H101 zenon_H20e zenon_Hfc zenon_H90 zenon_H231 zenon_H20d zenon_Hc9 zenon_H156 zenon_H218 zenon_H267 zenon_H1d2 zenon_H6b zenon_Hd0 zenon_H1dc zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.68 apply (zenon_L4_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.68 apply (zenon_L125_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.68 apply (zenon_L2218_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.68 apply (zenon_L49_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.68 apply (zenon_L2282_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.68 exact (zenon_H260 zenon_H142). % 30.58/30.68 apply (zenon_L690_); trivial. % 30.58/30.68 (* end of lemma zenon_L2283_ *) % 30.58/30.68 assert (zenon_L2284_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.68 do 0 intro. intros zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_H1d8 zenon_He9 zenon_H3f zenon_H20d zenon_Hc9 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_H156 zenon_H60 zenon_He1 zenon_H218 zenon_H267 zenon_H231 zenon_H20e zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.68 apply (zenon_L49_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.68 apply (zenon_L2248_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.68 exact (zenon_H260 zenon_H142). % 30.58/30.68 apply (zenon_L690_); trivial. % 30.58/30.68 (* end of lemma zenon_L2284_ *) % 30.58/30.68 assert (zenon_L2285_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 30.58/30.68 do 0 intro. intros zenon_H1dc zenon_Hd0 zenon_H6b zenon_H1d2 zenon_H267 zenon_H218 zenon_H20d zenon_H231 zenon_H90 zenon_Hfc zenon_H20e zenon_H101 zenon_H296 zenon_H35 zenon_H13b zenon_H30b zenon_H1c7 zenon_H1e6 zenon_H6f zenon_H3f zenon_H97 zenon_Haa zenon_H42 zenon_H19e zenon_H102 zenon_H113 zenon_H2d zenon_H108 zenon_Hf9 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H208 zenon_Hb8 zenon_He1 zenon_H1ba zenon_H222 zenon_H1af zenon_H10e zenon_H1fd zenon_Hb1 zenon_Hf6 zenon_H260 zenon_H1bd zenon_H5e zenon_Hde zenon_Hc9 zenon_H200 zenon_H3c zenon_He9 zenon_H60 zenon_H156 zenon_H182. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.68 apply (zenon_L2281_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.68 apply (zenon_L2225_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.68 apply (zenon_L219_); trivial. % 30.58/30.68 apply (zenon_L934_); trivial. % 30.58/30.68 (* end of lemma zenon_L2285_ *) % 30.58/30.68 assert (zenon_L2286_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.68 do 0 intro. intros zenon_H1fd zenon_H20e zenon_H2c zenon_H90 zenon_Hb8 zenon_H102 zenon_H42 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_H231 zenon_H20d zenon_H156 zenon_H267 zenon_H92 zenon_Hd9 zenon_H26 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.68 apply (zenon_L87_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.68 apply (zenon_L2278_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.68 apply (zenon_L628_); trivial. % 30.58/30.68 apply (zenon_L2245_); trivial. % 30.58/30.68 (* end of lemma zenon_L2286_ *) % 30.58/30.68 assert (zenon_L2287_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.68 do 0 intro. intros zenon_H1fd zenon_H10e zenon_H231 zenon_H1af zenon_H20e zenon_Hf6 zenon_Hde zenon_Hc9 zenon_H200 zenon_H156 zenon_Hb8 zenon_H102 zenon_H19e zenon_H2fb zenon_H1d8 zenon_H42 zenon_H6f zenon_H1e6 zenon_H218 zenon_H1c7 zenon_H30b zenon_H17d zenon_H2fc zenon_H13b zenon_H35 zenon_H296 zenon_H2d zenon_H267 zenon_H1a0 zenon_H208 zenon_H6b zenon_H1ba zenon_H5e zenon_H1bd zenon_H3f zenon_H2c zenon_H222 zenon_H60 zenon_H97 zenon_H90 zenon_Hb1 zenon_H113 zenon_Haa zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H1dc. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.68 apply (zenon_L87_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.68 apply (zenon_L2278_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.68 apply (zenon_L751_); trivial. % 30.58/30.68 apply (zenon_L2242_); trivial. % 30.58/30.68 (* end of lemma zenon_L2287_ *) % 30.58/30.68 assert (zenon_L2288_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 30.58/30.68 do 0 intro. intros zenon_H1dc zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_Haa zenon_H90 zenon_H97 zenon_H60 zenon_H222 zenon_H2c zenon_H3f zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H267 zenon_H2d zenon_H296 zenon_H35 zenon_H13b zenon_H2fc zenon_H17d zenon_H30b zenon_H1c7 zenon_H218 zenon_H1e6 zenon_H6f zenon_H42 zenon_H1d8 zenon_H2fb zenon_H19e zenon_H102 zenon_Hb8 zenon_H156 zenon_H200 zenon_Hc9 zenon_Hde zenon_Hf6 zenon_H20e zenon_H1af zenon_H231 zenon_H10e zenon_H1fd zenon_He1 zenon_H20d zenon_He9 zenon_Hf9 zenon_H92 zenon_Hd9 zenon_H8d zenon_H174 zenon_Hcd zenon_H1d5 zenon_Hd6 zenon_H1a2 zenon_H3c zenon_Hb1 zenon_H113. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.58/30.68 apply (zenon_L4_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.58/30.68 apply (zenon_L2167_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.58/30.68 apply (zenon_L2286_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.58/30.68 apply (zenon_L2247_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.58/30.68 apply (zenon_L219_); trivial. % 30.58/30.68 apply (zenon_L2287_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.68 apply (zenon_L608_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.68 apply (zenon_L1866_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.58/30.68 apply (zenon_L2286_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.58/30.68 apply (zenon_L2085_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.58/30.68 apply (zenon_L1274_); trivial. % 30.58/30.68 apply (zenon_L2287_); trivial. % 30.58/30.68 apply (zenon_L798_); trivial. % 30.58/30.68 (* end of lemma zenon_L2288_ *) % 30.58/30.68 assert (zenon_L2289_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.68 do 0 intro. intros zenon_H208 zenon_H6b zenon_Hb1 zenon_Hf6 zenon_H1bd zenon_H5e zenon_Hde zenon_Hc9 zenon_H200 zenon_H20e zenon_H19a zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.68 apply (zenon_L2105_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.68 apply (zenon_L2225_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.68 apply (zenon_L225_); trivial. % 30.58/30.68 apply (zenon_L2084_); trivial. % 30.58/30.68 (* end of lemma zenon_L2289_ *) % 30.58/30.68 assert (zenon_L2290_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.68 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H218 zenon_H17b zenon_H60 zenon_H208 zenon_H6b zenon_Hb1 zenon_Hf6 zenon_H1bd zenon_H5e zenon_Hde zenon_Hc9 zenon_H200 zenon_H20e zenon_H19a zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H1dc. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.68 apply (zenon_L87_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.68 apply (zenon_L235_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.68 apply (zenon_L259_); trivial. % 30.58/30.68 apply (zenon_L2289_); trivial. % 30.58/30.68 (* end of lemma zenon_L2290_ *) % 30.58/30.68 assert (zenon_L2291_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.58/30.68 do 0 intro. intros zenon_H225 zenon_Hc8 zenon_H231 zenon_H267 zenon_He1 zenon_H156 zenon_H20d zenon_H3f zenon_H1d8 zenon_Hf9 zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H218 zenon_H60 zenon_H208 zenon_H6b zenon_Hb1 zenon_Hf6 zenon_H1bd zenon_H5e zenon_Hde zenon_Hc9 zenon_H200 zenon_H20e zenon_H19a zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H1dc. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.58/30.68 apply (zenon_L43_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.58/30.68 apply (zenon_L2284_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.58/30.68 apply (zenon_L192_); trivial. % 30.58/30.68 apply (zenon_L2290_); trivial. % 30.58/30.68 (* end of lemma zenon_L2291_ *) % 30.58/30.68 assert (zenon_L2292_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.68 do 0 intro. intros zenon_H20d zenon_H156 zenon_H267 zenon_H231 zenon_H90 zenon_H1a2 zenon_Hfc zenon_H225 zenon_Hc8 zenon_Had zenon_H1a8 zenon_H3c zenon_H101 zenon_H1fd zenon_H20e zenon_Hb8 zenon_Hc0 zenon_H30d zenon_H102 zenon_H42 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_Ha4 zenon_H2bd zenon_H110 zenon_H2b1 zenon_H23b zenon_Hd9 zenon_H92 zenon_H2c1 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.58/30.68 apply (zenon_L43_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.58/30.68 apply (zenon_L639_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.58/30.68 apply (zenon_L2283_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.58/30.68 apply (zenon_L2284_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.68 apply (zenon_L49_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.68 apply (zenon_L2285_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.68 exact (zenon_H260 zenon_H142). % 30.58/30.68 apply (zenon_L690_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.58/30.68 apply (zenon_L2167_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.58/30.68 apply (zenon_L639_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.68 apply (zenon_L2288_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.68 apply (zenon_L125_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.68 apply (zenon_L2218_); trivial. % 30.58/30.68 apply (zenon_L2282_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.58/30.68 apply (zenon_L2291_); trivial. % 30.58/30.68 apply (zenon_L2285_); trivial. % 30.58/30.68 apply (zenon_L798_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.68 apply (zenon_L2288_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.68 apply (zenon_L87_); trivial. % 30.58/30.68 apply (zenon_L2270_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.58/30.68 apply (zenon_L192_); trivial. % 30.58/30.68 apply (zenon_L2275_); trivial. % 30.58/30.68 (* end of lemma zenon_L2292_ *) % 30.58/30.68 assert (zenon_L2293_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.68 do 0 intro. intros zenon_H16f zenon_H26 zenon_H20d zenon_H156 zenon_H267 zenon_H231 zenon_H1a2 zenon_Hfc zenon_H225 zenon_Hc8 zenon_Had zenon_H1a8 zenon_H3c zenon_H101 zenon_H1fd zenon_H20e zenon_Hb8 zenon_Hc0 zenon_H30d zenon_H102 zenon_H42 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_Ha4 zenon_H2bd zenon_H110 zenon_H2b1 zenon_H23b zenon_Hd9 zenon_H92 zenon_H2c1 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.58/30.68 apply (zenon_L797_); trivial. % 30.58/30.68 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.58/30.69 apply (zenon_L2276_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.58/30.69 apply (zenon_L2246_); trivial. % 30.58/30.69 apply (zenon_L2292_); trivial. % 30.58/30.69 (* end of lemma zenon_L2293_ *) % 30.58/30.69 assert (zenon_L2294_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.69 do 0 intro. intros zenon_H267 zenon_H218 zenon_H1dc zenon_H1a0 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H1e5 zenon_H260 zenon_H1d2 zenon_He1 zenon_H1c5 zenon_H231. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.58/30.69 apply (zenon_L2091_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.58/30.69 apply (zenon_L2057_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.58/30.69 apply (zenon_L221_); trivial. % 30.58/30.69 exact (zenon_H231 zenon_Hf4). % 30.58/30.69 (* end of lemma zenon_L2294_ *) % 30.58/30.69 assert (zenon_L2295_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.69 do 0 intro. intros zenon_H1d5 zenon_Hc9 zenon_H1af zenon_Hd6 zenon_Hb1 zenon_H267 zenon_H218 zenon_H1dc zenon_H1a0 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H1e5 zenon_H260 zenon_H1d2 zenon_He1 zenon_H231. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.58/30.69 apply (zenon_L273_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.58/30.69 apply (zenon_L2091_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.58/30.69 apply (zenon_L2057_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.58/30.69 apply (zenon_L144_); trivial. % 30.58/30.69 exact (zenon_H231 zenon_Hf4). % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.58/30.69 apply (zenon_L751_); trivial. % 30.58/30.69 apply (zenon_L2294_); trivial. % 30.58/30.69 (* end of lemma zenon_L2295_ *) % 30.58/30.69 assert (zenon_L2296_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H16f zenon_H20d zenon_H156 zenon_H267 zenon_H231 zenon_H1a2 zenon_Hfc zenon_H225 zenon_Hc8 zenon_Had zenon_H1a8 zenon_H3c zenon_H101 zenon_H1fd zenon_H20e zenon_Hb8 zenon_Hc0 zenon_H30d zenon_H102 zenon_H42 zenon_H1c7 zenon_H30b zenon_H13b zenon_H35 zenon_Ha4 zenon_H2bd zenon_H110 zenon_H2b1 zenon_H23b zenon_Hd9 zenon_H92 zenon_H2c1 zenon_H8d zenon_H1d8 zenon_H17d zenon_H2fc zenon_H2fb zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_Haa zenon_H19e zenon_H296 zenon_H2d zenon_H10e zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.58/30.69 apply (zenon_L998_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.69 apply (zenon_L2250_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.69 apply (zenon_L2225_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.69 apply (zenon_L219_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.58/30.69 apply (zenon_L2293_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.58/30.69 apply (zenon_L2085_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.58/30.69 apply (zenon_L1274_); trivial. % 30.58/30.69 apply (zenon_L2295_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.58/30.69 apply (zenon_L192_); trivial. % 30.58/30.69 apply (zenon_L2275_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.58/30.69 apply (zenon_L43_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.69 apply (zenon_L2253_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.58/30.69 apply (zenon_L4_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.58/30.69 apply (zenon_L2167_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.69 apply (zenon_L2249_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.69 apply (zenon_L608_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.69 apply (zenon_L2264_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.58/30.69 apply (zenon_L797_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.58/30.69 apply (zenon_L2085_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.58/30.69 apply (zenon_L2264_); trivial. % 30.58/30.69 apply (zenon_L2295_); trivial. % 30.58/30.69 apply (zenon_L798_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.69 apply (zenon_L87_); trivial. % 30.58/30.69 apply (zenon_L2270_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.58/30.69 apply (zenon_L192_); trivial. % 30.58/30.69 apply (zenon_L2275_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.58/30.69 apply (zenon_L2276_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.58/30.69 apply (zenon_L2250_); trivial. % 30.58/30.69 apply (zenon_L2292_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.58/30.69 apply (zenon_L2293_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.58/30.69 apply (zenon_L940_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.58/30.69 apply (zenon_L2276_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.58/30.69 apply (zenon_L2250_); trivial. % 30.58/30.69 apply (zenon_L2292_); trivial. % 30.58/30.69 (* end of lemma zenon_L2296_ *) % 30.58/30.69 assert (zenon_L2297_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H174 zenon_Hcd zenon_Hf9 zenon_H113 zenon_H3f zenon_H222 zenon_H60 zenon_H97 zenon_H90 zenon_Haa zenon_H19e zenon_H2d zenon_H296 zenon_H10d zenon_H200 zenon_Hde zenon_H1dc zenon_Hb6 zenon_Hd0 zenon_H108 zenon_H1d2 zenon_H1d5 zenon_He1 zenon_Hc9 zenon_Hd6 zenon_H1e6 zenon_H6f zenon_H1af zenon_H218 zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.58/30.69 apply (zenon_L2241_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.58/30.69 apply (zenon_L2243_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.58/30.69 apply (zenon_L151_); trivial. % 30.58/30.69 apply (zenon_L2238_); trivial. % 30.58/30.69 (* end of lemma zenon_L2297_ *) % 30.58/30.69 assert (zenon_L2298_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.69 do 0 intro. intros zenon_H16f zenon_H68 zenon_Hfd zenon_H6f zenon_H19a zenon_H1d5 zenon_Hc8 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_H222 zenon_He1 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb8 zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H218 zenon_H267 zenon_H1af zenon_H156. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.58/30.69 apply (zenon_L18_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.58/30.69 apply (zenon_L158_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.58/30.69 apply (zenon_L235_); trivial. % 30.58/30.69 apply (zenon_L2219_); trivial. % 30.58/30.69 (* end of lemma zenon_L2298_ *) % 30.58/30.69 assert (zenon_L2299_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.69 do 0 intro. intros zenon_H16f zenon_H68 zenon_H9d zenon_H6f zenon_H19a zenon_H1d5 zenon_Hc8 zenon_H2d zenon_Hb1 zenon_H200 zenon_Hde zenon_H1dc zenon_Hd0 zenon_H108 zenon_H1d2 zenon_Hf9 zenon_H222 zenon_He1 zenon_H2fc zenon_H17d zenon_H89 zenon_H1d8 zenon_H2fb zenon_H1bd zenon_H5e zenon_H6b zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb8 zenon_H231 zenon_H20d zenon_Hc9 zenon_H60 zenon_H218 zenon_H267 zenon_H1af zenon_H156. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.58/30.69 apply (zenon_L18_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.58/30.69 apply (zenon_L320_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.58/30.69 apply (zenon_L235_); trivial. % 30.58/30.69 apply (zenon_L2219_); trivial. % 30.58/30.69 (* end of lemma zenon_L2299_ *) % 30.58/30.69 assert (zenon_L2300_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.69 do 0 intro. intros zenon_H208 zenon_H6b zenon_Hb1 zenon_Hf6 zenon_H1bd zenon_H5e zenon_Hde zenon_Hc9 zenon_H200 zenon_H20e zenon_H19a zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H60 zenon_H155 zenon_H156. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.69 apply (zenon_L2054_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.69 apply (zenon_L2225_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.69 apply (zenon_L225_); trivial. % 30.58/30.69 apply (zenon_L2057_); trivial. % 30.58/30.69 (* end of lemma zenon_L2300_ *) % 30.58/30.69 assert (zenon_L2301_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.58/30.69 do 0 intro. intros zenon_H208 zenon_H20d zenon_H6b zenon_Hb1 zenon_Hf6 zenon_H1bd zenon_H5e zenon_Hde zenon_Hc9 zenon_H200 zenon_H20e zenon_H19a zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_Hd6 zenon_H3d zenon_H1af zenon_H231. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.69 apply (zenon_L2055_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.69 apply (zenon_L2225_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.69 apply (zenon_L225_); trivial. % 30.58/30.69 apply (zenon_L2058_); trivial. % 30.58/30.69 (* end of lemma zenon_L2301_ *) % 30.58/30.69 assert (zenon_L2302_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H200 zenon_Hde zenon_H40 zenon_H1af zenon_H222 zenon_H19a zenon_H20e zenon_H1bd zenon_H5e zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H1d2 zenon_Hc9 zenon_H20d zenon_H231 zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.58/30.69 apply (zenon_L49_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.69 apply (zenon_L2055_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.69 apply (zenon_L608_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.69 apply (zenon_L225_); trivial. % 30.58/30.69 apply (zenon_L1337_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.58/30.69 exact (zenon_H260 zenon_H142). % 30.58/30.69 apply (zenon_L690_); trivial. % 30.58/30.69 (* end of lemma zenon_L2302_ *) % 30.58/30.69 assert (zenon_L2303_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_He1 zenon_Hfd zenon_Hd6 zenon_H108 zenon_H200 zenon_Hde zenon_H1af zenon_H222 zenon_H19a zenon_H20e zenon_H1bd zenon_H5e zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H1d2 zenon_Hc9 zenon_H20d zenon_H231 zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.69 apply (zenon_L4_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.69 apply (zenon_L158_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.69 apply (zenon_L2301_); trivial. % 30.58/30.69 apply (zenon_L2302_); trivial. % 30.58/30.69 (* end of lemma zenon_L2303_ *) % 30.58/30.69 assert (zenon_L2304_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H231 zenon_H1af zenon_Hd6 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H19a zenon_H20e zenon_H200 zenon_Hc9 zenon_Hde zenon_H5e zenon_H1bd zenon_Hf6 zenon_Hb1 zenon_H6b zenon_H20d zenon_H208 zenon_He1 zenon_H9d. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.69 apply (zenon_L4_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.69 apply (zenon_L320_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.69 apply (zenon_L2301_); trivial. % 30.58/30.69 apply (zenon_L1354_); trivial. % 30.58/30.69 (* end of lemma zenon_L2304_ *) % 30.58/30.69 assert (zenon_L2305_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 30.58/30.69 do 0 intro. intros zenon_H101 zenon_H3c zenon_H1d5 zenon_H222 zenon_H42 zenon_H2d zenon_H1e zenon_H231 zenon_H1af zenon_Hd6 zenon_H1d2 zenon_H260 zenon_H108 zenon_Hd0 zenon_H60 zenon_H156 zenon_H218 zenon_H267 zenon_H19a zenon_H20e zenon_H200 zenon_Hc9 zenon_Hde zenon_H5e zenon_H1bd zenon_Hf6 zenon_Hb1 zenon_H6b zenon_H20d zenon_H208 zenon_He1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.69 apply (zenon_L2214_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.69 apply (zenon_L2303_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.69 apply (zenon_L282_); trivial. % 30.58/30.69 apply (zenon_L2304_); trivial. % 30.58/30.69 (* end of lemma zenon_L2305_ *) % 30.58/30.69 assert (zenon_L2306_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H42 zenon_H1d5 zenon_Haa zenon_H113 zenon_H90 zenon_H97 zenon_H3f zenon_He1 zenon_Hfd zenon_Hd6 zenon_H108 zenon_H200 zenon_Hde zenon_H1af zenon_H222 zenon_H19a zenon_H20e zenon_H1bd zenon_H5e zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H1d2 zenon_Hc9 zenon_H20d zenon_H231 zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.69 apply (zenon_L2226_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.69 apply (zenon_L158_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.69 apply (zenon_L2301_); trivial. % 30.58/30.69 apply (zenon_L2302_); trivial. % 30.58/30.69 (* end of lemma zenon_L2306_ *) % 30.58/30.69 assert (zenon_L2307_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H42 zenon_He1 zenon_H1d5 zenon_Haa zenon_H113 zenon_H90 zenon_H97 zenon_H3f zenon_H9d zenon_Hd6 zenon_H108 zenon_H200 zenon_Hde zenon_H1af zenon_H222 zenon_H19a zenon_H20e zenon_H1bd zenon_H5e zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H1d2 zenon_Hc9 zenon_H20d zenon_H231 zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.58/30.69 apply (zenon_L2226_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.58/30.69 apply (zenon_L320_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.58/30.69 apply (zenon_L2301_); trivial. % 30.58/30.69 apply (zenon_L2302_); trivial. % 30.58/30.69 (* end of lemma zenon_L2307_ *) % 30.58/30.69 assert (zenon_L2308_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H101 zenon_H3c zenon_H1ba zenon_H42 zenon_He1 zenon_H1d5 zenon_Haa zenon_H113 zenon_H90 zenon_H97 zenon_H3f zenon_Hd6 zenon_H108 zenon_H200 zenon_Hde zenon_H1af zenon_H222 zenon_H19a zenon_H20e zenon_H1bd zenon_H5e zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H1d2 zenon_Hc9 zenon_H20d zenon_H231 zenon_H208 zenon_H260 zenon_Hf6 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.69 apply (zenon_L2072_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.69 apply (zenon_L2306_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.69 apply (zenon_L282_); trivial. % 30.58/30.69 apply (zenon_L2307_); trivial. % 30.58/30.69 (* end of lemma zenon_L2308_ *) % 30.58/30.69 assert (zenon_L2309_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H301 zenon_H113 zenon_Haa zenon_H97 zenon_H19e zenon_H296 zenon_H8d zenon_Hfc zenon_H16f zenon_H2fc zenon_H17d zenon_Hb8 zenon_Hcd zenon_H173 zenon_H2fb zenon_H20 zenon_H92 zenon_Hd6 zenon_H1af zenon_H42 zenon_H222 zenon_H1d5 zenon_H3c zenon_H101 zenon_H1dc zenon_Hd0 zenon_H108 zenon_H260 zenon_H1d2 zenon_H19a zenon_H20e zenon_H200 zenon_Hc9 zenon_Hde zenon_H5e zenon_H1bd zenon_Hf6 zenon_H6b zenon_H208 zenon_H60 zenon_H218 zenon_H6f zenon_H2d zenon_H1fd zenon_Hf9 zenon_H1d8 zenon_H3f zenon_H20d zenon_H156 zenon_He1 zenon_H267 zenon_H231 zenon_Hc8 zenon_H225 zenon_Ha4 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.58/30.69 apply (zenon_L912_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.58/30.69 apply (zenon_L48_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.58/30.69 apply (zenon_L2298_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.58/30.69 apply (zenon_L2214_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.58/30.69 apply (zenon_L58_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.58/30.69 apply (zenon_L282_); trivial. % 30.58/30.69 apply (zenon_L2299_); trivial. % 30.58/30.69 apply (zenon_L2300_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.58/30.69 apply (zenon_L18_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.58/30.69 apply (zenon_L273_); trivial. % 30.58/30.69 exact (zenon_H2fb zenon_H8a). % 30.58/30.69 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.58/30.69 apply (zenon_L2055_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.58/30.69 apply (zenon_L2305_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.58/30.69 apply (zenon_L2167_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.58/30.69 apply (zenon_L2308_); trivial. % 30.58/30.69 apply (zenon_L798_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.58/30.69 apply (zenon_L2305_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.58/30.69 apply (zenon_L2291_); trivial. % 30.58/30.69 apply (zenon_L869_); trivial. % 30.58/30.69 (* end of lemma zenon_L2309_ *) % 30.58/30.69 assert (zenon_L2310_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 30.58/30.69 do 0 intro. intros zenon_H25c zenon_H301 zenon_Ha4 zenon_H1fd zenon_H225 zenon_H20 zenon_H8d zenon_Hcd zenon_H16f zenon_Hc8 zenon_Hb8 zenon_H2d zenon_Hde zenon_Hc9 zenon_H208 zenon_H108 zenon_H1d8 zenon_H60 zenon_H2fc zenon_Hb1 zenon_H17d zenon_Hf9 zenon_H5e zenon_H1bd zenon_H260 zenon_H6b zenon_H1dc zenon_H1d2 zenon_Hf6 zenon_H200 zenon_H222 zenon_H2fb zenon_H267 zenon_H20d zenon_H156 zenon_H218 zenon_H1af zenon_H1d5 zenon_H19a zenon_He1 zenon_H6f zenon_H101 zenon_Hfc zenon_Hd6 zenon_H3c zenon_H20e zenon_H173 zenon_H296 zenon_Haa zenon_H3f zenon_H97 zenon_H113 zenon_H19e zenon_H42 zenon_H92 zenon_H25b. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.58/30.69 apply (zenon_L2309_); trivial. % 30.58/30.69 apply (zenon_L2289_); trivial. % 30.58/30.69 apply (zenon_L552_); trivial. % 30.58/30.69 (* end of lemma zenon_L2310_ *) % 30.58/30.69 assert (zenon_L2311_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H1fd zenon_H10d zenon_H97 zenon_Hb9 zenon_Hee zenon_H2c zenon_H3f zenon_H2fb zenon_Hb8 zenon_H1db zenon_Hb5 zenon_Hb3 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.69 apply (zenon_L1426_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.69 apply (zenon_L1427_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.69 exact (zenon_H1db zenon_H1b9). % 30.58/30.69 apply (zenon_L37_); trivial. % 30.58/30.69 (* end of lemma zenon_L2311_ *) % 30.58/30.69 assert (zenon_L2312_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H1fd zenon_Hb9 zenon_H10d zenon_H97 zenon_H2fb zenon_Hb8 zenon_H37 zenon_Hfc zenon_H1db zenon_Hb5 zenon_Hb3 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.69 apply (zenon_L1426_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.69 apply (zenon_L203_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.69 exact (zenon_H1db zenon_H1b9). % 30.58/30.69 apply (zenon_L37_); trivial. % 30.58/30.69 (* end of lemma zenon_L2312_ *) % 30.58/30.69 assert (zenon_L2313_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e0)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H1fd zenon_H10d zenon_H97 zenon_Hb9 zenon_Hee zenon_H3d zenon_H222 zenon_H2fb zenon_Hb8 zenon_H1db zenon_Hb5 zenon_Hb3 zenon_Hb1. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.58/30.69 apply (zenon_L1426_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.58/30.69 apply (zenon_L1428_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.58/30.69 exact (zenon_H1db zenon_H1b9). % 30.58/30.69 apply (zenon_L37_); trivial. % 30.58/30.69 (* end of lemma zenon_L2313_ *) % 30.58/30.69 assert (zenon_L2314_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H56 zenon_H55 zenon_Hd6 zenon_H27 zenon_H36 zenon_H17b. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.58/30.69 exact (zenon_H260 zenon_H142). % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.58/30.69 exact (zenon_H56 zenon_H25). % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.58/30.69 apply (zenon_L555_); trivial. % 30.58/30.69 apply (zenon_L1141_); trivial. % 30.58/30.69 (* end of lemma zenon_L2314_ *) % 30.58/30.69 assert (zenon_L2315_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H225 zenon_Hcd zenon_H88 zenon_H198 zenon_H65 zenon_Hde zenon_H10e zenon_H1d2 zenon_H260 zenon_H56 zenon_H55 zenon_Hd6 zenon_H27 zenon_H36. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.58/30.69 apply (zenon_L998_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.58/30.69 apply (zenon_L818_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.58/30.69 apply (zenon_L192_); trivial. % 30.58/30.69 apply (zenon_L2314_); trivial. % 30.58/30.69 (* end of lemma zenon_L2315_ *) % 30.58/30.69 assert (zenon_L2316_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e1)) = (e3)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H208 zenon_H88 zenon_Hc8 zenon_H55 zenon_Hcd zenon_H56 zenon_H218 zenon_H188 zenon_H2c. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.58/30.69 apply (zenon_L809_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.58/30.69 apply (zenon_L212_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.58/30.69 exact (zenon_H56 zenon_H25). % 30.58/30.69 apply (zenon_L1132_); trivial. % 30.58/30.69 (* end of lemma zenon_L2316_ *) % 30.58/30.69 assert (zenon_L2317_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H267 zenon_H36 zenon_H27 zenon_Hd6 zenon_H56 zenon_H260 zenon_H1d2 zenon_H16a zenon_H55 zenon_H1c7 zenon_Ha4 zenon_H198 zenon_H117. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.58/30.69 apply (zenon_L2314_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.58/30.69 apply (zenon_L1004_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.58/30.69 apply (zenon_L1253_); trivial. % 30.58/30.69 apply (zenon_L1006_); trivial. % 30.58/30.69 (* end of lemma zenon_L2317_ *) % 30.58/30.69 assert (zenon_L2318_ : (((op (e1) (op (e1) (e0))) = (e0))/\(((op (e1) (op (e1) (e1))) = (e1))/\(((op (e1) (op (e1) (e2))) = (e2))/\(((op (e1) (op (e1) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2)))/\((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3)))))))))) -> (~((op (e0) (e1)) = (e0))) -> ((op (e0) (e0)) = (e1)) -> False). % 30.58/30.69 do 0 intro. intros zenon_H45 zenon_H317 zenon_H88. % 30.58/30.69 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.58/30.69 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.58/30.69 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.58/30.69 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.58/30.69 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.58/30.69 exact (zenon_H84 zenon_H88). % 30.58/30.69 exact (zenon_H317 zenon_H1e). % 30.58/30.69 (* end of lemma zenon_L2318_ *) % 30.58/30.69 assert (zenon_L2319_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.69 do 0 intro. intros zenon_H1d2 zenon_H55 zenon_H1bd zenon_H56 zenon_Hd0 zenon_H60 zenon_H17b zenon_H218. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.58/30.69 apply (zenon_L165_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.58/30.69 exact (zenon_H56 zenon_H25). % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.58/30.69 exact (zenon_Hd0 zenon_Hcc). % 30.58/30.69 apply (zenon_L259_); trivial. % 30.58/30.69 (* end of lemma zenon_L2319_ *) % 30.58/30.69 assert (zenon_L2320_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.58/30.69 do 0 intro. intros zenon_H1d2 zenon_H55 zenon_H1bd zenon_H56 zenon_Hd0 zenon_H60 zenon_H155 zenon_H156. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.58/30.69 apply (zenon_L165_); trivial. % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.58/30.69 exact (zenon_H56 zenon_H25). % 30.58/30.69 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.58/30.69 exact (zenon_Hd0 zenon_Hcc). % 30.58/30.69 apply (zenon_L179_); trivial. % 30.58/30.69 (* end of lemma zenon_L2320_ *) % 30.58/30.69 assert (zenon_L2321_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H267 zenon_H218 zenon_H156 zenon_H60 zenon_Hd0 zenon_H56 zenon_H1bd zenon_H55 zenon_H1d2 zenon_H20e zenon_H15e zenon_H1af zenon_H231. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.63/30.70 apply (zenon_L2319_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.63/30.70 apply (zenon_L2320_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.63/30.70 apply (zenon_L358_); trivial. % 30.63/30.70 exact (zenon_H231 zenon_Hf4). % 30.63/30.70 (* end of lemma zenon_L2321_ *) % 30.63/30.70 assert (zenon_L2322_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1d2 zenon_H6b zenon_Hdf zenon_H56 zenon_Hd0 zenon_H60 zenon_H55 zenon_H1c7. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.70 apply (zenon_L303_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.70 exact (zenon_Hd0 zenon_Hcc). % 30.63/30.70 apply (zenon_L216_); trivial. % 30.63/30.70 (* end of lemma zenon_L2322_ *) % 30.63/30.70 assert (zenon_L2323_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1d2 zenon_Hd6 zenon_H1ba zenon_H56 zenon_Hd0 zenon_Hb6 zenon_H1dc. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.70 apply (zenon_L161_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.70 exact (zenon_Hd0 zenon_Hcc). % 30.63/30.70 apply (zenon_L200_); trivial. % 30.63/30.70 (* end of lemma zenon_L2323_ *) % 30.63/30.70 assert (zenon_L2324_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1d2 zenon_H1e1 zenon_H108 zenon_H56 zenon_Hd0 zenon_H60 zenon_H55 zenon_H1c7. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.70 apply (zenon_L296_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.70 exact (zenon_Hd0 zenon_Hcc). % 30.63/30.70 apply (zenon_L216_); trivial. % 30.63/30.70 (* end of lemma zenon_L2324_ *) % 30.63/30.70 assert (zenon_L2325_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H200 zenon_H6b zenon_H1dc zenon_Hb6 zenon_Hd6 zenon_H1bd zenon_H1d2 zenon_H108 zenon_H56 zenon_Hd0 zenon_H60 zenon_H55 zenon_H1c7. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.63/30.70 apply (zenon_L2322_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.63/30.70 apply (zenon_L2323_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.63/30.70 apply (zenon_L165_); trivial. % 30.63/30.70 apply (zenon_L2324_); trivial. % 30.63/30.70 (* end of lemma zenon_L2325_ *) % 30.63/30.70 assert (zenon_L2326_ : (((op (e2) (op (e2) (e0))) = (e0))/\(((op (e2) (op (e2) (e1))) = (e1))/\(((op (e2) (op (e2) (e2))) = (e2))/\(((op (e2) (op (e2) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0)))/\(((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3)))))))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H5a zenon_H1fd zenon_H6b zenon_H1dc zenon_Hd6 zenon_H108 zenon_H200 zenon_H1c7 zenon_H20e zenon_H1d2 zenon_H218 zenon_H56 zenon_H55 zenon_H1bd zenon_H156 zenon_H27 zenon_H267. % 30.63/30.70 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.63/30.70 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.63/30.70 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.63/30.70 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.63/30.70 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.63/30.70 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.63/30.70 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.63/30.70 apply (zenon_L2319_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.63/30.70 apply (zenon_L2320_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.63/30.70 apply (zenon_L183_); trivial. % 30.63/30.70 exact (zenon_H231 zenon_Hf4). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.70 apply (zenon_L2321_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.70 apply (zenon_L216_); trivial. % 30.63/30.70 apply (zenon_L2325_); trivial. % 30.63/30.70 apply (zenon_L2325_); trivial. % 30.63/30.70 apply (zenon_L575_); trivial. % 30.63/30.70 (* end of lemma zenon_L2326_ *) % 30.63/30.70 assert (zenon_L2327_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1d2 zenon_H6b zenon_Hdf zenon_H56 zenon_H55 zenon_Hd6 zenon_H1db. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.70 apply (zenon_L303_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.70 apply (zenon_L555_); trivial. % 30.63/30.70 exact (zenon_H1db zenon_H1b9). % 30.63/30.70 (* end of lemma zenon_L2327_ *) % 30.63/30.70 assert (zenon_L2328_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1d2 zenon_H1ba zenon_H56 zenon_H55 zenon_Hd6 zenon_H1db. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.70 apply (zenon_L161_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.70 apply (zenon_L555_); trivial. % 30.63/30.70 exact (zenon_H1db zenon_H1b9). % 30.63/30.70 (* end of lemma zenon_L2328_ *) % 30.63/30.70 assert (zenon_L2329_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> False). % 30.63/30.70 do 0 intro. intros zenon_H30b zenon_Hb3 zenon_H112 zenon_Hb6. % 30.63/30.70 cut (((op (e3) (op (e3) (e3))) = (e3)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 30.63/30.70 intro zenon_D_pnotp. % 30.63/30.70 apply zenon_H30b. % 30.63/30.70 rewrite <- zenon_D_pnotp. % 30.63/30.70 exact zenon_Hb3. % 30.63/30.70 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 30.63/30.70 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26e]. % 30.63/30.70 congruence. % 30.63/30.70 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H1b5 ]. % 30.63/30.70 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (op (e3) (e3))) = (op (e3) (e1)))). % 30.63/30.70 intro zenon_D_pnotp. % 30.63/30.70 apply zenon_H26e. % 30.63/30.70 rewrite <- zenon_D_pnotp. % 30.63/30.70 exact zenon_H1b4. % 30.63/30.70 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 30.63/30.70 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H26c]. % 30.63/30.70 congruence. % 30.63/30.70 apply (zenon_L719_); trivial. % 30.63/30.70 apply zenon_H1b5. apply refl_equal. % 30.63/30.70 apply zenon_H1b5. apply refl_equal. % 30.63/30.70 apply zenon_Hb7. apply sym_equal. exact zenon_Hb6. % 30.63/30.70 (* end of lemma zenon_L2329_ *) % 30.63/30.70 assert (zenon_L2330_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H11b zenon_Hb5 zenon_Hb6 zenon_Hb3 zenon_H30b zenon_H1e5 zenon_H142 zenon_Hb9. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.63/30.70 apply (zenon_L37_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.63/30.70 apply (zenon_L2329_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.63/30.70 apply (zenon_L944_); trivial. % 30.63/30.70 exact (zenon_Hb9 zenon_Hbc). % 30.63/30.70 (* end of lemma zenon_L2330_ *) % 30.63/30.70 assert (zenon_L2331_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H10e zenon_H6f zenon_H19a zenon_H1db zenon_H11b zenon_Hb5 zenon_Hb3 zenon_H30b zenon_H1e5 zenon_H142 zenon_Hb9. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.70 apply (zenon_L87_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.70 apply (zenon_L235_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.70 exact (zenon_H1db zenon_H1b9). % 30.63/30.70 apply (zenon_L2330_); trivial. % 30.63/30.70 (* end of lemma zenon_L2331_ *) % 30.63/30.70 assert (zenon_L2332_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1d2 zenon_H1e1 zenon_H108 zenon_H56 zenon_H55 zenon_Hd6 zenon_H1db. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.70 apply (zenon_L296_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.70 apply (zenon_L555_); trivial. % 30.63/30.70 exact (zenon_H1db zenon_H1b9). % 30.63/30.70 (* end of lemma zenon_L2332_ *) % 30.63/30.70 assert (zenon_L2333_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> False). % 30.63/30.70 do 0 intro. intros zenon_H23b zenon_H88 zenon_He7 zenon_Hb9 zenon_H117 zenon_H10d zenon_H6f zenon_H6e zenon_Had zenon_Hb8 zenon_H19a zenon_Hee zenon_Hf6 zenon_H1e5. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.63/30.70 apply (zenon_L1053_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.63/30.70 apply (zenon_L1494_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.63/30.70 apply (zenon_L337_); trivial. % 30.63/30.70 apply (zenon_L187_); trivial. % 30.63/30.70 (* end of lemma zenon_L2333_ *) % 30.63/30.70 assert (zenon_L2334_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1a2 zenon_Hd9 zenon_H1e5 zenon_Hf6 zenon_Hee zenon_Hb8 zenon_Had zenon_H6e zenon_H6f zenon_H10d zenon_H117 zenon_Hb9 zenon_He7 zenon_H88 zenon_H23b zenon_H56 zenon_H9b zenon_H55 zenon_H222. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.63/30.70 apply (zenon_L797_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.63/30.70 apply (zenon_L2333_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_L1297_); trivial. % 30.63/30.70 (* end of lemma zenon_L2334_ *) % 30.63/30.70 assert (zenon_L2335_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1fd zenon_H222 zenon_H55 zenon_H9b zenon_H56 zenon_H23b zenon_H88 zenon_He7 zenon_H10d zenon_H6e zenon_Had zenon_Hb8 zenon_Hee zenon_Hf6 zenon_Hd9 zenon_H1a2 zenon_H6f zenon_H19a zenon_H1db zenon_H11b zenon_Hb5 zenon_Hb3 zenon_H30b zenon_H1e5 zenon_H142 zenon_Hb9. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.70 apply (zenon_L2334_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.70 apply (zenon_L235_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.70 exact (zenon_H1db zenon_H1b9). % 30.63/30.70 apply (zenon_L2330_); trivial. % 30.63/30.70 (* end of lemma zenon_L2335_ *) % 30.63/30.70 assert (zenon_L2336_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H200 zenon_H6b zenon_H222 zenon_H9b zenon_H1fd zenon_H23b zenon_H88 zenon_He7 zenon_H10d zenon_H6e zenon_Had zenon_Hb8 zenon_Hee zenon_Hf6 zenon_Hd9 zenon_H1a2 zenon_H6f zenon_H11b zenon_Hb5 zenon_Hb3 zenon_H30b zenon_Hb9 zenon_Hcd zenon_Hc8 zenon_H208 zenon_H1d2 zenon_H108 zenon_H56 zenon_H55 zenon_Hd6 zenon_H1db. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.63/30.70 apply (zenon_L2327_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.63/30.70 apply (zenon_L2328_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.63/30.70 apply (zenon_L809_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.63/30.70 apply (zenon_L212_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.63/30.70 apply (zenon_L797_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.63/30.70 apply (zenon_L2335_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_L1297_); trivial. % 30.63/30.70 apply (zenon_L2332_); trivial. % 30.63/30.70 (* end of lemma zenon_L2336_ *) % 30.63/30.70 assert (zenon_L2337_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_Hf9 zenon_Hde zenon_H8b zenon_H55 zenon_H222 zenon_Hda zenon_Hb3 zenon_H117 zenon_H10d. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.63/30.70 apply (zenon_L288_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.63/30.70 apply (zenon_L264_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.63/30.70 apply (zenon_L64_); trivial. % 30.63/30.70 apply (zenon_L68_); trivial. % 30.63/30.70 (* end of lemma zenon_L2337_ *) % 30.63/30.70 assert (zenon_L2338_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1fd zenon_H10d zenon_Hb3 zenon_Hda zenon_H6f zenon_H19a zenon_H1db zenon_Hf9 zenon_Hde zenon_H8b zenon_H55 zenon_H222 zenon_He1 zenon_H142 zenon_H1e5. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.70 apply (zenon_L2337_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.70 apply (zenon_L235_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.70 exact (zenon_H1db zenon_H1b9). % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.63/30.70 apply (zenon_L288_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.63/30.70 apply (zenon_L264_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.63/30.70 apply (zenon_L204_); trivial. % 30.63/30.70 apply (zenon_L944_); trivial. % 30.63/30.70 (* end of lemma zenon_L2338_ *) % 30.63/30.70 assert (zenon_L2339_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 30.63/30.70 do 0 intro. intros zenon_H208 zenon_H88 zenon_Hc8 zenon_Hcd zenon_H56 zenon_Hbd zenon_He1 zenon_H222 zenon_H55 zenon_Hde zenon_Hf9 zenon_H1db zenon_H19a zenon_H6f zenon_Hda zenon_Hb3 zenon_H1fd zenon_Hb9 zenon_H117 zenon_H10d zenon_H2d zenon_H76 zenon_H1d8 zenon_Hb8 zenon_H142 zenon_H1dc zenon_Ha4 zenon_H185. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.63/30.70 apply (zenon_L809_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.63/30.70 apply (zenon_L212_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.63/30.70 apply (zenon_L2338_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.63/30.70 apply (zenon_L1269_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.63/30.70 apply (zenon_L177_); trivial. % 30.63/30.70 apply (zenon_L869_); trivial. % 30.63/30.70 (* end of lemma zenon_L2339_ *) % 30.63/30.70 assert (zenon_L2340_ : ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H185 zenon_Ha4 zenon_H1dc zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H2d zenon_H10d zenon_H1fd zenon_Hda zenon_Hf9 zenon_Hde zenon_H55 zenon_H222 zenon_He1 zenon_Hbd zenon_H56 zenon_Hcd zenon_Hc8 zenon_H88 zenon_H208 zenon_H6f zenon_H19a zenon_H1db zenon_H11b zenon_Hb5 zenon_Hb3 zenon_H30b zenon_H1e5 zenon_H142 zenon_Hb9. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.70 apply (zenon_L2339_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.70 apply (zenon_L235_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.70 exact (zenon_H1db zenon_H1b9). % 30.63/30.70 apply (zenon_L2330_); trivial. % 30.63/30.70 (* end of lemma zenon_L2340_ *) % 30.63/30.70 assert (zenon_L2341_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (op (e3) (e2))) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H200 zenon_H6b zenon_H222 zenon_H9b zenon_H185 zenon_Ha4 zenon_H1dc zenon_Hb8 zenon_H1d8 zenon_H76 zenon_H2d zenon_H10d zenon_H1fd zenon_Hda zenon_Hf9 zenon_Hde zenon_He1 zenon_Hbd zenon_Hcd zenon_Hc8 zenon_H88 zenon_H208 zenon_H6f zenon_H11b zenon_Hb5 zenon_Hb3 zenon_H30b zenon_Hb9 zenon_Hd9 zenon_H1a2 zenon_H1d2 zenon_H108 zenon_H56 zenon_H55 zenon_Hd6 zenon_H1db. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.63/30.70 apply (zenon_L2327_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.63/30.70 apply (zenon_L2328_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.63/30.70 apply (zenon_L809_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.63/30.70 apply (zenon_L212_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.63/30.70 apply (zenon_L797_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.63/30.70 apply (zenon_L2340_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_L1297_); trivial. % 30.63/30.70 apply (zenon_L2332_); trivial. % 30.63/30.70 (* end of lemma zenon_L2341_ *) % 30.63/30.70 assert (zenon_L2342_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_Hf9 zenon_H8a zenon_He1 zenon_H55 zenon_H222 zenon_Hda zenon_Hb3 zenon_H117 zenon_H10d. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.63/30.70 apply (zenon_L50_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.63/30.70 apply (zenon_L264_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.63/30.70 apply (zenon_L64_); trivial. % 30.63/30.70 apply (zenon_L68_); trivial. % 30.63/30.70 (* end of lemma zenon_L2342_ *) % 30.63/30.70 assert (zenon_L2343_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1fd zenon_H10d zenon_Hb3 zenon_Hda zenon_H222 zenon_H55 zenon_He1 zenon_Hf9 zenon_H6f zenon_H19a zenon_H1db zenon_H8a zenon_Hb5. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.70 apply (zenon_L2342_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.70 apply (zenon_L235_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.70 exact (zenon_H1db zenon_H1b9). % 30.63/30.70 apply (zenon_L461_); trivial. % 30.63/30.70 (* end of lemma zenon_L2343_ *) % 30.63/30.70 assert (zenon_L2344_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (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))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H225 zenon_H3c zenon_H222 zenon_H55 zenon_H9b zenon_H56 zenon_H1fd zenon_H10d zenon_Hb3 zenon_He1 zenon_Hf9 zenon_H6f zenon_H1db zenon_Hb5 zenon_H88 zenon_Hd9 zenon_H1a2 zenon_H200 zenon_H6b zenon_Ha4 zenon_H1dc zenon_Hb8 zenon_H1d8 zenon_H2d zenon_Hbd zenon_Hcd zenon_Hc8 zenon_H208 zenon_H11b zenon_H30b zenon_Hb9 zenon_H1d2 zenon_H108 zenon_Hd6 zenon_H23b zenon_He7 zenon_Had zenon_Hee zenon_Hf6 zenon_H8d zenon_H185 zenon_Hde. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.63/30.70 apply (zenon_L998_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.63/30.70 apply (zenon_L88_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.63/30.70 apply (zenon_L734_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.63/30.70 apply (zenon_L2336_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.63/30.70 apply (zenon_L2341_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.63/30.70 apply (zenon_L797_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.63/30.70 apply (zenon_L2343_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_L1297_); trivial. % 30.63/30.70 apply (zenon_L817_); trivial. % 30.63/30.70 (* end of lemma zenon_L2344_ *) % 30.63/30.70 assert (zenon_L2345_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1d2 zenon_H9c zenon_H1dc zenon_H56 zenon_H55 zenon_Hd6 zenon_H1db. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.70 apply (zenon_L177_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.70 apply (zenon_L555_); trivial. % 30.63/30.70 exact (zenon_H1db zenon_H1b9). % 30.63/30.70 (* end of lemma zenon_L2345_ *) % 30.63/30.70 assert (zenon_L2346_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (op (e3) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((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))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H225 zenon_Hcd zenon_H3c zenon_H222 zenon_H55 zenon_H9b zenon_H56 zenon_H2b7 zenon_H1db zenon_Hd6 zenon_H1dc zenon_H1d2 zenon_Hee zenon_H10d zenon_H110 zenon_Hbc zenon_H88 zenon_Hd9 zenon_H1a2 zenon_H185 zenon_Hde. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.63/30.70 apply (zenon_L998_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.63/30.70 apply (zenon_L88_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.63/30.70 apply (zenon_L797_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H9c | zenon_intro zenon_H2b8 ]. % 30.63/30.70 apply (zenon_L2345_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H2b9 ]. % 30.63/30.70 apply (zenon_L337_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hb6 ]. % 30.63/30.70 apply (zenon_L64_); trivial. % 30.63/30.70 apply (zenon_L1303_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_L1297_); trivial. % 30.63/30.70 apply (zenon_L817_); trivial. % 30.63/30.70 (* end of lemma zenon_L2346_ *) % 30.63/30.70 assert (zenon_L2347_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H56 zenon_H55 zenon_Hd6 zenon_Hb6 zenon_H1dc. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.70 exact (zenon_H260 zenon_H142). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.70 apply (zenon_L555_); trivial. % 30.63/30.70 apply (zenon_L200_); trivial. % 30.63/30.70 (* end of lemma zenon_L2347_ *) % 30.63/30.70 assert (zenon_L2348_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1a8 zenon_H18c zenon_H18e zenon_He1 zenon_H188 zenon_H42 zenon_H1dc zenon_Hd6 zenon_H55 zenon_H56 zenon_H260 zenon_H1d2 zenon_H6c zenon_H73 zenon_H6f zenon_H267 zenon_H36 zenon_H27 zenon_H16a zenon_H1c7 zenon_Ha4 zenon_H198 zenon_H1fd zenon_H112 zenon_H14e. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.63/30.70 apply (zenon_L120_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.63/30.70 apply (zenon_L127_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.70 apply (zenon_L2317_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.70 apply (zenon_L235_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.70 apply (zenon_L244_); trivial. % 30.63/30.70 apply (zenon_L2347_); trivial. % 30.63/30.70 apply (zenon_L137_); trivial. % 30.63/30.70 (* end of lemma zenon_L2348_ *) % 30.63/30.70 assert (zenon_L2349_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 30.63/30.70 do 0 intro. intros zenon_H208 zenon_H14e zenon_H1fd zenon_H198 zenon_Ha4 zenon_H1c7 zenon_H16a zenon_H27 zenon_H36 zenon_H267 zenon_H6f zenon_H73 zenon_H1d2 zenon_H260 zenon_Hd6 zenon_H1dc zenon_H42 zenon_H188 zenon_He1 zenon_H18e zenon_H18c zenon_H1a8 zenon_H55 zenon_Hcd zenon_H56 zenon_Hf6 zenon_H112. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.63/30.70 apply (zenon_L2348_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.63/30.70 apply (zenon_L212_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_L187_); trivial. % 30.63/30.70 (* end of lemma zenon_L2349_ *) % 30.63/30.70 assert (zenon_L2350_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H56 zenon_H55 zenon_Hd6 zenon_H112 zenon_H9c. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.70 exact (zenon_H260 zenon_H142). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.70 exact (zenon_H56 zenon_H25). % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.70 apply (zenon_L555_); trivial. % 30.63/30.70 apply (zenon_L198_); trivial. % 30.63/30.70 (* end of lemma zenon_L2350_ *) % 30.63/30.70 assert (zenon_L2351_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H42 zenon_H188 zenon_H117 zenon_H198 zenon_Ha4 zenon_H10d zenon_Hda zenon_H8a zenon_Hf9 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hd6 zenon_H112 zenon_H222 zenon_H2d zenon_Hbd zenon_He1 zenon_H55 zenon_H18e. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.70 apply (zenon_L124_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.63/30.70 apply (zenon_L25_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.63/30.70 apply (zenon_L1539_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.63/30.70 apply (zenon_L2350_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.63/30.70 apply (zenon_L50_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.63/30.70 apply (zenon_L320_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.63/30.70 apply (zenon_L64_); trivial. % 30.63/30.70 apply (zenon_L1006_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.70 apply (zenon_L126_); trivial. % 30.63/30.70 exact (zenon_H18e zenon_H40). % 30.63/30.70 (* end of lemma zenon_L2351_ *) % 30.63/30.70 assert (zenon_L2352_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H42 zenon_H112 zenon_H188 zenon_Ha4 zenon_H15e zenon_Hfc zenon_He1 zenon_H55 zenon_H18e. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.70 apply (zenon_L124_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.70 apply (zenon_L203_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.70 apply (zenon_L126_); trivial. % 30.63/30.70 exact (zenon_H18e zenon_H40). % 30.63/30.70 (* end of lemma zenon_L2352_ *) % 30.63/30.70 assert (zenon_L2353_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.63/30.70 do 0 intro. intros zenon_H16f zenon_Had zenon_H8a zenon_Hd2 zenon_H6f zenon_H18e zenon_H55 zenon_He1 zenon_Hfc zenon_Ha4 zenon_H188 zenon_H112 zenon_H42 zenon_H16a zenon_H36 zenon_H16b. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.70 apply (zenon_L34_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.70 apply (zenon_L125_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.70 apply (zenon_L2352_); trivial. % 30.63/30.70 apply (zenon_L1541_); trivial. % 30.63/30.70 (* end of lemma zenon_L2353_ *) % 30.63/30.70 assert (zenon_L2354_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H174 zenon_He7 zenon_Hd6 zenon_H56 zenon_H260 zenon_H1d2 zenon_H1a8 zenon_Hcd zenon_Hdc zenon_H42 zenon_H188 zenon_Ha4 zenon_Hfc zenon_H18e zenon_H36 zenon_H16a zenon_H6f zenon_H1d5 zenon_H1d8 zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H256 zenon_Hf9 zenon_H8a zenon_He1 zenon_H55 zenon_H222 zenon_Hda zenon_H198 zenon_H10d zenon_H2d zenon_Hbd zenon_H218 zenon_Had zenon_H16f zenon_H112 zenon_H14e. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.63/30.70 apply (zenon_L199_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.63/30.70 apply (zenon_L124_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.63/30.70 apply (zenon_L2351_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.63/30.70 apply (zenon_L48_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.63/30.70 apply (zenon_L2353_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.70 apply (zenon_L34_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.70 apply (zenon_L174_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.70 apply (zenon_L126_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.70 apply (zenon_L1543_); trivial. % 30.63/30.70 apply (zenon_L1038_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.70 apply (zenon_L235_); trivial. % 30.63/30.70 apply (zenon_L1541_); trivial. % 30.63/30.70 apply (zenon_L137_); trivial. % 30.63/30.70 (* end of lemma zenon_L2354_ *) % 30.63/30.70 assert (zenon_L2355_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_Hb8 zenon_H14e zenon_H16f zenon_Had zenon_H218 zenon_Hbd zenon_H2d zenon_H10d zenon_H198 zenon_Hda zenon_H222 zenon_H55 zenon_He1 zenon_Hf9 zenon_H256 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H1d8 zenon_H1d5 zenon_H16a zenon_H36 zenon_Hfc zenon_Ha4 zenon_H188 zenon_H42 zenon_Hdc zenon_Hcd zenon_H1a8 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hd6 zenon_He7 zenon_H174 zenon_H18e zenon_H1dc zenon_H1b9 zenon_H112 zenon_H6f. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.63/30.70 apply (zenon_L2354_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.63/30.70 exact (zenon_H18e zenon_H40). % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.63/30.70 apply (zenon_L200_); trivial. % 30.63/30.70 apply (zenon_L152_); trivial. % 30.63/30.70 (* end of lemma zenon_L2355_ *) % 30.63/30.70 assert (zenon_L2356_ : ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1e zenon_H1dc zenon_Hd6 zenon_H56 zenon_H260 zenon_H1d2 zenon_Hb8 zenon_H14e zenon_H16f zenon_Had zenon_H218 zenon_Hbd zenon_H2d zenon_H10d zenon_H198 zenon_Hda zenon_H222 zenon_Hf9 zenon_H256 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H1d8 zenon_H1d5 zenon_H16a zenon_H36 zenon_Hfc zenon_Ha4 zenon_H188 zenon_H42 zenon_Hdc zenon_Hcd zenon_H1a8 zenon_He7 zenon_H174 zenon_H112 zenon_H6f zenon_H267 zenon_H27 zenon_H1c7 zenon_H1fd zenon_He1 zenon_H55 zenon_H18e. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.70 apply (zenon_L4_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.70 apply (zenon_L2317_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.70 apply (zenon_L203_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.70 apply (zenon_L2355_); trivial. % 30.63/30.70 apply (zenon_L2347_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.70 apply (zenon_L126_); trivial. % 30.63/30.70 exact (zenon_H18e zenon_H40). % 30.63/30.70 (* end of lemma zenon_L2356_ *) % 30.63/30.70 assert (zenon_L2357_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.63/30.70 do 0 intro. intros zenon_H1fd zenon_H155 zenon_H198 zenon_H16a zenon_H18e zenon_He1 zenon_Hfc zenon_Ha4 zenon_H188 zenon_H42 zenon_H122 zenon_H112 zenon_H3f zenon_H1e zenon_He2 zenon_Hde zenon_Hbd zenon_H1d2 zenon_H260 zenon_H56 zenon_H55 zenon_Hd6 zenon_H1dc. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.70 apply (zenon_L1004_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.70 apply (zenon_L2352_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.63/30.70 apply (zenon_L288_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.63/30.70 apply (zenon_L29_); trivial. % 30.63/30.70 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.63/30.70 apply (zenon_L198_); trivial. % 30.63/30.70 exact (zenon_H122 zenon_Hb1). % 30.63/30.70 apply (zenon_L2347_); trivial. % 30.63/30.70 (* end of lemma zenon_L2357_ *) % 30.63/30.70 assert (zenon_L2358_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H173 zenon_H1c7 zenon_H27 zenon_H267 zenon_H6f zenon_H174 zenon_He7 zenon_H1a8 zenon_Hcd zenon_H36 zenon_H1d5 zenon_H1d8 zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H256 zenon_Hf9 zenon_H222 zenon_H10d zenon_H2d zenon_H218 zenon_Had zenon_H16f zenon_H14e zenon_Hb8 zenon_H19e zenon_Hda zenon_H1a5 zenon_H1fd zenon_H198 zenon_H16a zenon_H18e zenon_He1 zenon_Hfc zenon_Ha4 zenon_H188 zenon_H42 zenon_H122 zenon_H112 zenon_H3f zenon_H1e zenon_He2 zenon_Hde zenon_Hbd zenon_H1d2 zenon_H260 zenon_H56 zenon_H55 zenon_Hd6 zenon_H1dc. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.71 apply (zenon_L2356_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.71 apply (zenon_L787_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.71 apply (zenon_L1030_); trivial. % 30.63/30.71 apply (zenon_L2357_); trivial. % 30.63/30.71 (* end of lemma zenon_L2358_ *) % 30.63/30.71 assert (zenon_L2359_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.63/30.71 do 0 intro. intros zenon_He4 zenon_Hd9 zenon_H1bd zenon_H173 zenon_H1c7 zenon_H27 zenon_H267 zenon_H6f zenon_H174 zenon_He7 zenon_H1a8 zenon_Hcd zenon_H36 zenon_H1d5 zenon_H1d8 zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H256 zenon_Hf9 zenon_H222 zenon_H10d zenon_H2d zenon_H218 zenon_Had zenon_H16f zenon_H14e zenon_Hb8 zenon_H19e zenon_Hda zenon_H1a5 zenon_H1fd zenon_H198 zenon_H16a zenon_H18e zenon_He1 zenon_Hfc zenon_Ha4 zenon_H188 zenon_H42 zenon_H122 zenon_H112 zenon_H3f zenon_H1e zenon_Hde zenon_Hbd zenon_H1d2 zenon_H260 zenon_H56 zenon_H55 zenon_Hd6 zenon_H1dc. % 30.63/30.71 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.63/30.71 apply (zenon_L47_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.63/30.71 apply (zenon_L2356_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.63/30.71 apply (zenon_L282_); trivial. % 30.63/30.71 apply (zenon_L2358_); trivial. % 30.63/30.71 (* end of lemma zenon_L2359_ *) % 30.63/30.71 assert (zenon_L2360_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H174 zenon_He1 zenon_H73 zenon_H112 zenon_H188 zenon_H198 zenon_Ha4 zenon_H1c7 zenon_H55 zenon_H16a zenon_H1d2 zenon_H260 zenon_H56 zenon_Hd6 zenon_H27 zenon_H36 zenon_H267 zenon_H185 zenon_H2d. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.63/30.71 apply (zenon_L232_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.63/30.71 apply (zenon_L124_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.63/30.71 apply (zenon_L2317_); trivial. % 30.63/30.71 apply (zenon_L848_); trivial. % 30.63/30.71 (* end of lemma zenon_L2360_ *) % 30.63/30.71 assert (zenon_L2361_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.63/30.71 do 0 intro. intros zenon_Hc8 zenon_H1fd zenon_H185 zenon_Hde zenon_H267 zenon_H6f zenon_H112 zenon_H18e zenon_H174 zenon_He7 zenon_H1a8 zenon_Hcd zenon_Hdc zenon_H42 zenon_H188 zenon_Ha4 zenon_Hfc zenon_H36 zenon_H16a zenon_H1d5 zenon_H1d8 zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H256 zenon_Hf9 zenon_He1 zenon_H222 zenon_Hda zenon_H198 zenon_H10d zenon_H2d zenon_Hbd zenon_H218 zenon_Had zenon_H16f zenon_H14e zenon_Hb8 zenon_H1d2 zenon_H260 zenon_H56 zenon_H55 zenon_Hd6 zenon_H1dc. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.71 apply (zenon_L1001_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.71 apply (zenon_L126_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.71 apply (zenon_L2355_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.71 apply (zenon_L1007_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.71 apply (zenon_L2352_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.71 apply (zenon_L2355_); trivial. % 30.63/30.71 apply (zenon_L2347_); trivial. % 30.63/30.71 (* end of lemma zenon_L2361_ *) % 30.63/30.71 assert (zenon_L2362_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H174 zenon_He2 zenon_H112 zenon_H188 zenon_H198 zenon_Ha4 zenon_H1c7 zenon_H55 zenon_H16a zenon_H1d2 zenon_H260 zenon_H56 zenon_Hd6 zenon_H27 zenon_H36 zenon_H267 zenon_H185 zenon_H2d. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.63/30.71 apply (zenon_L252_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.63/30.71 apply (zenon_L124_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.63/30.71 apply (zenon_L2317_); trivial. % 30.63/30.71 apply (zenon_L848_); trivial. % 30.63/30.71 (* end of lemma zenon_L2362_ *) % 30.63/30.71 assert (zenon_L2363_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H208 zenon_H68 zenon_H18c zenon_H55 zenon_Hcd zenon_H56 zenon_Hf6 zenon_H112. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.63/30.71 apply (zenon_L120_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.63/30.71 apply (zenon_L212_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.63/30.71 exact (zenon_H56 zenon_H25). % 30.63/30.71 apply (zenon_L187_); trivial. % 30.63/30.71 (* end of lemma zenon_L2363_ *) % 30.63/30.71 assert (zenon_L2364_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H16f zenon_Had zenon_H218 zenon_H6c zenon_H73 zenon_H19e zenon_H8a zenon_H1d8 zenon_H1d5 zenon_H6f zenon_H19a zenon_H16a zenon_H36 zenon_H16b. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.71 apply (zenon_L34_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.71 apply (zenon_L1039_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.71 apply (zenon_L235_); trivial. % 30.63/30.71 apply (zenon_L1541_); trivial. % 30.63/30.71 (* end of lemma zenon_L2364_ *) % 30.63/30.71 assert (zenon_L2365_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H1a8 zenon_H18c zenon_H42 zenon_H188 zenon_Ha4 zenon_Hfc zenon_He1 zenon_H18e zenon_Hf6 zenon_H56 zenon_Hcd zenon_H55 zenon_H16f zenon_Had zenon_H218 zenon_H73 zenon_H19e zenon_H8a zenon_H1d8 zenon_H1d5 zenon_H6f zenon_H16a zenon_H36 zenon_H16b zenon_H208 zenon_H112 zenon_H14e. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.63/30.71 apply (zenon_L2363_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.63/30.71 apply (zenon_L2353_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.63/30.71 apply (zenon_L2364_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.63/30.71 apply (zenon_L212_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.63/30.71 exact (zenon_H56 zenon_H25). % 30.63/30.71 apply (zenon_L187_); trivial. % 30.63/30.71 apply (zenon_L137_); trivial. % 30.63/30.71 (* end of lemma zenon_L2365_ *) % 30.63/30.71 assert (zenon_L2366_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_He4 zenon_Hd9 zenon_H14e zenon_H112 zenon_H16f zenon_Had zenon_H218 zenon_Hbd zenon_H2d zenon_H10d zenon_H198 zenon_Hda zenon_H222 zenon_Hf9 zenon_H256 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H1d8 zenon_H1d5 zenon_H6f zenon_H16a zenon_H36 zenon_H18e zenon_Hfc zenon_Ha4 zenon_H188 zenon_H42 zenon_Hcd zenon_H1a8 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hd6 zenon_He7 zenon_H174 zenon_H1bd zenon_H55 zenon_He1 zenon_H8a. % 30.63/30.71 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.63/30.71 apply (zenon_L47_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.63/30.71 apply (zenon_L2354_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.63/30.71 apply (zenon_L282_); trivial. % 30.63/30.71 apply (zenon_L50_); trivial. % 30.63/30.71 (* end of lemma zenon_L2366_ *) % 30.63/30.71 assert (zenon_L2367_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H174 zenon_H198 zenon_H1c7 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hd6 zenon_H27 zenon_H267 zenon_H1a8 zenon_H18c zenon_H42 zenon_H188 zenon_Ha4 zenon_Hfc zenon_He1 zenon_H55 zenon_H18e zenon_H36 zenon_H16a zenon_H6f zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H19e zenon_H73 zenon_H6c zenon_H218 zenon_Had zenon_H16f zenon_H112 zenon_H14e. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.63/30.71 apply (zenon_L232_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.63/30.71 apply (zenon_L124_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.63/30.71 apply (zenon_L2317_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.63/30.71 apply (zenon_L120_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.63/30.71 apply (zenon_L2353_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.63/30.71 apply (zenon_L2364_); trivial. % 30.63/30.71 apply (zenon_L137_); trivial. % 30.63/30.71 (* end of lemma zenon_L2367_ *) % 30.63/30.71 assert (zenon_L2368_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H42 zenon_H112 zenon_H188 zenon_Ha4 zenon_H33 zenon_H36 zenon_H35 zenon_He1 zenon_H55 zenon_H18e. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.71 apply (zenon_L124_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.71 apply (zenon_L6_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.71 apply (zenon_L126_); trivial. % 30.63/30.71 exact (zenon_H18e zenon_H40). % 30.63/30.71 (* end of lemma zenon_L2368_ *) % 30.63/30.71 assert (zenon_L2369_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H174 zenon_H2d zenon_H10e zenon_H1a8 zenon_H18c zenon_H42 zenon_H188 zenon_Ha4 zenon_Hfc zenon_He1 zenon_H18e zenon_Hf6 zenon_H56 zenon_Hcd zenon_H55 zenon_H16f zenon_Had zenon_H218 zenon_H73 zenon_H19e zenon_H8a zenon_H1d8 zenon_H1d5 zenon_H6f zenon_H16a zenon_H36 zenon_H208 zenon_H112 zenon_H14e. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.63/30.71 apply (zenon_L232_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.63/30.71 apply (zenon_L124_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.63/30.71 apply (zenon_L87_); trivial. % 30.63/30.71 apply (zenon_L2365_); trivial. % 30.63/30.71 (* end of lemma zenon_L2369_ *) % 30.63/30.71 assert (zenon_L2370_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H225 zenon_H267 zenon_H36 zenon_H27 zenon_H16a zenon_H1c7 zenon_H3c zenon_H2d zenon_H42 zenon_H188 zenon_H198 zenon_Ha4 zenon_H10d zenon_H8a zenon_Hf9 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hd6 zenon_H112 zenon_H222 zenon_Hbd zenon_He1 zenon_H55 zenon_H18e zenon_He7 zenon_H174 zenon_H185 zenon_Hde. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.63/30.71 apply (zenon_L2360_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.63/30.71 apply (zenon_L88_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.63/30.71 apply (zenon_L199_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.63/30.71 apply (zenon_L124_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.63/30.71 apply (zenon_L2351_); trivial. % 30.63/30.71 apply (zenon_L848_); trivial. % 30.63/30.71 apply (zenon_L817_); trivial. % 30.63/30.71 (* end of lemma zenon_L2370_ *) % 30.63/30.71 assert (zenon_L2371_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H2bd zenon_H64 zenon_H2d6 zenon_H2c1 zenon_H37 zenon_H35 zenon_H218 zenon_Hf5 zenon_Ha4 zenon_H36 zenon_Hbc. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H185 | zenon_intro zenon_H2be ]. % 30.63/30.71 apply (zenon_L1050_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H33 | zenon_intro zenon_H2bf ]. % 30.63/30.71 apply (zenon_L6_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H17b | zenon_intro zenon_H16b ]. % 30.63/30.71 apply (zenon_L405_); trivial. % 30.63/30.71 apply (zenon_L1142_); trivial. % 30.63/30.71 (* end of lemma zenon_L2371_ *) % 30.63/30.71 assert (zenon_L2372_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_Hb8 zenon_He2 zenon_He1 zenon_H100 zenon_H10d zenon_H117 zenon_H2bd zenon_H64 zenon_H2d6 zenon_H2c1 zenon_H37 zenon_H35 zenon_H218 zenon_Hf5 zenon_Ha4 zenon_H36. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.63/30.71 apply (zenon_L50_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.63/30.71 apply (zenon_L150_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.63/30.71 apply (zenon_L151_); trivial. % 30.63/30.71 apply (zenon_L2371_); trivial. % 30.63/30.71 (* end of lemma zenon_L2372_ *) % 30.63/30.71 assert (zenon_L2373_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H42 zenon_H112 zenon_H188 zenon_H117 zenon_H198 zenon_Ha4 zenon_Hb8 zenon_He2 zenon_H100 zenon_H10d zenon_H2bd zenon_H64 zenon_H2d6 zenon_H2c1 zenon_H35 zenon_H218 zenon_H36 zenon_H16a zenon_H1d2 zenon_H260 zenon_H56 zenon_Hd6 zenon_H27 zenon_H267 zenon_He1 zenon_H55 zenon_H18e. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.71 apply (zenon_L124_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.63/30.71 apply (zenon_L2314_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.63/30.71 apply (zenon_L1004_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.63/30.71 apply (zenon_L2372_); trivial. % 30.63/30.71 apply (zenon_L1006_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.71 apply (zenon_L126_); trivial. % 30.63/30.71 exact (zenon_H18e zenon_H40). % 30.63/30.71 (* end of lemma zenon_L2373_ *) % 30.63/30.71 assert (zenon_L2374_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_Hf9 zenon_H18e zenon_He1 zenon_H267 zenon_H27 zenon_Hd6 zenon_H56 zenon_H260 zenon_H1d2 zenon_H16a zenon_H36 zenon_H218 zenon_H35 zenon_H2c1 zenon_H2d6 zenon_H64 zenon_H2bd zenon_H100 zenon_Hb8 zenon_Ha4 zenon_H198 zenon_H117 zenon_H188 zenon_H112 zenon_H42 zenon_H55 zenon_H222 zenon_Hda zenon_H10d zenon_H95 zenon_H37. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.63/30.71 apply (zenon_L2373_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.63/30.71 apply (zenon_L264_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.63/30.71 apply (zenon_L64_); trivial. % 30.63/30.71 apply (zenon_L513_); trivial. % 30.63/30.71 (* end of lemma zenon_L2374_ *) % 30.63/30.71 assert (zenon_L2375_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 30.63/30.71 do 0 intro. intros zenon_Hbd zenon_H64 zenon_H2d6 zenon_He7 zenon_H37 zenon_H10d zenon_H198 zenon_Hda zenon_H222 zenon_H55 zenon_He1 zenon_H8a zenon_Hf9 zenon_H1b9 zenon_H112 zenon_H14e zenon_H14f. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.63/30.71 apply (zenon_L2041_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.63/30.71 apply (zenon_L1539_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.63/30.71 apply (zenon_L198_); trivial. % 30.63/30.71 apply (zenon_L84_); trivial. % 30.63/30.71 (* end of lemma zenon_L2375_ *) % 30.63/30.71 assert (zenon_L2376_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H14f zenon_H14e zenon_H112 zenon_Hf9 zenon_H8a zenon_He1 zenon_H55 zenon_H222 zenon_Hda zenon_H198 zenon_H10d zenon_H37 zenon_He7 zenon_H2d6 zenon_H64 zenon_Hbd zenon_H218 zenon_H36 zenon_H16b. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.71 apply (zenon_L174_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.71 apply (zenon_L126_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.71 apply (zenon_L2375_); trivial. % 30.63/30.71 apply (zenon_L1038_); trivial. % 30.63/30.71 (* end of lemma zenon_L2376_ *) % 30.63/30.71 assert (zenon_L2377_ : (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H2d zenon_H1b9 zenon_H256 zenon_Hbd zenon_H64 zenon_H2d6 zenon_He7 zenon_H37 zenon_H10d zenon_H198 zenon_Hda zenon_H222 zenon_H55 zenon_He1 zenon_H8a zenon_Hf9 zenon_H1d8 zenon_H1d5 zenon_H14e zenon_H218 zenon_H156 zenon_Hf6 zenon_H112 zenon_H1e6 zenon_H16a zenon_H36 zenon_H16b. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.63/30.71 apply (zenon_L25_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.63/30.71 apply (zenon_L1539_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.63/30.71 apply (zenon_L198_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 30.63/30.71 apply (zenon_L2376_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 30.63/30.71 apply (zenon_L137_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 30.63/30.71 apply (zenon_L1540_); trivial. % 30.63/30.71 apply (zenon_L1541_); trivial. % 30.63/30.71 (* end of lemma zenon_L2377_ *) % 30.63/30.71 assert (zenon_L2378_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.63/30.71 do 0 intro. intros zenon_Hb8 zenon_H16b zenon_H36 zenon_H16a zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H218 zenon_H14e zenon_H1d5 zenon_H1d8 zenon_Hf9 zenon_He1 zenon_H55 zenon_H222 zenon_Hda zenon_H198 zenon_H10d zenon_H37 zenon_He7 zenon_H2d6 zenon_H64 zenon_Hbd zenon_H256 zenon_H2d zenon_H18e zenon_H1dc zenon_H1b9 zenon_H112 zenon_H6f. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.63/30.71 apply (zenon_L2377_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.63/30.71 exact (zenon_H18e zenon_H40). % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.63/30.71 apply (zenon_L200_); trivial. % 30.63/30.71 apply (zenon_L152_); trivial. % 30.63/30.71 (* end of lemma zenon_L2378_ *) % 30.63/30.71 assert (zenon_L2379_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H1fd zenon_H76 zenon_Hfc zenon_Ha4 zenon_H188 zenon_H42 zenon_H6f zenon_H112 zenon_H18e zenon_H2d zenon_H256 zenon_Hbd zenon_H64 zenon_H2d6 zenon_He7 zenon_H37 zenon_H10d zenon_H198 zenon_Hda zenon_H222 zenon_He1 zenon_Hf9 zenon_H1d8 zenon_H1d5 zenon_H14e zenon_H218 zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H16a zenon_H36 zenon_H16b zenon_Hb8 zenon_H1d2 zenon_H260 zenon_H56 zenon_H55 zenon_Hd6 zenon_H1dc. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.71 apply (zenon_L339_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.71 apply (zenon_L2352_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.71 apply (zenon_L2378_); trivial. % 30.63/30.71 apply (zenon_L2347_); trivial. % 30.63/30.71 (* end of lemma zenon_L2379_ *) % 30.63/30.71 assert (zenon_L2380_ : ((op (e0) (e3)) = (e3)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H16b zenon_H36 zenon_H218 zenon_Hb8 zenon_H16a zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H14e zenon_H1d5 zenon_H1d8 zenon_Hf9 zenon_H222 zenon_Hda zenon_H198 zenon_H10d zenon_He7 zenon_H2d6 zenon_H64 zenon_Hbd zenon_H256 zenon_H2d zenon_H1dc zenon_H112 zenon_H6f zenon_H1fd zenon_Hfc zenon_Ha4 zenon_H188 zenon_H42 zenon_H1d2 zenon_H260 zenon_H56 zenon_Hd6 zenon_He1 zenon_H55 zenon_H18e. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.71 apply (zenon_L124_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.71 apply (zenon_L2379_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.71 apply (zenon_L126_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.71 apply (zenon_L2378_); trivial. % 30.63/30.71 apply (zenon_L1038_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.71 apply (zenon_L126_); trivial. % 30.63/30.71 exact (zenon_H18e zenon_H40). % 30.63/30.71 (* end of lemma zenon_L2380_ *) % 30.63/30.71 assert (zenon_L2381_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H16f zenon_Had zenon_H218 zenon_H2d zenon_H256 zenon_Hbd zenon_H64 zenon_H2d6 zenon_He7 zenon_H10d zenon_H198 zenon_Hda zenon_H222 zenon_H8a zenon_Hf9 zenon_H1d8 zenon_H1d5 zenon_H14e zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H19e zenon_H18e zenon_H55 zenon_He1 zenon_Hfc zenon_Ha4 zenon_H188 zenon_H112 zenon_H42 zenon_H16a zenon_H36 zenon_H16b. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.71 apply (zenon_L34_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.71 apply (zenon_L174_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.71 apply (zenon_L131_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.71 apply (zenon_L2377_); trivial. % 30.63/30.71 apply (zenon_L1038_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.71 apply (zenon_L2352_); trivial. % 30.63/30.71 apply (zenon_L1541_); trivial. % 30.63/30.71 (* end of lemma zenon_L2381_ *) % 30.63/30.71 assert (zenon_L2382_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H174 zenon_Hd6 zenon_H56 zenon_H260 zenon_H1d2 zenon_H16f zenon_Had zenon_H218 zenon_H2d zenon_H256 zenon_Hbd zenon_H64 zenon_H2d6 zenon_He7 zenon_H10d zenon_H198 zenon_Hda zenon_H222 zenon_H8a zenon_Hf9 zenon_H1d8 zenon_H1d5 zenon_H14e zenon_H156 zenon_Hf6 zenon_H1e6 zenon_H19e zenon_H18e zenon_H55 zenon_He1 zenon_Hfc zenon_Ha4 zenon_H188 zenon_H112 zenon_H42 zenon_H16a zenon_H36. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.63/30.71 apply (zenon_L199_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.63/30.71 apply (zenon_L124_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.63/30.71 apply (zenon_L2351_); trivial. % 30.63/30.71 apply (zenon_L2381_); trivial. % 30.63/30.71 (* end of lemma zenon_L2382_ *) % 30.63/30.71 assert (zenon_L2383_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H225 zenon_Hde zenon_H3c zenon_H16a zenon_H42 zenon_H112 zenon_H188 zenon_Ha4 zenon_Hfc zenon_He1 zenon_H18e zenon_H19e zenon_H1e6 zenon_Hf6 zenon_H156 zenon_H14e zenon_H1d5 zenon_H1d8 zenon_Hf9 zenon_H8a zenon_H222 zenon_H198 zenon_H10d zenon_He7 zenon_H2d6 zenon_H64 zenon_Hbd zenon_H256 zenon_H2d zenon_H218 zenon_Had zenon_H16f zenon_H174 zenon_H1d2 zenon_H260 zenon_H56 zenon_H55 zenon_Hd6 zenon_H27 zenon_H36. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.63/30.71 apply (zenon_L1209_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.63/30.71 apply (zenon_L88_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.63/30.71 apply (zenon_L2382_); trivial. % 30.63/30.71 apply (zenon_L2314_); trivial. % 30.63/30.71 (* end of lemma zenon_L2383_ *) % 30.63/30.71 assert (zenon_L2384_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_H4e zenon_Hf5 zenon_Hde zenon_H14e zenon_H48 zenon_H6e. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.63/30.71 exact (zenon_H30a zenon_H185). % 30.63/30.71 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.63/30.71 apply (zenon_L744_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.63/30.71 apply (zenon_L294_); trivial. % 30.63/30.71 apply (zenon_L770_); trivial. % 30.63/30.71 (* end of lemma zenon_L2384_ *) % 30.63/30.71 assert (zenon_L2385_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H37 zenon_H19e zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.71 apply (zenon_L332_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.71 apply (zenon_L131_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.71 exact (zenon_H1db zenon_H1b9). % 30.63/30.71 apply (zenon_L221_); trivial. % 30.63/30.71 (* end of lemma zenon_L2385_ *) % 30.63/30.71 assert (zenon_L2386_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H1a5 zenon_H26 zenon_H4a zenon_H19e zenon_H3d. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.63/30.71 apply (zenon_L42_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.63/30.71 exact (zenon_H18f zenon_Hd2). % 30.63/30.71 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.63/30.71 apply (zenon_L748_); trivial. % 30.63/30.71 apply (zenon_L131_); trivial. % 30.63/30.71 (* end of lemma zenon_L2386_ *) % 30.63/30.71 assert (zenon_L2387_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H40 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.71 apply (zenon_L332_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.71 apply (zenon_L775_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.71 exact (zenon_H1db zenon_H1b9). % 30.63/30.71 apply (zenon_L221_); trivial. % 30.63/30.71 (* end of lemma zenon_L2387_ *) % 30.63/30.71 assert (zenon_L2388_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H15e zenon_Hfc zenon_H182 zenon_H4e zenon_H19e zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.71 apply (zenon_L4_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.71 apply (zenon_L203_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.71 apply (zenon_L731_); trivial. % 30.63/30.71 apply (zenon_L2387_); trivial. % 30.63/30.71 (* end of lemma zenon_L2388_ *) % 30.63/30.71 assert (zenon_L2389_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_H256 zenon_Hb1 zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H19e zenon_Hfc zenon_H15e zenon_H1e zenon_H2d zenon_H42 zenon_Hfd zenon_H159 zenon_H14e zenon_H4e zenon_Hbc. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 30.63/30.71 apply (zenon_L84_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 30.63/30.71 apply (zenon_L2388_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 30.63/30.71 apply (zenon_L93_); trivial. % 30.63/30.71 apply (zenon_L875_); trivial. % 30.63/30.71 (* end of lemma zenon_L2389_ *) % 30.63/30.71 assert (zenon_L2390_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 30.63/30.71 do 0 intro. intros zenon_Hb8 zenon_He2 zenon_H1a0 zenon_H6f zenon_H102 zenon_H35 zenon_H18f zenon_H4e zenon_H14e zenon_H159 zenon_H42 zenon_H2d zenon_H1e zenon_H15e zenon_Hfc zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1 zenon_Hb1 zenon_H256 zenon_H19e zenon_H3d. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.63/30.71 apply (zenon_L50_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.63/30.71 apply (zenon_L775_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.63/30.71 apply (zenon_L540_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.63/30.71 apply (zenon_L42_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.63/30.71 exact (zenon_H18f zenon_Hd2). % 30.63/30.71 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.63/30.71 apply (zenon_L2389_); trivial. % 30.63/30.71 apply (zenon_L131_); trivial. % 30.63/30.71 (* end of lemma zenon_L2390_ *) % 30.63/30.71 assert (zenon_L2391_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.71 do 0 intro. intros zenon_H19e zenon_H256 zenon_Hfc zenon_H15e zenon_H1e zenon_H2d zenon_H42 zenon_H159 zenon_H14e zenon_H4e zenon_H18f zenon_H35 zenon_H102 zenon_H6f zenon_He2 zenon_Hb8 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H56 zenon_H1a5 zenon_H4a zenon_H1a2 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.71 apply (zenon_L4_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.71 apply (zenon_L203_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.63/30.71 apply (zenon_L2386_); trivial. % 30.63/30.71 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.63/30.72 apply (zenon_L235_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.63/30.72 exact (zenon_H56 zenon_H25). % 30.63/30.72 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.63/30.72 exact (zenon_H30a zenon_H185). % 30.63/30.72 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.63/30.72 apply (zenon_L744_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.63/30.72 apply (zenon_L294_); trivial. % 30.63/30.72 apply (zenon_L2390_); trivial. % 30.63/30.72 apply (zenon_L2387_); trivial. % 30.63/30.72 (* end of lemma zenon_L2391_ *) % 30.63/30.72 assert (zenon_L2392_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1fd zenon_H2d zenon_H10e zenon_H19a zenon_H1db zenon_H23b zenon_Hcd zenon_He2 zenon_H1f zenon_H3f zenon_H6f zenon_H1ab. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.72 apply (zenon_L87_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.72 apply (zenon_L235_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.63/30.72 apply (zenon_L386_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.63/30.72 apply (zenon_L336_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.63/30.72 apply (zenon_L540_); trivial. % 30.63/30.72 exact (zenon_H1ab zenon_H112). % 30.63/30.72 (* end of lemma zenon_L2392_ *) % 30.63/30.72 assert (zenon_L2393_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H19e zenon_H142 zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.72 apply (zenon_L332_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.72 apply (zenon_L1466_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 apply (zenon_L221_); trivial. % 30.63/30.72 (* end of lemma zenon_L2393_ *) % 30.63/30.72 assert (zenon_L2394_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.63/30.72 do 0 intro. intros zenon_Hb8 zenon_H90 zenon_H6f zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H10d zenon_H117 zenon_H14e zenon_H4e zenon_H16c. % 30.63/30.72 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.63/30.72 apply (zenon_L39_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.63/30.72 apply (zenon_L2387_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.63/30.72 apply (zenon_L151_); trivial. % 30.63/30.72 apply (zenon_L875_); trivial. % 30.63/30.72 (* end of lemma zenon_L2394_ *) % 30.63/30.72 assert (zenon_L2395_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1fd zenon_H1ab zenon_Hee zenon_Hb8 zenon_He2 zenon_He1 zenon_H14e zenon_H4e zenon_H16c zenon_Hf5 zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H10d zenon_H23b zenon_H6f zenon_H19a zenon_H1db zenon_H2d zenon_H9c. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.63/30.72 apply (zenon_L2394_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.63/30.72 apply (zenon_L1723_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.63/30.72 apply (zenon_L337_); trivial. % 30.63/30.72 exact (zenon_H1ab zenon_H112). % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.72 apply (zenon_L235_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 apply (zenon_L304_); trivial. % 30.63/30.72 (* end of lemma zenon_L2395_ *) % 30.63/30.72 assert (zenon_L2396_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1a2 zenon_H19e zenon_H4a zenon_H1a5 zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_H9c zenon_H2d zenon_H1db zenon_H23b zenon_H10d zenon_H1d5 zenon_Hc8 zenon_Hf5 zenon_He1 zenon_He2 zenon_Hee zenon_H1ab zenon_H1fd zenon_H56 zenon_Hb8 zenon_He7 zenon_H89 zenon_H222 zenon_H3d zenon_H6f zenon_H14e zenon_H4e zenon_H16c. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.63/30.72 apply (zenon_L2386_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.63/30.72 apply (zenon_L2395_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.63/30.72 exact (zenon_H56 zenon_H25). % 30.63/30.72 apply (zenon_L877_); trivial. % 30.63/30.72 (* end of lemma zenon_L2396_ *) % 30.63/30.72 assert (zenon_L2397_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H173 zenon_H68 zenon_He9 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H14b zenon_Hcd zenon_H1f zenon_H3f zenon_H4c zenon_H1b1 zenon_H1a2 zenon_H19e zenon_H4a zenon_H1a5 zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_H2d zenon_H23b zenon_H10d zenon_He2 zenon_Hee zenon_H1ab zenon_H1fd zenon_H56 zenon_Hb8 zenon_He7 zenon_H6f zenon_H14e zenon_H4e zenon_H42 zenon_H256 zenon_Hfc zenon_H159 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H48 zenon_H16f zenon_Hf5 zenon_H156. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.72 apply (zenon_L48_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.72 apply (zenon_L95_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.72 apply (zenon_L2384_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.72 apply (zenon_L2385_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.72 apply (zenon_L2391_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.72 apply (zenon_L4_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.72 apply (zenon_L2385_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.63/30.72 apply (zenon_L2386_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.63/30.72 apply (zenon_L2392_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.63/30.72 exact (zenon_H56 zenon_H25). % 30.63/30.72 apply (zenon_L877_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.63/30.72 apply (zenon_L1177_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.63/30.72 apply (zenon_L2393_); trivial. % 30.63/30.72 apply (zenon_L2396_); trivial. % 30.63/30.72 apply (zenon_L2387_); trivial. % 30.63/30.72 apply (zenon_L90_); trivial. % 30.63/30.72 (* end of lemma zenon_L2397_ *) % 30.63/30.72 assert (zenon_L2398_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H2b1 zenon_H16a zenon_H4a zenon_Hfc zenon_Hed zenon_H18f zenon_H1ba zenon_H102 zenon_H3d zenon_H4e zenon_H19e zenon_Hf5 zenon_Hcd zenon_H1ab. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.63/30.72 apply (zenon_L1716_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.63/30.72 apply (zenon_L731_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.63/30.72 apply (zenon_L1017_); trivial. % 30.63/30.72 exact (zenon_H1ab zenon_H112). % 30.63/30.72 (* end of lemma zenon_L2398_ *) % 30.63/30.72 assert (zenon_L2399_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H1ab zenon_Hcd zenon_H19e zenon_H4e zenon_H102 zenon_H1ba zenon_H18f zenon_Hed zenon_Hfc zenon_H4a zenon_H16a zenon_H2b1 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.72 apply (zenon_L332_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.72 apply (zenon_L2398_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 apply (zenon_L221_); trivial. % 30.63/30.72 (* end of lemma zenon_L2399_ *) % 30.63/30.72 assert (zenon_L2400_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H310 zenon_H6b zenon_H142 zenon_Hc3 zenon_H4a zenon_H18c zenon_He2 zenon_H1d8 zenon_Hc8 zenon_H89. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_Hdf | zenon_intro zenon_H311 ]. % 30.63/30.72 apply (zenon_L303_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H6c | zenon_intro zenon_H312 ]. % 30.63/30.72 apply (zenon_L763_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H76 ]. % 30.63/30.72 apply (zenon_L307_); trivial. % 30.63/30.72 apply (zenon_L332_); trivial. % 30.63/30.72 (* end of lemma zenon_L2400_ *) % 30.63/30.72 assert (zenon_L2401_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H200 zenon_H69 zenon_H48 zenon_He1 zenon_H1db zenon_H2b1 zenon_H16a zenon_Hfc zenon_Hed zenon_H18f zenon_H102 zenon_H4e zenon_H19e zenon_Hcd zenon_H1ab zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H1d8 zenon_He2 zenon_H18c zenon_H4a zenon_Hc3 zenon_H6b zenon_H310 zenon_Hde zenon_Hf5. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.63/30.72 apply (zenon_L740_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.63/30.72 apply (zenon_L2399_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.63/30.72 apply (zenon_L2400_); trivial. % 30.63/30.72 apply (zenon_L294_); trivial. % 30.63/30.72 (* end of lemma zenon_L2401_ *) % 30.63/30.72 assert (zenon_L2402_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H173 zenon_H68 zenon_H35 zenon_He9 zenon_He1 zenon_H1db zenon_H2b1 zenon_H16a zenon_H4a zenon_Hfc zenon_H18f zenon_H1ba zenon_H102 zenon_H4e zenon_H19e zenon_Hcd zenon_H1ab zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hf5 zenon_H156. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.72 apply (zenon_L48_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.72 apply (zenon_L95_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.72 apply (zenon_L2399_); trivial. % 30.63/30.72 apply (zenon_L90_); trivial. % 30.63/30.72 (* end of lemma zenon_L2402_ *) % 30.63/30.72 assert (zenon_L2403_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1d2 zenon_H6b zenon_Hdf zenon_H56 zenon_H108 zenon_Hf5 zenon_H1db. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.72 apply (zenon_L303_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.72 exact (zenon_H56 zenon_H25). % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.72 apply (zenon_L62_); trivial. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 (* end of lemma zenon_L2403_ *) % 30.63/30.72 assert (zenon_L2404_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H200 zenon_H1db zenon_H108 zenon_H56 zenon_H6b zenon_H1d2 zenon_H1ab zenon_Hcd zenon_H4e zenon_Hed zenon_Hfc zenon_H4a zenon_H16a zenon_H2b1 zenon_H3d zenon_H19e zenon_H18f zenon_H100 zenon_H95 zenon_H102 zenon_Hde zenon_Hf5. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.63/30.72 apply (zenon_L2403_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.63/30.72 apply (zenon_L2398_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.63/30.72 apply (zenon_L1708_); trivial. % 30.63/30.72 apply (zenon_L294_); trivial. % 30.63/30.72 (* end of lemma zenon_L2404_ *) % 30.63/30.72 assert (zenon_L2405_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_Hde zenon_H102 zenon_H95 zenon_H100 zenon_H18f zenon_H19e zenon_H2b1 zenon_H16a zenon_H4a zenon_Hfc zenon_Hed zenon_H4e zenon_Hcd zenon_H1ab zenon_H1d2 zenon_H6b zenon_H56 zenon_H108 zenon_H200 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.72 apply (zenon_L332_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.72 apply (zenon_L2404_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 apply (zenon_L221_); trivial. % 30.63/30.72 (* end of lemma zenon_L2405_ *) % 30.63/30.72 assert (zenon_L2406_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H296 zenon_H16f zenon_H2b4 zenon_H30a zenon_H15a zenon_H159 zenon_H256 zenon_H42 zenon_H14e zenon_H6f zenon_He7 zenon_Hb8 zenon_H1fd zenon_Hee zenon_H10d zenon_H23b zenon_H2d zenon_H1a5 zenon_H1a2 zenon_H1b1 zenon_H4c zenon_H3f zenon_H1f zenon_H14b zenon_H222 zenon_H69 zenon_H48 zenon_H1d8 zenon_He2 zenon_H18c zenon_H310 zenon_H173 zenon_H68 zenon_H35 zenon_He9 zenon_He1 zenon_H1db zenon_H200 zenon_H108 zenon_H56 zenon_H6b zenon_H1d2 zenon_H1ab zenon_Hcd zenon_H4e zenon_Hfc zenon_H4a zenon_H16a zenon_H2b1 zenon_H19e zenon_H18f zenon_H100 zenon_H102 zenon_Hde zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hf5 zenon_H156. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.63/30.72 apply (zenon_L2397_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.72 apply (zenon_L48_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.72 apply (zenon_L95_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.72 apply (zenon_L2401_); trivial. % 30.63/30.72 apply (zenon_L90_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.63/30.72 apply (zenon_L2402_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.72 apply (zenon_L48_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.72 apply (zenon_L95_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.72 apply (zenon_L2405_); trivial. % 30.63/30.72 apply (zenon_L90_); trivial. % 30.63/30.72 (* end of lemma zenon_L2406_ *) % 30.63/30.72 assert (zenon_L2407_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H200 zenon_H1db zenon_H108 zenon_H56 zenon_H1d2 zenon_H19e zenon_H89 zenon_Hc8 zenon_H1d8 zenon_He2 zenon_H18c zenon_H4a zenon_Hc3 zenon_H6b zenon_H310 zenon_Hde zenon_Hf5. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.63/30.72 apply (zenon_L2403_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.63/30.72 apply (zenon_L347_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.63/30.72 apply (zenon_L2400_); trivial. % 30.63/30.72 apply (zenon_L294_); trivial. % 30.63/30.72 (* end of lemma zenon_L2407_ *) % 30.63/30.72 assert (zenon_L2408_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.63/30.72 do 0 intro. intros zenon_He4 zenon_H20d zenon_H172 zenon_H156 zenon_H1d5 zenon_H102 zenon_H100 zenon_H18f zenon_H2b1 zenon_H16a zenon_Hfc zenon_Hcd zenon_H1ab zenon_He1 zenon_He9 zenon_H35 zenon_H68 zenon_H173 zenon_H48 zenon_H222 zenon_H14b zenon_H1f zenon_H3f zenon_H1b1 zenon_H1a2 zenon_H1a5 zenon_H2d zenon_H23b zenon_H10d zenon_Hee zenon_H1fd zenon_Hb8 zenon_He7 zenon_H6f zenon_H14e zenon_H42 zenon_H256 zenon_H159 zenon_H30a zenon_H2b4 zenon_H16f zenon_H296 zenon_Hf5 zenon_Hde zenon_H310 zenon_H6b zenon_H4a zenon_H18c zenon_H1d8 zenon_Hc8 zenon_H19e zenon_H1d2 zenon_H56 zenon_H108 zenon_H1db zenon_H200 zenon_H4c zenon_Had zenon_H4e zenon_H89 zenon_H15a. % 30.63/30.72 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.63/30.72 apply (zenon_L232_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.63/30.72 apply (zenon_L48_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.63/30.72 apply (zenon_L627_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.63/30.72 apply (zenon_L2406_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.63/30.72 apply (zenon_L2407_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.63/30.72 apply (zenon_L742_); trivial. % 30.63/30.72 apply (zenon_L744_); trivial. % 30.63/30.72 (* end of lemma zenon_L2408_ *) % 30.63/30.72 assert (zenon_L2409_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1d2 zenon_H20e zenon_Hfe zenon_H56 zenon_H108 zenon_Hf5 zenon_H1db. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.63/30.72 apply (zenon_L350_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.63/30.72 exact (zenon_H56 zenon_H25). % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.63/30.72 apply (zenon_L62_); trivial. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 (* end of lemma zenon_L2409_ *) % 30.63/30.72 assert (zenon_L2410_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H16f zenon_H68 zenon_H2b4 zenon_H30a zenon_H15a zenon_H159 zenon_Hfc zenon_H256 zenon_H42 zenon_H4e zenon_H14e zenon_H6f zenon_He7 zenon_Hb8 zenon_H56 zenon_H1fd zenon_H1ab zenon_Hee zenon_He2 zenon_H10d zenon_H23b zenon_H2d zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H1a5 zenon_H4a zenon_H19e zenon_H1a2 zenon_H1d2 zenon_H20e zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.72 apply (zenon_L18_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.72 apply (zenon_L2385_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.72 apply (zenon_L2391_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.72 apply (zenon_L4_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.72 apply (zenon_L2385_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.63/30.72 apply (zenon_L192_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.63/30.72 apply (zenon_L2409_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.63/30.72 apply (zenon_L1466_); trivial. % 30.63/30.72 apply (zenon_L2396_); trivial. % 30.63/30.72 apply (zenon_L2387_); trivial. % 30.63/30.72 (* end of lemma zenon_L2410_ *) % 30.63/30.72 assert (zenon_L2411_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H42 zenon_H35 zenon_H15e zenon_Hfc zenon_H182 zenon_H4e zenon_H19e zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.72 apply (zenon_L730_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.72 apply (zenon_L203_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.72 apply (zenon_L731_); trivial. % 30.63/30.72 apply (zenon_L2387_); trivial. % 30.63/30.72 (* end of lemma zenon_L2411_ *) % 30.63/30.72 assert (zenon_L2412_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H256 zenon_Hb1 zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H19e zenon_Hfc zenon_H15e zenon_H35 zenon_H42 zenon_Hfd zenon_H159 zenon_H14e zenon_H4e zenon_Hbc. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 30.63/30.72 apply (zenon_L84_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 30.63/30.72 apply (zenon_L2411_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 30.63/30.72 apply (zenon_L93_); trivial. % 30.63/30.72 apply (zenon_L875_); trivial. % 30.63/30.72 (* end of lemma zenon_L2412_ *) % 30.63/30.72 assert (zenon_L2413_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He2 zenon_H3d zenon_Hee zenon_H256 zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H19e zenon_Hfc zenon_H15e zenon_H35 zenon_H42 zenon_Hfd zenon_H159 zenon_H14e zenon_H4e. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.63/30.72 exact (zenon_H30a zenon_H185). % 30.63/30.72 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.63/30.72 apply (zenon_L744_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.63/30.72 apply (zenon_L294_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.63/30.72 apply (zenon_L50_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.63/30.72 apply (zenon_L775_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.63/30.72 apply (zenon_L490_); trivial. % 30.63/30.72 apply (zenon_L2412_); trivial. % 30.63/30.72 (* end of lemma zenon_L2413_ *) % 30.63/30.72 assert (zenon_L2414_ : ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H4e zenon_H14e zenon_H159 zenon_Hfd zenon_H42 zenon_H35 zenon_H15e zenon_Hfc zenon_H19e zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H256 zenon_Hee zenon_He2 zenon_Hb8 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.72 apply (zenon_L332_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.72 apply (zenon_L2413_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 apply (zenon_L221_); trivial. % 30.63/30.72 (* end of lemma zenon_L2414_ *) % 30.63/30.72 assert (zenon_L2415_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_Hfd zenon_H142 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.72 apply (zenon_L332_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.72 apply (zenon_L79_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 apply (zenon_L221_); trivial. % 30.63/30.72 (* end of lemma zenon_L2415_ *) % 30.63/30.72 assert (zenon_L2416_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1d5 zenon_Hc8 zenon_H14e zenon_H6f zenon_H1a0 zenon_H222 zenon_H89 zenon_He7 zenon_Hb8 zenon_H1db zenon_H156 zenon_H4e zenon_H16c. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.72 apply (zenon_L332_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.72 apply (zenon_L877_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 apply (zenon_L779_); trivial. % 30.63/30.72 (* end of lemma zenon_L2416_ *) % 30.63/30.72 assert (zenon_L2417_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1a2 zenon_H1a5 zenon_Hfd zenon_H4a zenon_H9c zenon_H2d zenon_H23b zenon_H10d zenon_Hf5 zenon_He1 zenon_He2 zenon_Hee zenon_H1ab zenon_H1fd zenon_H56 zenon_H1d5 zenon_Hc8 zenon_H14e zenon_H6f zenon_H222 zenon_H89 zenon_He7 zenon_Hb8 zenon_H1db zenon_H156 zenon_H4e zenon_H16c. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.63/30.72 apply (zenon_L748_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.63/30.72 apply (zenon_L2395_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.63/30.72 exact (zenon_H56 zenon_H25). % 30.63/30.72 apply (zenon_L2416_); trivial. % 30.63/30.72 (* end of lemma zenon_L2417_ *) % 30.63/30.72 assert (zenon_L2418_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H16f zenon_H68 zenon_H2b4 zenon_H30a zenon_H15a zenon_H256 zenon_H19e zenon_Hfc zenon_H35 zenon_H42 zenon_H159 zenon_H14b zenon_Hde zenon_Hda zenon_H108 zenon_H20e zenon_H1d2 zenon_H1a2 zenon_H1a5 zenon_Hfd zenon_H4a zenon_H2d zenon_H23b zenon_H10d zenon_Hf5 zenon_He1 zenon_He2 zenon_Hee zenon_H1ab zenon_H1fd zenon_H56 zenon_H1d5 zenon_Hc8 zenon_H14e zenon_H6f zenon_H222 zenon_H89 zenon_He7 zenon_Hb8 zenon_H1db zenon_H156 zenon_H4e. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.72 apply (zenon_L18_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.72 apply (zenon_L158_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.72 apply (zenon_L2414_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.63/30.72 apply (zenon_L192_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.63/30.72 apply (zenon_L2409_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.63/30.72 apply (zenon_L2415_); trivial. % 30.63/30.72 apply (zenon_L2417_); trivial. % 30.63/30.72 (* end of lemma zenon_L2418_ *) % 30.63/30.72 assert (zenon_L2419_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H19e zenon_He9 zenon_H35 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.72 apply (zenon_L332_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.72 apply (zenon_L922_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 apply (zenon_L221_); trivial. % 30.63/30.72 (* end of lemma zenon_L2419_ *) % 30.63/30.72 assert (zenon_L2420_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H19e zenon_He9 zenon_H35 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_H1db zenon_H156 zenon_H4e zenon_H16c. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.72 apply (zenon_L332_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.72 apply (zenon_L922_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.72 exact (zenon_H1db zenon_H1b9). % 30.63/30.72 apply (zenon_L779_); trivial. % 30.63/30.72 (* end of lemma zenon_L2420_ *) % 30.63/30.72 assert (zenon_L2421_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.63/30.72 do 0 intro. intros zenon_H16f zenon_H48 zenon_H14e zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_He1 zenon_Hf5 zenon_H6f zenon_H19a zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H19e zenon_He9 zenon_H35 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_H1db zenon_H156 zenon_H4e. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.72 apply (zenon_L2384_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.72 apply (zenon_L2385_); trivial. % 30.63/30.72 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.72 apply (zenon_L235_); trivial. % 30.63/30.72 apply (zenon_L2420_); trivial. % 30.63/30.72 (* end of lemma zenon_L2421_ *) % 30.63/30.72 assert (zenon_L2422_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.63/30.73 do 0 intro. intros zenon_H101 zenon_H4e zenon_H156 zenon_H1db zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H35 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_Hf5 zenon_He1 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_H14e zenon_H48 zenon_H16f zenon_Hdc zenon_Hd1 zenon_H19e zenon_H100 zenon_H4c zenon_H19a. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.63/30.73 apply (zenon_L2421_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.63/30.73 apply (zenon_L154_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.63/30.73 apply (zenon_L824_); trivial. % 30.63/30.73 apply (zenon_L1184_); trivial. % 30.63/30.73 (* end of lemma zenon_L2422_ *) % 30.63/30.73 assert (zenon_L2423_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H16f zenon_Hd1 zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H19e zenon_H4e zenon_Hfc zenon_H35 zenon_H42 zenon_H182 zenon_H6f. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.73 apply (zenon_L729_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.73 apply (zenon_L2385_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.73 apply (zenon_L2411_); trivial. % 30.63/30.73 apply (zenon_L758_); trivial. % 30.63/30.73 (* end of lemma zenon_L2423_ *) % 30.63/30.73 assert (zenon_L2424_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H1a8 zenon_Hcd zenon_H4c zenon_H100 zenon_Hdc zenon_H48 zenon_H14e zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_H156 zenon_H101 zenon_H16f zenon_Hd1 zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H19e zenon_H4e zenon_Hfc zenon_H35 zenon_H42 zenon_H6f. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.63/30.73 exact (zenon_H18f zenon_Hd2). % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.63/30.73 apply (zenon_L2422_); trivial. % 30.63/30.73 apply (zenon_L2423_); trivial. % 30.63/30.73 (* end of lemma zenon_L2424_ *) % 30.63/30.73 assert (zenon_L2425_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H42 zenon_H16c zenon_H4e zenon_H14e zenon_H6f zenon_He7 zenon_Hb8 zenon_H56 zenon_H1fd zenon_H1ab zenon_Hee zenon_He2 zenon_H10d zenon_H23b zenon_H2d zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H1a5 zenon_H4a zenon_H19e zenon_H1a2 zenon_Hfd zenon_H1d2 zenon_H20e zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.73 apply (zenon_L4_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.73 apply (zenon_L158_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.63/30.73 apply (zenon_L192_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.63/30.73 apply (zenon_L2409_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.63/30.73 apply (zenon_L79_); trivial. % 30.63/30.73 apply (zenon_L2396_); trivial. % 30.63/30.73 apply (zenon_L2387_); trivial. % 30.63/30.73 (* end of lemma zenon_L2425_ *) % 30.63/30.73 assert (zenon_L2426_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H19e zenon_He9 zenon_H35 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.73 apply (zenon_L4_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.73 apply (zenon_L2385_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.73 apply (zenon_L922_); trivial. % 30.63/30.73 apply (zenon_L2387_); trivial. % 30.63/30.73 (* end of lemma zenon_L2426_ *) % 30.63/30.73 assert (zenon_L2427_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.63/30.73 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_H4e zenon_Hf5 zenon_Hde zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_Hed zenon_Hfc zenon_H9d. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.63/30.73 exact (zenon_H30a zenon_H185). % 30.63/30.73 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.63/30.73 apply (zenon_L744_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.63/30.73 apply (zenon_L294_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.63/30.73 apply (zenon_L42_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.63/30.73 exact (zenon_H18f zenon_Hd2). % 30.63/30.73 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.63/30.73 apply (zenon_L58_); trivial. % 30.63/30.73 apply (zenon_L320_); trivial. % 30.63/30.73 (* end of lemma zenon_L2427_ *) % 30.63/30.73 assert (zenon_L2428_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H101 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H6c zenon_H4a zenon_H18c zenon_H19e zenon_H2d zenon_H42 zenon_H1c7 zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_H4e zenon_Hf5 zenon_Hde zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_Hed zenon_Hfc. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.63/30.73 apply (zenon_L2426_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.63/30.73 apply (zenon_L58_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.63/30.73 apply (zenon_L1253_); trivial. % 30.63/30.73 apply (zenon_L2427_); trivial. % 30.63/30.73 (* end of lemma zenon_L2428_ *) % 30.63/30.73 assert (zenon_L2429_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H16f zenon_H48 zenon_H15a zenon_H30a zenon_H2b4 zenon_H19a zenon_H42 zenon_H4e zenon_H14e zenon_H6f zenon_He7 zenon_Hb8 zenon_H56 zenon_H1fd zenon_H1ab zenon_Hee zenon_He2 zenon_H10d zenon_H23b zenon_H2d zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H1a5 zenon_H4a zenon_H19e zenon_H1a2 zenon_Hfd zenon_H1d2 zenon_H20e zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.73 apply (zenon_L2384_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.73 apply (zenon_L158_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.73 apply (zenon_L235_); trivial. % 30.63/30.73 apply (zenon_L2425_); trivial. % 30.63/30.73 (* end of lemma zenon_L2429_ *) % 30.63/30.73 assert (zenon_L2430_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H16f zenon_Hd1 zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H19e zenon_H4e zenon_Hfc zenon_H1e zenon_H2d zenon_H42 zenon_H182 zenon_H6f. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.73 apply (zenon_L729_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.73 apply (zenon_L2385_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.73 apply (zenon_L2388_); trivial. % 30.63/30.73 apply (zenon_L758_); trivial. % 30.63/30.73 (* end of lemma zenon_L2430_ *) % 30.63/30.73 assert (zenon_L2431_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H1a8 zenon_H156 zenon_H1c7 zenon_H159 zenon_H256 zenon_Hcd zenon_H173 zenon_H4c zenon_H100 zenon_H48 zenon_H15a zenon_H30a zenon_H2b4 zenon_H14e zenon_He7 zenon_Hb8 zenon_H56 zenon_H1fd zenon_H1ab zenon_Hee zenon_He2 zenon_H10d zenon_H23b zenon_H102 zenon_H35 zenon_H18f zenon_H1a5 zenon_H4a zenon_H1a2 zenon_H1d2 zenon_H20e zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_H18c zenon_H6c zenon_H101 zenon_H16f zenon_Hd1 zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H19e zenon_H4e zenon_Hfc zenon_H1e zenon_H2d zenon_H42 zenon_H6f. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.73 apply (zenon_L18_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.73 apply (zenon_L158_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.73 apply (zenon_L2391_); trivial. % 30.63/30.73 apply (zenon_L2425_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.73 apply (zenon_L2428_); trivial. % 30.63/30.73 apply (zenon_L90_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.63/30.73 exact (zenon_H18f zenon_Hd2). % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.63/30.73 apply (zenon_L2426_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.63/30.73 apply (zenon_L2429_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.63/30.73 apply (zenon_L824_); trivial. % 30.63/30.73 apply (zenon_L1184_); trivial. % 30.63/30.73 apply (zenon_L2430_); trivial. % 30.63/30.73 (* end of lemma zenon_L2431_ *) % 30.63/30.73 assert (zenon_L2432_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H14b zenon_H3f zenon_H1f zenon_Hcd zenon_H4c zenon_Had zenon_Hd6 zenon_H1ba zenon_H1fd zenon_H1ab zenon_Hee zenon_Hb8 zenon_He2 zenon_He1 zenon_H14e zenon_H4e zenon_H16c zenon_Hf5 zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H10d zenon_H23b zenon_H6f zenon_H19a zenon_H1db zenon_H2d. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.63/30.73 apply (zenon_L2392_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.63/30.73 apply (zenon_L742_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.63/30.73 apply (zenon_L161_); trivial. % 30.63/30.73 apply (zenon_L2395_); trivial. % 30.63/30.73 (* end of lemma zenon_L2432_ *) % 30.63/30.73 assert (zenon_L2433_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H6c zenon_H4a zenon_H18c zenon_H1db zenon_Hf5 zenon_H108 zenon_H56 zenon_H20e zenon_H1d2 zenon_H4e zenon_H89 zenon_H15a. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.63/30.73 apply (zenon_L740_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.63/30.73 apply (zenon_L763_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.63/30.73 apply (zenon_L2409_); trivial. % 30.63/30.73 apply (zenon_L744_); trivial. % 30.63/30.73 (* end of lemma zenon_L2433_ *) % 30.63/30.73 assert (zenon_L2434_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.63/30.73 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H19e zenon_H142 zenon_H18f zenon_H100 zenon_H95 zenon_H102 zenon_H1db zenon_H156 zenon_H4e zenon_H16c. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.73 apply (zenon_L332_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.73 apply (zenon_L1708_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.73 exact (zenon_H1db zenon_H1b9). % 30.63/30.73 apply (zenon_L779_); trivial. % 30.63/30.73 (* end of lemma zenon_L2434_ *) % 30.63/30.73 assert (zenon_L2435_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 30.63/30.73 do 0 intro. intros zenon_H101 zenon_H89 zenon_H90 zenon_H10d zenon_Hda zenon_H3f zenon_Hcd zenon_Hf9 zenon_Hdc zenon_Hd1 zenon_Hf5 zenon_H1c7 zenon_H100 zenon_H4c zenon_H19a. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.63/30.73 apply (zenon_L1627_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.63/30.73 apply (zenon_L154_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.63/30.73 apply (zenon_L1253_); trivial. % 30.63/30.73 apply (zenon_L1184_); trivial. % 30.63/30.73 (* end of lemma zenon_L2435_ *) % 30.63/30.73 assert (zenon_L2436_ : ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H4c zenon_Hed zenon_Hdc zenon_H1b1. % 30.63/30.73 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 30.63/30.73 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e0)) = (op (e1) (e2)))). % 30.63/30.73 intro zenon_D_pnotp. % 30.63/30.73 apply zenon_H1b1. % 30.63/30.73 rewrite <- zenon_D_pnotp. % 30.63/30.73 exact zenon_H19b. % 30.63/30.73 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 30.63/30.73 cut (((op (e1) (e2)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H318]. % 30.63/30.73 congruence. % 30.63/30.73 cut (((op (e1) (op (e1) (e2))) = (e2)) = ((op (e1) (e2)) = (op (e1) (e0)))). % 30.63/30.73 intro zenon_D_pnotp. % 30.63/30.73 apply zenon_H318. % 30.63/30.73 rewrite <- zenon_D_pnotp. % 30.63/30.73 exact zenon_H4c. % 30.63/30.73 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 30.63/30.73 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e9]. % 30.63/30.73 congruence. % 30.63/30.73 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H19c ]. % 30.63/30.73 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (op (e1) (e2))) = (op (e1) (e2)))). % 30.63/30.73 intro zenon_D_pnotp. % 30.63/30.73 apply zenon_H2e9. % 30.63/30.73 rewrite <- zenon_D_pnotp. % 30.63/30.73 exact zenon_H19b. % 30.63/30.73 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 30.63/30.73 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2e8]. % 30.63/30.73 congruence. % 30.63/30.73 apply (zenon_L1206_); trivial. % 30.63/30.73 apply zenon_H19c. apply refl_equal. % 30.63/30.73 apply zenon_H19c. apply refl_equal. % 30.63/30.73 apply zenon_H15b. apply sym_equal. exact zenon_Hdc. % 30.63/30.73 apply zenon_H19c. apply refl_equal. % 30.63/30.73 apply zenon_H19c. apply refl_equal. % 30.63/30.73 (* end of lemma zenon_L2436_ *) % 30.63/30.73 assert (zenon_L2437_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e2)) -> False). % 30.63/30.73 do 0 intro. intros zenon_H1fd zenon_H16c zenon_H4e zenon_H14e zenon_H10d zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_Hf5 zenon_H90 zenon_Hb8 zenon_H6f zenon_H19a zenon_H1db zenon_He1 zenon_Heb. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.63/30.73 apply (zenon_L2394_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.63/30.73 apply (zenon_L235_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.63/30.73 exact (zenon_H1db zenon_H1b9). % 30.63/30.73 apply (zenon_L204_); trivial. % 30.63/30.73 (* end of lemma zenon_L2437_ *) % 30.63/30.73 assert (zenon_L2438_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H125 zenon_H100 zenon_H1c7 zenon_Hd1 zenon_Hf9 zenon_Hcd zenon_H3f zenon_H101 zenon_H1b1 zenon_Hdc zenon_H4c zenon_H108 zenon_H1fd zenon_H16c zenon_H4e zenon_H14e zenon_H10d zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_Hf5 zenon_H90 zenon_Hb8 zenon_H6f zenon_H19a zenon_H1db zenon_He1. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.63/30.73 apply (zenon_L2435_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.63/30.73 apply (zenon_L2436_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.63/30.73 apply (zenon_L62_); trivial. % 30.63/30.73 apply (zenon_L2437_); trivial. % 30.63/30.73 (* end of lemma zenon_L2438_ *) % 30.63/30.73 assert (zenon_L2439_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H16f zenon_H48 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H19e zenon_H125 zenon_H100 zenon_H1c7 zenon_Hd1 zenon_Hf9 zenon_Hcd zenon_H3f zenon_H101 zenon_H1b1 zenon_Hdc zenon_H4c zenon_H108 zenon_H1fd zenon_H4e zenon_H14e zenon_H10d zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_Hf5 zenon_H90 zenon_Hb8 zenon_H6f zenon_H19a zenon_H1db zenon_He1. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.73 apply (zenon_L2384_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.73 apply (zenon_L2385_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.73 apply (zenon_L235_); trivial. % 30.63/30.73 apply (zenon_L2438_); trivial. % 30.63/30.73 (* end of lemma zenon_L2439_ *) % 30.63/30.73 assert (zenon_L2440_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.63/30.73 do 0 intro. intros zenon_He4 zenon_H6f zenon_H42 zenon_H35 zenon_Hfc zenon_H4e zenon_H19e zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He1 zenon_Hd1 zenon_H16f zenon_H48 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H125 zenon_H100 zenon_H1c7 zenon_Hf9 zenon_H3f zenon_H101 zenon_H1b1 zenon_H4c zenon_H108 zenon_H1fd zenon_H14e zenon_H10d zenon_Hb8 zenon_H18f zenon_Had zenon_H1a8 zenon_Hf5 zenon_H20d zenon_H90 zenon_Hcd. % 30.63/30.73 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.63/30.73 apply (zenon_L232_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.63/30.73 apply (zenon_L639_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.63/30.73 exact (zenon_H18f zenon_Hd2). % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.63/30.73 apply (zenon_L2439_); trivial. % 30.63/30.73 apply (zenon_L2423_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.63/30.73 apply (zenon_L627_); trivial. % 30.63/30.73 apply (zenon_L386_); trivial. % 30.63/30.73 (* end of lemma zenon_L2440_ *) % 30.63/30.73 assert (zenon_L2441_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H42 zenon_H2d zenon_H19e zenon_H4a zenon_H26 zenon_H1a5 zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.73 apply (zenon_L4_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.73 apply (zenon_L2385_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.73 apply (zenon_L2386_); trivial. % 30.63/30.73 apply (zenon_L2387_); trivial. % 30.63/30.73 (* end of lemma zenon_L2441_ *) % 30.63/30.73 assert (zenon_L2442_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H173 zenon_H68 zenon_H1a5 zenon_H26 zenon_He1 zenon_H1db zenon_H200 zenon_H108 zenon_H56 zenon_H6b zenon_H1d2 zenon_H1ab zenon_Hcd zenon_H4e zenon_Hfc zenon_H4a zenon_H16a zenon_H2b1 zenon_H19e zenon_H18f zenon_H100 zenon_H95 zenon_H102 zenon_Hde zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hf5 zenon_H156. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.73 apply (zenon_L748_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.73 apply (zenon_L2405_); trivial. % 30.63/30.73 apply (zenon_L90_); trivial. % 30.63/30.73 (* end of lemma zenon_L2442_ *) % 30.63/30.73 assert (zenon_L2443_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H296 zenon_H222 zenon_H2d zenon_H42 zenon_H69 zenon_H48 zenon_H1d8 zenon_He2 zenon_H18c zenon_H310 zenon_He9 zenon_H35 zenon_H173 zenon_H68 zenon_H1a5 zenon_H26 zenon_He1 zenon_H1db zenon_H200 zenon_H108 zenon_H56 zenon_H6b zenon_H1d2 zenon_H1ab zenon_Hcd zenon_H4e zenon_Hfc zenon_H4a zenon_H16a zenon_H2b1 zenon_H19e zenon_H18f zenon_H100 zenon_H102 zenon_Hde zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hf5 zenon_H156. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.63/30.73 apply (zenon_L2441_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.73 apply (zenon_L748_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.73 apply (zenon_L2401_); trivial. % 30.63/30.73 apply (zenon_L90_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.63/30.73 apply (zenon_L2402_); trivial. % 30.63/30.73 apply (zenon_L2442_); trivial. % 30.63/30.73 (* end of lemma zenon_L2443_ *) % 30.63/30.73 assert (zenon_L2444_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.63/30.73 do 0 intro. intros zenon_He4 zenon_H64 zenon_H20d zenon_H172 zenon_H156 zenon_H1d5 zenon_H102 zenon_H100 zenon_H18f zenon_H2b1 zenon_H16a zenon_Hfc zenon_Hcd zenon_H1ab zenon_He1 zenon_H26 zenon_H1a5 zenon_H68 zenon_H173 zenon_H35 zenon_He9 zenon_H48 zenon_H42 zenon_H2d zenon_H222 zenon_H296 zenon_Hf5 zenon_Hde zenon_H310 zenon_H6b zenon_H4a zenon_H18c zenon_H1d8 zenon_Hc8 zenon_H19e zenon_H1d2 zenon_H56 zenon_H108 zenon_H1db zenon_H200 zenon_H4c zenon_Had zenon_H4e zenon_H89 zenon_H15a. % 30.63/30.73 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.63/30.73 apply (zenon_L1209_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.63/30.73 apply (zenon_L627_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.63/30.73 apply (zenon_L2443_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.63/30.73 apply (zenon_L2407_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.63/30.73 apply (zenon_L742_); trivial. % 30.63/30.73 apply (zenon_L744_); trivial. % 30.63/30.73 (* end of lemma zenon_L2444_ *) % 30.63/30.73 assert (zenon_L2445_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H173 zenon_H68 zenon_H1a5 zenon_H26 zenon_He1 zenon_H1db zenon_H2b1 zenon_H16a zenon_H4a zenon_Hfc zenon_H18f zenon_H1ba zenon_H102 zenon_H4e zenon_H19e zenon_Hcd zenon_H1ab zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hf5 zenon_H156. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.73 apply (zenon_L748_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.73 apply (zenon_L2399_); trivial. % 30.63/30.73 apply (zenon_L90_); trivial. % 30.63/30.73 (* end of lemma zenon_L2445_ *) % 30.63/30.73 assert (zenon_L2446_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_He4 zenon_Hd9 zenon_H20d zenon_H1a8 zenon_H156 zenon_H1c7 zenon_H159 zenon_H256 zenon_Hcd zenon_H173 zenon_H4c zenon_H100 zenon_H48 zenon_H15a zenon_H30a zenon_H2b4 zenon_H14e zenon_He7 zenon_Hb8 zenon_H56 zenon_H1fd zenon_H1ab zenon_Hee zenon_H10d zenon_H23b zenon_H102 zenon_H35 zenon_H18f zenon_H1a5 zenon_H4a zenon_H1a2 zenon_H1d2 zenon_H20e zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_H18c zenon_H6c zenon_H101 zenon_H16f zenon_Hd1 zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H19e zenon_H4e zenon_Hfc zenon_H1e zenon_H2d zenon_H42 zenon_H6f. % 30.63/30.73 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.63/30.73 apply (zenon_L47_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.63/30.73 exact (zenon_H18f zenon_Hd2). % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.63/30.73 apply (zenon_L2426_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.63/30.73 apply (zenon_L154_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.63/30.73 apply (zenon_L824_); trivial. % 30.63/30.73 apply (zenon_L1184_); trivial. % 30.63/30.73 apply (zenon_L2430_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.63/30.73 apply (zenon_L627_); trivial. % 30.63/30.73 apply (zenon_L2431_); trivial. % 30.63/30.73 (* end of lemma zenon_L2446_ *) % 30.63/30.73 assert (zenon_L2447_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H18c zenon_H35 zenon_H1e zenon_H1db zenon_Hf5 zenon_H108 zenon_H56 zenon_H20e zenon_H1d2 zenon_H4e zenon_H89 zenon_H15a. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.63/30.73 apply (zenon_L740_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.63/30.73 apply (zenon_L42_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.63/30.73 apply (zenon_L2409_); trivial. % 30.63/30.73 apply (zenon_L744_); trivial. % 30.63/30.73 (* end of lemma zenon_L2447_ *) % 30.63/30.73 assert (zenon_L2448_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 30.63/30.73 do 0 intro. intros zenon_H200 zenon_H15a zenon_H89 zenon_H4e zenon_H1d2 zenon_H20e zenon_H56 zenon_H108 zenon_H1db zenon_H18c zenon_H48 zenon_H172 zenon_H16a zenon_H33 zenon_H4a zenon_Hfc zenon_Hed zenon_H3d zenon_H19e zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Hde zenon_Hf5. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.63/30.73 apply (zenon_L2447_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.63/30.73 apply (zenon_L1716_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.63/30.73 apply (zenon_L1466_); trivial. % 30.63/30.73 apply (zenon_L294_); trivial. % 30.63/30.73 (* end of lemma zenon_L2448_ *) % 30.63/30.73 assert (zenon_L2449_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H173 zenon_Hcd zenon_H68 zenon_He9 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H200 zenon_H15a zenon_H4e zenon_H1d2 zenon_H20e zenon_H56 zenon_H108 zenon_H18c zenon_H48 zenon_H172 zenon_H16a zenon_H33 zenon_H4a zenon_Hfc zenon_H19e zenon_H18f zenon_H1e zenon_H35 zenon_H102 zenon_Hde zenon_H2d zenon_H42 zenon_Hf5 zenon_H156. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.73 apply (zenon_L95_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.73 apply (zenon_L4_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.73 apply (zenon_L839_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.73 apply (zenon_L2448_); trivial. % 30.63/30.73 apply (zenon_L2387_); trivial. % 30.63/30.73 apply (zenon_L90_); trivial. % 30.63/30.73 (* end of lemma zenon_L2449_ *) % 30.63/30.73 assert (zenon_L2450_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 30.63/30.73 do 0 intro. intros zenon_H200 zenon_H1db zenon_H108 zenon_H56 zenon_H6b zenon_H1d2 zenon_H16a zenon_H33 zenon_H4a zenon_Hfc zenon_Hed zenon_H3d zenon_H19e zenon_H18f zenon_H100 zenon_H95 zenon_H102 zenon_Hde zenon_Hf5. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.63/30.73 apply (zenon_L2403_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.63/30.73 apply (zenon_L1716_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.63/30.73 apply (zenon_L1708_); trivial. % 30.63/30.73 apply (zenon_L294_); trivial. % 30.63/30.73 (* end of lemma zenon_L2450_ *) % 30.63/30.73 assert (zenon_L2451_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H1d5 zenon_H89 zenon_Hc8 zenon_Hde zenon_H102 zenon_H95 zenon_H100 zenon_H18f zenon_H19e zenon_Hed zenon_Hfc zenon_H4a zenon_H33 zenon_H16a zenon_H1d2 zenon_H6b zenon_H56 zenon_H108 zenon_H200 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.63/30.73 apply (zenon_L332_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.63/30.73 apply (zenon_L2450_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.63/30.73 exact (zenon_H1db zenon_H1b9). % 30.63/30.73 apply (zenon_L221_); trivial. % 30.63/30.73 (* end of lemma zenon_L2451_ *) % 30.63/30.73 assert (zenon_L2452_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.63/30.73 do 0 intro. intros zenon_H296 zenon_H42 zenon_H2d zenon_H172 zenon_H20e zenon_H4e zenon_H15a zenon_H222 zenon_H69 zenon_H48 zenon_H1d8 zenon_He2 zenon_H18c zenon_H310 zenon_H173 zenon_Hcd zenon_H68 zenon_H35 zenon_He9 zenon_He1 zenon_H1db zenon_H200 zenon_H108 zenon_H56 zenon_H6b zenon_H1d2 zenon_H16a zenon_H33 zenon_H4a zenon_Hfc zenon_H19e zenon_H18f zenon_H100 zenon_H102 zenon_Hde zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hf5 zenon_H156. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.63/30.73 apply (zenon_L2449_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.73 apply (zenon_L95_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.63/30.73 apply (zenon_L740_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.63/30.73 apply (zenon_L1716_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.63/30.73 apply (zenon_L2400_); trivial. % 30.63/30.73 apply (zenon_L294_); trivial. % 30.63/30.73 apply (zenon_L90_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.73 apply (zenon_L95_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.73 apply (zenon_L1716_); trivial. % 30.63/30.73 apply (zenon_L90_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.73 apply (zenon_L48_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.73 apply (zenon_L95_); trivial. % 30.63/30.73 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.74 apply (zenon_L2451_); trivial. % 30.63/30.74 apply (zenon_L90_); trivial. % 30.63/30.74 (* end of lemma zenon_L2452_ *) % 30.63/30.74 assert (zenon_L2453_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.63/30.74 do 0 intro. intros zenon_He4 zenon_H20d zenon_H156 zenon_H1d5 zenon_H102 zenon_H100 zenon_H18f zenon_Hfc zenon_H33 zenon_H16a zenon_He1 zenon_He9 zenon_H35 zenon_H68 zenon_Hcd zenon_H173 zenon_H48 zenon_H222 zenon_H172 zenon_H2d zenon_H42 zenon_H296 zenon_Hde zenon_H310 zenon_H6b zenon_H4a zenon_H18c zenon_H1d8 zenon_Hc8 zenon_H19e zenon_H200 zenon_H1db zenon_Hf5 zenon_H108 zenon_H56 zenon_H20e zenon_H1d2 zenon_H4e zenon_H89 zenon_H15a. % 30.63/30.74 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.63/30.74 apply (zenon_L232_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.63/30.74 apply (zenon_L48_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.63/30.74 apply (zenon_L627_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.63/30.74 apply (zenon_L2452_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.63/30.74 apply (zenon_L2407_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.63/30.74 apply (zenon_L2409_); trivial. % 30.63/30.74 apply (zenon_L744_); trivial. % 30.63/30.74 (* end of lemma zenon_L2453_ *) % 30.63/30.74 assert (zenon_L2454_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.74 do 0 intro. intros zenon_He4 zenon_Hd9 zenon_Hcd zenon_H20d zenon_H16f zenon_H68 zenon_H2b4 zenon_H30a zenon_H15a zenon_H159 zenon_Hfc zenon_H256 zenon_H42 zenon_H4e zenon_H14e zenon_H6f zenon_He7 zenon_Hb8 zenon_H56 zenon_H1fd zenon_H1ab zenon_Hee zenon_H10d zenon_H23b zenon_H2d zenon_H102 zenon_H35 zenon_H1e zenon_H18f zenon_H1a5 zenon_H4a zenon_H19e zenon_H1a2 zenon_H1d2 zenon_H20e zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.74 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.63/30.74 apply (zenon_L47_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.63/30.74 apply (zenon_L48_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.63/30.74 apply (zenon_L627_); trivial. % 30.63/30.74 apply (zenon_L2410_); trivial. % 30.63/30.74 (* end of lemma zenon_L2454_ *) % 30.63/30.74 assert (zenon_L2455_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.63/30.74 do 0 intro. intros zenon_H225 zenon_He1 zenon_H1db zenon_H102 zenon_H6c zenon_H4a zenon_H18c zenon_H18f zenon_H35 zenon_H19e zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hde zenon_H10e zenon_Hf5 zenon_H218. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.63/30.74 apply (zenon_L232_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.63/30.74 apply (zenon_L2419_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.63/30.74 apply (zenon_L192_); trivial. % 30.63/30.74 apply (zenon_L405_); trivial. % 30.63/30.74 (* end of lemma zenon_L2455_ *) % 30.63/30.74 assert (zenon_L2456_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> False). % 30.63/30.74 do 0 intro. intros zenon_H92 zenon_H84 zenon_H296 zenon_H2d zenon_H172 zenon_H20e zenon_H69 zenon_H1d8 zenon_H310 zenon_H173 zenon_H200 zenon_H56 zenon_H6b zenon_H1d2 zenon_H16a zenon_H33 zenon_H156 zenon_H218 zenon_H10e zenon_H18c zenon_H4a zenon_H102 zenon_H225 zenon_He4 zenon_H6f zenon_H42 zenon_H35 zenon_Hfc zenon_H4e zenon_H19e zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He1 zenon_Hd1 zenon_H16f zenon_H48 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H125 zenon_H100 zenon_H1c7 zenon_Hf9 zenon_H3f zenon_H101 zenon_H1b1 zenon_H4c zenon_H108 zenon_H1fd zenon_H14e zenon_H10d zenon_Hb8 zenon_H18f zenon_Had zenon_H1a8 zenon_Hf5 zenon_H20d zenon_Hcd. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.63/30.74 exact (zenon_H84 zenon_H88). % 30.63/30.74 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.63/30.74 apply (zenon_L232_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.63/30.74 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.63/30.74 apply (zenon_L232_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.63/30.74 apply (zenon_L48_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.63/30.74 apply (zenon_L627_); trivial. % 30.63/30.74 apply (zenon_L2452_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.63/30.74 apply (zenon_L192_); trivial. % 30.63/30.74 apply (zenon_L405_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.63/30.74 apply (zenon_L2455_); trivial. % 30.63/30.74 apply (zenon_L2440_); trivial. % 30.63/30.74 (* end of lemma zenon_L2456_ *) % 30.63/30.74 assert (zenon_L2457_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.63/30.74 do 0 intro. intros zenon_H14b zenon_Hcd zenon_H20d zenon_H1a8 zenon_Had zenon_H18f zenon_H4c zenon_H1b1 zenon_H101 zenon_H3f zenon_Hf9 zenon_H1c7 zenon_H100 zenon_H125 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_H48 zenon_H16f zenon_Hd1 zenon_H19e zenon_Hfc zenon_H35 zenon_H42 zenon_He4 zenon_H225 zenon_H102 zenon_H18c zenon_H218 zenon_H33 zenon_H16a zenon_H6b zenon_H200 zenon_H173 zenon_H310 zenon_H1d8 zenon_H69 zenon_H172 zenon_H296 zenon_H84 zenon_H92 zenon_H108 zenon_H20e zenon_H1d2 zenon_Hd6 zenon_H1ba zenon_H1a2 zenon_H1a5 zenon_Hfd zenon_H4a zenon_H2d zenon_H23b zenon_H10d zenon_Hf5 zenon_He1 zenon_He2 zenon_Hee zenon_H1ab zenon_H1fd zenon_H56 zenon_H1d5 zenon_Hc8 zenon_H14e zenon_H6f zenon_H222 zenon_H89 zenon_He7 zenon_Hb8 zenon_H1db zenon_H156 zenon_H4e zenon_H16c. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.63/30.74 apply (zenon_L2456_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.63/30.74 apply (zenon_L2409_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.63/30.74 apply (zenon_L161_); trivial. % 30.63/30.74 apply (zenon_L2417_); trivial. % 30.63/30.74 (* end of lemma zenon_L2457_ *) % 30.63/30.74 assert (zenon_L2458_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.63/30.74 do 0 intro. intros zenon_H256 zenon_H159 zenon_H14b zenon_Hcd zenon_H20d zenon_H1a8 zenon_Had zenon_H18f zenon_H4c zenon_H1b1 zenon_H101 zenon_H3f zenon_Hf9 zenon_H1c7 zenon_H100 zenon_H125 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_H48 zenon_H16f zenon_Hd1 zenon_H19e zenon_Hfc zenon_H35 zenon_H42 zenon_He4 zenon_H225 zenon_H102 zenon_H18c zenon_H218 zenon_H33 zenon_H16a zenon_H6b zenon_H200 zenon_H173 zenon_H310 zenon_H1d8 zenon_H69 zenon_H172 zenon_H296 zenon_H84 zenon_H92 zenon_H108 zenon_H20e zenon_H1d2 zenon_Hd6 zenon_H1ba zenon_H1a2 zenon_H1a5 zenon_Hfd zenon_H4a zenon_H2d zenon_H23b zenon_H10d zenon_Hf5 zenon_He1 zenon_He2 zenon_Hee zenon_H1ab zenon_H1fd zenon_H56 zenon_H1d5 zenon_Hc8 zenon_H14e zenon_H6f zenon_H222 zenon_H89 zenon_He7 zenon_Hb8 zenon_H1db zenon_H156 zenon_H4e. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.74 apply (zenon_L2384_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.74 apply (zenon_L158_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.74 apply (zenon_L2414_); trivial. % 30.63/30.74 apply (zenon_L2457_); trivial. % 30.63/30.74 (* end of lemma zenon_L2458_ *) % 30.63/30.74 assert (zenon_L2459_ : ((op (e1) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.63/30.74 do 0 intro. intros zenon_H68 zenon_Hb8 zenon_He7 zenon_H222 zenon_H6f zenon_H14e zenon_H56 zenon_H1fd zenon_Hee zenon_He2 zenon_H10d zenon_H23b zenon_H2d zenon_H1a5 zenon_H1a2 zenon_Hd6 zenon_H1d2 zenon_H20e zenon_H108 zenon_H92 zenon_H84 zenon_H296 zenon_H172 zenon_H69 zenon_H1d8 zenon_H310 zenon_H173 zenon_H200 zenon_H6b zenon_H33 zenon_H218 zenon_H18c zenon_H225 zenon_He4 zenon_H42 zenon_H35 zenon_Hd1 zenon_H16f zenon_H48 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H125 zenon_H100 zenon_H1c7 zenon_Hf9 zenon_H3f zenon_H101 zenon_H1b1 zenon_H4c zenon_Had zenon_H1a8 zenon_H20d zenon_H14b zenon_H159 zenon_H256 zenon_He1 zenon_H1db zenon_H2b1 zenon_H16a zenon_H4a zenon_Hfc zenon_H18f zenon_H1ba zenon_H102 zenon_H4e zenon_H19e zenon_Hcd zenon_H1ab zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hf5 zenon_H156. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.63/30.74 apply (zenon_L48_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.63/30.74 apply (zenon_L2458_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.63/30.74 apply (zenon_L2399_); trivial. % 30.63/30.74 apply (zenon_L90_); trivial. % 30.63/30.74 (* end of lemma zenon_L2459_ *) % 30.63/30.74 assert (zenon_L2460_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 30.63/30.74 do 0 intro. intros zenon_H42 zenon_H35 zenon_H16a zenon_H33 zenon_H4a zenon_H182 zenon_H4e zenon_H19e zenon_H2d zenon_H95. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.74 apply (zenon_L730_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.74 apply (zenon_L839_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.74 apply (zenon_L731_); trivial. % 30.63/30.74 apply (zenon_L766_); trivial. % 30.63/30.74 (* end of lemma zenon_L2460_ *) % 30.63/30.74 assert (zenon_L2461_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.63/30.74 do 0 intro. intros zenon_H14b zenon_Hde zenon_Hda zenon_H4c zenon_Had zenon_Hfd zenon_H3d zenon_Hb8 zenon_He2 zenon_He1 zenon_H98 zenon_H6f zenon_H2d zenon_H14e zenon_H4e zenon_H16c. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.63/30.74 apply (zenon_L192_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.63/30.74 apply (zenon_L742_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.63/30.74 apply (zenon_L79_); trivial. % 30.63/30.74 apply (zenon_L1723_); trivial. % 30.63/30.74 (* end of lemma zenon_L2461_ *) % 30.63/30.74 assert (zenon_L2462_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.74 do 0 intro. intros zenon_H42 zenon_H1e zenon_H16a zenon_H33 zenon_H4a zenon_H16c zenon_H4e zenon_H14e zenon_H2d zenon_H6f zenon_H98 zenon_He2 zenon_Hb8 zenon_Hfd zenon_Had zenon_H4c zenon_Hda zenon_Hde zenon_H14b zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.74 apply (zenon_L4_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.74 apply (zenon_L839_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.74 apply (zenon_L2461_); trivial. % 30.63/30.74 apply (zenon_L2387_); trivial. % 30.63/30.74 (* end of lemma zenon_L2462_ *) % 30.63/30.74 assert (zenon_L2463_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.74 do 0 intro. intros zenon_H16f zenon_H48 zenon_H15a zenon_H30a zenon_H2b4 zenon_H19a zenon_H42 zenon_H1e zenon_H16a zenon_H33 zenon_H4a zenon_H4e zenon_H14e zenon_H2d zenon_H6f zenon_H98 zenon_He2 zenon_Hb8 zenon_Hfd zenon_Had zenon_H4c zenon_Hda zenon_Hde zenon_H14b zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.74 apply (zenon_L2384_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.74 apply (zenon_L839_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.74 apply (zenon_L235_); trivial. % 30.63/30.74 apply (zenon_L2462_); trivial. % 30.63/30.74 (* end of lemma zenon_L2463_ *) % 30.63/30.74 assert (zenon_L2464_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 30.63/30.74 do 0 intro. intros zenon_H102 zenon_H35 zenon_H18f zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H14b zenon_Hde zenon_Hda zenon_H4c zenon_Had zenon_Hb8 zenon_He2 zenon_H98 zenon_H6f zenon_H2d zenon_H14e zenon_H4e zenon_H4a zenon_H33 zenon_H16a zenon_H1e zenon_H42 zenon_H19a zenon_H2b4 zenon_H30a zenon_H15a zenon_H48 zenon_H16f zenon_H19e zenon_H3d. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.63/30.74 apply (zenon_L42_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.63/30.74 exact (zenon_H18f zenon_Hd2). % 30.63/30.74 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.63/30.74 apply (zenon_L2463_); trivial. % 30.63/30.74 apply (zenon_L131_); trivial. % 30.63/30.74 (* end of lemma zenon_L2464_ *) % 30.63/30.74 assert (zenon_L2465_ : ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 30.63/30.74 do 0 intro. intros zenon_H16c zenon_H4e zenon_H14e zenon_H222 zenon_H89 zenon_He7 zenon_Hb8 zenon_H56 zenon_H102 zenon_H35 zenon_H18f zenon_He1 zenon_Hf5 zenon_H1db zenon_Hc8 zenon_H1d5 zenon_H14b zenon_Hde zenon_Hda zenon_H4c zenon_Had zenon_He2 zenon_H2d zenon_H4a zenon_H33 zenon_H16a zenon_H1e zenon_H42 zenon_H2b4 zenon_H30a zenon_H15a zenon_H48 zenon_H16f zenon_H19e zenon_H1a5 zenon_H1a2 zenon_H6f zenon_H98. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.74 apply (zenon_L4_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.74 apply (zenon_L839_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.63/30.74 apply (zenon_L2386_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.63/30.74 apply (zenon_L2464_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.63/30.74 exact (zenon_H56 zenon_H25). % 30.63/30.74 apply (zenon_L877_); trivial. % 30.63/30.74 apply (zenon_L80_); trivial. % 30.63/30.74 (* end of lemma zenon_L2465_ *) % 30.63/30.74 assert (zenon_L2466_ : ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 30.63/30.74 do 0 intro. intros zenon_H68 zenon_H159 zenon_Hfc zenon_H256 zenon_H4e zenon_H14e zenon_H222 zenon_H89 zenon_He7 zenon_Hb8 zenon_H56 zenon_H102 zenon_H35 zenon_H18f zenon_He1 zenon_Hf5 zenon_H1db zenon_Hc8 zenon_H1d5 zenon_H14b zenon_Hde zenon_Hda zenon_H4c zenon_Had zenon_He2 zenon_H2d zenon_H4a zenon_H33 zenon_H16a zenon_H1e zenon_H42 zenon_H2b4 zenon_H30a zenon_H15a zenon_H48 zenon_H16f zenon_H19e zenon_H1a5 zenon_H1a2 zenon_H6f zenon_H98. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.74 apply (zenon_L18_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.74 apply (zenon_L839_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.74 apply (zenon_L2391_); trivial. % 30.63/30.74 apply (zenon_L2465_); trivial. % 30.63/30.74 (* end of lemma zenon_L2466_ *) % 30.63/30.74 assert (zenon_L2467_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.63/30.74 do 0 intro. intros zenon_H42 zenon_H2d zenon_H1e zenon_H16a zenon_H33 zenon_H19e zenon_He9 zenon_H35 zenon_H18f zenon_H18c zenon_H4a zenon_H6c zenon_H102 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.74 apply (zenon_L4_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.74 apply (zenon_L839_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.74 apply (zenon_L922_); trivial. % 30.63/30.74 apply (zenon_L2387_); trivial. % 30.63/30.74 (* end of lemma zenon_L2467_ *) % 30.63/30.74 assert (zenon_L2468_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e1)) -> False). % 30.63/30.74 do 0 intro. intros zenon_H16f zenon_Hd1 zenon_H16a zenon_H33 zenon_H4a zenon_He1 zenon_Hf5 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H19e zenon_Hfc zenon_H1e zenon_H2d zenon_H42 zenon_H159 zenon_H4e zenon_H182. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.74 apply (zenon_L729_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.74 apply (zenon_L839_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.74 apply (zenon_L2388_); trivial. % 30.63/30.74 apply (zenon_L733_); trivial. % 30.63/30.74 (* end of lemma zenon_L2468_ *) % 30.63/30.74 assert (zenon_L2469_ : (((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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 30.63/30.74 do 0 intro. intros zenon_H200 zenon_H1d2 zenon_H20e zenon_H56 zenon_H108 zenon_H18c zenon_H4a zenon_H6c zenon_H48 zenon_H172 zenon_H4e zenon_H14e zenon_H159 zenon_H42 zenon_H2d zenon_H1e zenon_H15e zenon_Hfc zenon_H19e zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He1 zenon_H256 zenon_He7 zenon_Hb8 zenon_H15a zenon_H30a zenon_H2b4 zenon_Hd6 zenon_Had zenon_H4c zenon_He2 zenon_Hda zenon_H14b zenon_Hfd zenon_H3d zenon_Hde zenon_Hf5. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.63/30.74 apply (zenon_L2433_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.63/30.74 apply (zenon_L192_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.63/30.74 apply (zenon_L742_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.63/30.74 apply (zenon_L161_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.63/30.74 exact (zenon_H30a zenon_H185). % 30.63/30.74 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.63/30.74 apply (zenon_L744_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.63/30.74 apply (zenon_L294_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.63/30.74 apply (zenon_L199_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.63/30.74 apply (zenon_L2387_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.63/30.74 apply (zenon_L304_); trivial. % 30.63/30.74 apply (zenon_L2389_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.63/30.74 apply (zenon_L79_); trivial. % 30.63/30.74 apply (zenon_L294_); trivial. % 30.63/30.74 (* end of lemma zenon_L2469_ *) % 30.63/30.74 assert (zenon_L2470_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 30.63/30.74 do 0 intro. intros zenon_H14b zenon_Hde zenon_Hda zenon_H108 zenon_H56 zenon_H20e zenon_H1d2 zenon_Hfd zenon_H3d zenon_H1fd zenon_H1ab zenon_Hee zenon_Hb8 zenon_He2 zenon_He1 zenon_H14e zenon_H4e zenon_H16c zenon_Hf5 zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H10d zenon_H23b zenon_H6f zenon_H19a zenon_H1db zenon_H2d. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.63/30.74 apply (zenon_L192_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.63/30.74 apply (zenon_L2409_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.63/30.74 apply (zenon_L79_); trivial. % 30.63/30.74 apply (zenon_L2395_); trivial. % 30.63/30.74 (* end of lemma zenon_L2470_ *) % 30.63/30.74 assert (zenon_L2471_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.63/30.74 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_H40 zenon_H6f zenon_H19a zenon_Hee zenon_H1ab. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.63/30.74 apply (zenon_L386_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.63/30.74 apply (zenon_L80_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.63/30.74 apply (zenon_L337_); trivial. % 30.63/30.74 exact (zenon_H1ab zenon_H112). % 30.63/30.74 (* end of lemma zenon_L2471_ *) % 30.63/30.74 assert (zenon_L2472_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.63/30.74 do 0 intro. intros zenon_H16f zenon_H48 zenon_H15a zenon_H30a zenon_H2b4 zenon_H42 zenon_H1e zenon_H16a zenon_H33 zenon_H4a zenon_H2d zenon_H1db zenon_H10d zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_Hf5 zenon_H4e zenon_H14e zenon_He1 zenon_Hb8 zenon_H1fd zenon_Hfd zenon_H1d2 zenon_H20e zenon_H56 zenon_H108 zenon_Hda zenon_Hde zenon_H14b zenon_H23b zenon_Hcd zenon_He2 zenon_H6f zenon_H19a zenon_Hee zenon_H1ab. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.63/30.74 apply (zenon_L2384_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.63/30.74 apply (zenon_L839_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.63/30.74 apply (zenon_L235_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.74 apply (zenon_L4_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.74 apply (zenon_L839_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.74 apply (zenon_L2470_); trivial. % 30.63/30.74 apply (zenon_L2471_); trivial. % 30.63/30.74 (* end of lemma zenon_L2472_ *) % 30.63/30.74 assert (zenon_L2473_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e3)) -> False). % 30.63/30.74 do 0 intro. intros zenon_Hf9 zenon_Hcd zenon_H90 zenon_H40 zenon_He1 zenon_Hda zenon_H10d zenon_H14e zenon_H4c zenon_H15e. % 30.63/30.74 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.63/30.74 apply (zenon_L386_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.63/30.74 apply (zenon_L1354_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.63/30.74 apply (zenon_L64_); trivial. % 30.63/30.74 apply (zenon_L752_); trivial. % 30.63/30.74 (* end of lemma zenon_L2473_ *) % 30.63/30.74 assert (zenon_L2474_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e3)) -> False). % 30.63/30.74 do 0 intro. intros zenon_H42 zenon_H35 zenon_Hfc zenon_H182 zenon_H4e zenon_H19e zenon_Hf9 zenon_Hcd zenon_H90 zenon_He1 zenon_Hda zenon_H10d zenon_H14e zenon_H4c zenon_H15e. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.63/30.74 apply (zenon_L730_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.63/30.74 apply (zenon_L203_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.63/30.74 apply (zenon_L731_); trivial. % 30.63/30.74 apply (zenon_L2473_); trivial. % 30.63/30.74 (* end of lemma zenon_L2474_ *) % 30.63/30.74 assert (zenon_L2475_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.63/30.74 do 0 intro. intros zenon_Hb8 zenon_H6f zenon_H4c zenon_H10d zenon_Hda zenon_He1 zenon_H90 zenon_Hcd zenon_Hf9 zenon_Hee zenon_H15e zenon_H14e zenon_H4e zenon_H16c. % 30.63/30.74 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.63/30.74 apply (zenon_L39_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.63/30.74 apply (zenon_L2473_); trivial. % 30.63/30.74 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.68/30.75 apply (zenon_L490_); trivial. % 30.68/30.75 apply (zenon_L875_); trivial. % 30.68/30.75 (* end of lemma zenon_L2475_ *) % 30.68/30.75 assert (zenon_L2476_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 30.68/30.75 do 0 intro. intros zenon_H2f8 zenon_H20e zenon_H142 zenon_H1a5 zenon_H26 zenon_H1b1 zenon_Hdc zenon_H4c zenon_Hb6 zenon_Hee. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.75 apply (zenon_L350_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.75 apply (zenon_L136_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.75 apply (zenon_L2436_); trivial. % 30.68/30.75 apply (zenon_L490_); trivial. % 30.68/30.75 (* end of lemma zenon_L2476_ *) % 30.68/30.75 assert (zenon_L2477_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H1a2 zenon_Hee zenon_Hdc zenon_H1b1 zenon_H1a5 zenon_H142 zenon_H20e zenon_H2f8 zenon_H1db zenon_H10d zenon_Hda zenon_He1 zenon_H90 zenon_Hcd zenon_Hf9 zenon_H1fd zenon_H9d zenon_H4c zenon_H100 zenon_H56 zenon_Hb8 zenon_He7 zenon_H89 zenon_H222 zenon_H3d zenon_H6f zenon_H14e zenon_H4e zenon_H16c. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.75 apply (zenon_L598_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.75 apply (zenon_L2475_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.75 exact (zenon_H1db zenon_H1b9). % 30.68/30.75 apply (zenon_L2476_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.75 apply (zenon_L1184_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.75 exact (zenon_H56 zenon_H25). % 30.68/30.75 apply (zenon_L877_); trivial. % 30.68/30.75 (* end of lemma zenon_L2477_ *) % 30.68/30.75 assert (zenon_L2478_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H1fd zenon_H26 zenon_H16c zenon_H4e zenon_H14e zenon_Hee zenon_Hf9 zenon_Hcd zenon_H90 zenon_He1 zenon_Hda zenon_H10d zenon_H4c zenon_H6f zenon_Hb8 zenon_H1db zenon_H2d zenon_H9c. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.75 apply (zenon_L598_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.75 apply (zenon_L2475_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.75 exact (zenon_H1db zenon_H1b9). % 30.68/30.75 apply (zenon_L304_); trivial. % 30.68/30.75 (* end of lemma zenon_L2478_ *) % 30.68/30.75 assert (zenon_L2479_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H14b zenon_Hde zenon_Hf5 zenon_H108 zenon_H1d2 zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1b1 zenon_Hdc zenon_H1a2 zenon_H2d zenon_H1db zenon_H10d zenon_Hda zenon_He1 zenon_H90 zenon_Hcd zenon_Hf9 zenon_Hee zenon_H1fd zenon_H9d zenon_H4c zenon_H100 zenon_H56 zenon_Hb8 zenon_He7 zenon_H89 zenon_H222 zenon_H3d zenon_H6f zenon_H14e zenon_H4e zenon_H16c. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.75 apply (zenon_L192_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.75 apply (zenon_L2409_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.75 apply (zenon_L2477_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.75 apply (zenon_L2478_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.75 apply (zenon_L1184_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.75 exact (zenon_H56 zenon_H25). % 30.68/30.75 apply (zenon_L877_); trivial. % 30.68/30.75 (* end of lemma zenon_L2479_ *) % 30.68/30.75 assert (zenon_L2480_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H42 zenon_H1e zenon_H16a zenon_H33 zenon_H4a zenon_H16c zenon_H4e zenon_H14e zenon_H6f zenon_H222 zenon_H89 zenon_He7 zenon_Hb8 zenon_H56 zenon_H100 zenon_H4c zenon_H1fd zenon_Hee zenon_Hf9 zenon_Hcd zenon_H90 zenon_Hda zenon_H10d zenon_H1db zenon_H2d zenon_H1a2 zenon_Hdc zenon_H1b1 zenon_H1a5 zenon_H20e zenon_H2f8 zenon_H1d2 zenon_H108 zenon_Hf5 zenon_Hde zenon_H14b zenon_He1 zenon_H9d. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.75 apply (zenon_L4_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.75 apply (zenon_L839_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.75 apply (zenon_L2479_); trivial. % 30.68/30.75 apply (zenon_L1354_); trivial. % 30.68/30.75 (* end of lemma zenon_L2480_ *) % 30.68/30.75 assert (zenon_L2481_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.68/30.75 do 0 intro. intros zenon_He4 zenon_Hd9 zenon_He1 zenon_H14b zenon_Hde zenon_H108 zenon_H1d2 zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1b1 zenon_H1a2 zenon_H2d zenon_H1db zenon_H10d zenon_Hda zenon_Hf9 zenon_Hee zenon_H1fd zenon_H4c zenon_H100 zenon_H56 zenon_Hb8 zenon_He7 zenon_H89 zenon_H222 zenon_H6f zenon_H14e zenon_H4e zenon_H4a zenon_H33 zenon_H16a zenon_H1e zenon_H42 zenon_H35 zenon_Hfc zenon_H19e zenon_Hd1 zenon_H16f zenon_H1c7 zenon_H3f zenon_H101 zenon_H18f zenon_H1a8 zenon_Hf5 zenon_H20d zenon_H90 zenon_Hcd. % 30.68/30.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.75 apply (zenon_L47_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.75 apply (zenon_L48_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.75 exact (zenon_H18f zenon_Hd2). % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.75 apply (zenon_L2435_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.75 apply (zenon_L1627_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.75 apply (zenon_L154_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.75 apply (zenon_L1253_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.75 apply (zenon_L729_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.75 apply (zenon_L839_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.75 apply (zenon_L2474_); trivial. % 30.68/30.75 apply (zenon_L2480_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.75 apply (zenon_L627_); trivial. % 30.68/30.75 apply (zenon_L386_); trivial. % 30.68/30.75 (* end of lemma zenon_L2481_ *) % 30.68/30.75 assert (zenon_L2482_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.68/30.75 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H18c zenon_H20 zenon_Hd2 zenon_He2 zenon_H4c zenon_Had zenon_H4e zenon_H89 zenon_H15a. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.75 apply (zenon_L740_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.75 apply (zenon_L906_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.75 apply (zenon_L742_); trivial. % 30.68/30.75 apply (zenon_L744_); trivial. % 30.68/30.75 (* end of lemma zenon_L2482_ *) % 30.68/30.75 assert (zenon_L2483_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H256 zenon_Hb1 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e zenon_Hbc. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 30.68/30.75 apply (zenon_L84_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 30.68/30.75 apply (zenon_L872_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 30.68/30.75 apply (zenon_L90_); trivial. % 30.68/30.75 apply (zenon_L875_); trivial. % 30.68/30.75 (* end of lemma zenon_L2483_ *) % 30.68/30.75 assert (zenon_L2484_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_Hde zenon_Hb8 zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H6f zenon_H23b zenon_H222 zenon_H3d zenon_H9c zenon_H2d zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.75 exact (zenon_H30a zenon_H185). % 30.68/30.75 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.75 apply (zenon_L744_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.75 apply (zenon_L294_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.68/30.75 apply (zenon_L892_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.68/30.75 apply (zenon_L775_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.68/30.75 apply (zenon_L304_); trivial. % 30.68/30.75 apply (zenon_L2483_); trivial. % 30.68/30.75 (* end of lemma zenon_L2484_ *) % 30.68/30.75 assert (zenon_L2485_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_Hb8 zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H6f zenon_H23b zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Heb zenon_He1 zenon_H256 zenon_Hb1 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.68/30.75 apply (zenon_L892_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.68/30.75 apply (zenon_L2387_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.68/30.75 apply (zenon_L204_); trivial. % 30.68/30.75 apply (zenon_L2483_); trivial. % 30.68/30.75 (* end of lemma zenon_L2485_ *) % 30.68/30.75 assert (zenon_L2486_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H125 zenon_H10e zenon_H1b1 zenon_Hdc zenon_H4c zenon_H108 zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H2d zenon_H3d zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_Hb8 zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H6f zenon_H23b zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_He1 zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.68/30.75 apply (zenon_L192_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.68/30.75 apply (zenon_L2436_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.68/30.75 apply (zenon_L62_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.75 apply (zenon_L881_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.75 apply (zenon_L29_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.75 apply (zenon_L2484_); trivial. % 30.68/30.75 apply (zenon_L2485_); trivial. % 30.68/30.75 (* end of lemma zenon_L2486_ *) % 30.68/30.75 assert (zenon_L2487_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H14b zenon_He1 zenon_H1d5 zenon_Hc8 zenon_H3f zenon_H1e zenon_H20 zenon_Hbd zenon_H4c zenon_Hdc zenon_H1b1 zenon_H125 zenon_H1db zenon_H108 zenon_H56 zenon_H20e zenon_H1d2 zenon_Hd6 zenon_H1ba zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_Hde zenon_Hb8 zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H6f zenon_H23b zenon_H222 zenon_H3d zenon_H2d zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.75 apply (zenon_L2486_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.75 apply (zenon_L2409_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.75 apply (zenon_L161_); trivial. % 30.68/30.75 apply (zenon_L2484_); trivial. % 30.68/30.75 (* end of lemma zenon_L2487_ *) % 30.68/30.75 assert (zenon_L2488_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_Hbd zenon_H1ab zenon_H10d zenon_H100 zenon_H20 zenon_H23b zenon_H1e zenon_H3f zenon_H1dc zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Hee zenon_H4c zenon_Hdc zenon_H1b1 zenon_H26 zenon_H1a5 zenon_H142 zenon_H20e zenon_H2f8 zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.75 apply (zenon_L881_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.75 apply (zenon_L29_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.75 apply (zenon_L177_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.68/30.75 apply (zenon_L199_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.68/30.75 apply (zenon_L2387_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.68/30.75 apply (zenon_L2476_); trivial. % 30.68/30.75 apply (zenon_L2483_); trivial. % 30.68/30.75 (* end of lemma zenon_L2488_ *) % 30.68/30.75 assert (zenon_L2489_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H1a0 zenon_H6f zenon_H256 zenon_Hb1 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.68/30.75 apply (zenon_L199_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.68/30.75 apply (zenon_L2387_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.68/30.75 apply (zenon_L540_); trivial. % 30.68/30.75 apply (zenon_L2483_); trivial. % 30.68/30.75 (* end of lemma zenon_L2489_ *) % 30.68/30.75 assert (zenon_L2490_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H1a0 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.75 exact (zenon_H30a zenon_H185). % 30.68/30.75 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.75 apply (zenon_L744_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.75 apply (zenon_L294_); trivial. % 30.68/30.75 apply (zenon_L2489_); trivial. % 30.68/30.75 (* end of lemma zenon_L2490_ *) % 30.68/30.75 assert (zenon_L2491_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H1a2 zenon_H2d zenon_H9c zenon_H3d zenon_H23b zenon_H100 zenon_H10d zenon_H1ab zenon_H15e zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.75 apply (zenon_L2484_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.75 apply (zenon_L235_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.75 exact (zenon_H56 zenon_H25). % 30.68/30.75 apply (zenon_L2490_); trivial. % 30.68/30.75 (* end of lemma zenon_L2491_ *) % 30.68/30.75 assert (zenon_L2492_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 30.68/30.75 do 0 intro. intros zenon_H172 zenon_Hdf zenon_H48 zenon_H18c zenon_H90 zenon_H4a zenon_Had zenon_H1db zenon_Hf5 zenon_H108 zenon_H56 zenon_H20e zenon_H1d2 zenon_H4e zenon_H89 zenon_H15a. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.75 apply (zenon_L740_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.75 apply (zenon_L769_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.75 apply (zenon_L2409_); trivial. % 30.68/30.75 apply (zenon_L744_); trivial. % 30.68/30.75 (* end of lemma zenon_L2492_ *) % 30.68/30.75 assert (zenon_L2493_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.68/30.75 do 0 intro. intros zenon_He4 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H200 zenon_Had zenon_H18c zenon_H48 zenon_H172 zenon_H2d zenon_H6f zenon_H15a zenon_H30a zenon_H2b4 zenon_Hd6 zenon_H1d2 zenon_H56 zenon_H108 zenon_H125 zenon_H14b zenon_H4e zenon_H14e zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H26 zenon_H1b1 zenon_H4c zenon_Hee zenon_He7 zenon_Hb8 zenon_H1dc zenon_H3f zenon_H1e zenon_H23b zenon_H20 zenon_H100 zenon_H10d zenon_H1ab zenon_Hbd zenon_Hde zenon_H42 zenon_Hf5 zenon_H20d zenon_H90 zenon_Hcd. % 30.68/30.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.75 apply (zenon_L232_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.75 apply (zenon_L4_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.75 apply (zenon_L125_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.75 apply (zenon_L2492_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.75 apply (zenon_L2487_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.75 apply (zenon_L2488_); trivial. % 30.68/30.75 apply (zenon_L294_); trivial. % 30.68/30.75 apply (zenon_L2387_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.75 apply (zenon_L627_); trivial. % 30.68/30.75 apply (zenon_L386_); trivial. % 30.68/30.75 (* end of lemma zenon_L2493_ *) % 30.68/30.75 assert (zenon_L2494_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.75 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_Hd2 zenon_H4a zenon_H100 zenon_Hb6 zenon_H6f zenon_H1ab. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.75 apply (zenon_L386_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.75 apply (zenon_L880_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.75 apply (zenon_L540_); trivial. % 30.68/30.75 exact (zenon_H1ab zenon_H112). % 30.68/30.75 (* end of lemma zenon_L2494_ *) % 30.68/30.75 assert (zenon_L2495_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_Hbd zenon_Hde zenon_He2 zenon_H1e zenon_H3f zenon_H142 zenon_H1dc zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H1a0 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.75 apply (zenon_L288_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.75 apply (zenon_L29_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.75 apply (zenon_L177_); trivial. % 30.68/30.75 apply (zenon_L2489_); trivial. % 30.68/30.75 (* end of lemma zenon_L2495_ *) % 30.68/30.75 assert (zenon_L2496_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.75 do 0 intro. intros zenon_H23b zenon_Hcd zenon_H100 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He1 zenon_He7 zenon_Hb8 zenon_H1dc zenon_H142 zenon_H3f zenon_H1e zenon_He2 zenon_Hde zenon_Hbd zenon_H1ab. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.75 apply (zenon_L386_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.75 apply (zenon_L880_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.75 apply (zenon_L2495_); trivial. % 30.68/30.75 exact (zenon_H1ab zenon_H112). % 30.68/30.75 (* end of lemma zenon_L2496_ *) % 30.68/30.75 assert (zenon_L2497_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.75 do 0 intro. intros zenon_H173 zenon_H35 zenon_He9 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H1a2 zenon_H20d zenon_H42 zenon_H20 zenon_Hee zenon_H1a5 zenon_H20e zenon_H2f8 zenon_H14b zenon_H125 zenon_H108 zenon_H56 zenon_H1d2 zenon_Hd6 zenon_H172 zenon_H48 zenon_H18c zenon_Had zenon_H200 zenon_He4 zenon_H1fd zenon_H4c zenon_H1b1 zenon_Hbd zenon_He2 zenon_H1e zenon_H3f zenon_H1dc zenon_He7 zenon_Hcd zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H6f zenon_H23b zenon_H2d zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H14e zenon_H4e zenon_Hf5 zenon_H156. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.75 apply (zenon_L4_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.75 apply (zenon_L125_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.75 apply (zenon_L2482_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.75 apply (zenon_L2487_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.75 apply (zenon_L2488_); trivial. % 30.68/30.75 apply (zenon_L294_); trivial. % 30.68/30.75 apply (zenon_L2387_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.75 apply (zenon_L95_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.75 apply (zenon_L4_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.75 apply (zenon_L125_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.75 apply (zenon_L87_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.75 apply (zenon_L881_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.75 apply (zenon_L29_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.75 apply (zenon_L2491_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.75 apply (zenon_L2493_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.75 apply (zenon_L880_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.75 apply (zenon_L2489_); trivial. % 30.68/30.75 exact (zenon_H1ab zenon_H112). % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.75 exact (zenon_H1db zenon_H1b9). % 30.68/30.75 apply (zenon_L2494_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.75 apply (zenon_L1177_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.75 apply (zenon_L2496_); trivial. % 30.68/30.75 apply (zenon_L2484_); trivial. % 30.68/30.75 apply (zenon_L2387_); trivial. % 30.68/30.75 apply (zenon_L90_); trivial. % 30.68/30.75 (* end of lemma zenon_L2497_ *) % 30.68/30.75 assert (zenon_L2498_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_Hb8 zenon_H1ab zenon_H26 zenon_H100 zenon_H6f zenon_H23b zenon_H4c zenon_H10d zenon_Hda zenon_He1 zenon_H90 zenon_Hcd zenon_Hf9 zenon_Hee zenon_H15e zenon_H256 zenon_Hb1 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.68/30.75 apply (zenon_L892_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.68/30.75 apply (zenon_L2473_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.68/30.75 apply (zenon_L490_); trivial. % 30.68/30.75 apply (zenon_L2483_); trivial. % 30.68/30.75 (* end of lemma zenon_L2498_ *) % 30.68/30.75 assert (zenon_L2499_ : ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.75 do 0 intro. intros zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_Hb1 zenon_H256 zenon_H15e zenon_Hee zenon_Hf9 zenon_Hcd zenon_He1 zenon_Hda zenon_H4c zenon_H23b zenon_H6f zenon_Hb8 zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.75 apply (zenon_L2498_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.75 apply (zenon_L880_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.75 apply (zenon_L699_); trivial. % 30.68/30.75 exact (zenon_H1ab zenon_H112). % 30.68/30.75 (* end of lemma zenon_L2499_ *) % 30.68/30.75 assert (zenon_L2500_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.75 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H2d zenon_H3d zenon_H222 zenon_Hde zenon_H89 zenon_H15a zenon_H30a zenon_H2b4 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H256 zenon_H15e zenon_Hee zenon_Hf9 zenon_Hcd zenon_He1 zenon_Hda zenon_H4c zenon_H23b zenon_H6f zenon_Hb8 zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.75 apply (zenon_L881_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.75 apply (zenon_L29_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.75 apply (zenon_L2484_); trivial. % 30.68/30.75 apply (zenon_L2499_); trivial. % 30.68/30.75 (* end of lemma zenon_L2500_ *) % 30.68/30.75 assert (zenon_L2501_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.75 do 0 intro. intros zenon_H23b zenon_H89 zenon_H10d zenon_Hda zenon_H3f zenon_He9 zenon_Hcd zenon_Hf9 zenon_Hd2 zenon_H4a zenon_H100 zenon_H19a zenon_Hee zenon_H1ab. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.75 apply (zenon_L1627_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.75 apply (zenon_L880_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.75 apply (zenon_L337_); trivial. % 30.68/30.75 exact (zenon_H1ab zenon_H112). % 30.68/30.75 (* end of lemma zenon_L2501_ *) % 30.68/30.75 assert (zenon_L2502_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.68/30.75 do 0 intro. intros zenon_H42 zenon_H4e zenon_H14e zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H6f zenon_He7 zenon_Hb8 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H56 zenon_H23b zenon_H10d zenon_Hda zenon_H3f zenon_He9 zenon_Hcd zenon_Hf9 zenon_H100 zenon_Hee zenon_H1ab zenon_Hbd zenon_H20 zenon_H1e zenon_H2d zenon_H15e zenon_H4c zenon_H1a2 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.75 apply (zenon_L4_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.75 apply (zenon_L125_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.75 apply (zenon_L2500_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.75 apply (zenon_L2501_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.75 exact (zenon_H56 zenon_H25). % 30.68/30.75 apply (zenon_L2490_); trivial. % 30.68/30.75 apply (zenon_L2387_); trivial. % 30.68/30.75 (* end of lemma zenon_L2502_ *) % 30.68/30.75 assert (zenon_L2503_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.68/30.75 do 0 intro. intros zenon_H1a2 zenon_Hf5 zenon_H156 zenon_H159 zenon_H256 zenon_H2f8 zenon_H20e zenon_H142 zenon_H1a5 zenon_H1b1 zenon_Hdc zenon_H4c zenon_H1d5 zenon_Hc8 zenon_H1db zenon_He1 zenon_H1dc zenon_H1e zenon_H20 zenon_Hbd zenon_H1ab zenon_Hee zenon_H100 zenon_H4a zenon_Hd2 zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_Hda zenon_H10d zenon_H23b zenon_H56 zenon_Hb8 zenon_He7 zenon_H89 zenon_H222 zenon_H3d zenon_H6f zenon_H14e zenon_H4e zenon_H16c. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.75 apply (zenon_L2488_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.75 apply (zenon_L2501_); trivial. % 30.68/30.75 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.75 exact (zenon_H56 zenon_H25). % 30.68/30.75 apply (zenon_L877_); trivial. % 30.68/30.75 (* end of lemma zenon_L2503_ *) % 30.68/30.75 assert (zenon_L2504_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1a2 zenon_H2d zenon_H9c zenon_H3d zenon_H1ab zenon_Hee zenon_H100 zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_Hda zenon_H10d zenon_H23b zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2484_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L2501_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L2490_); trivial. % 30.68/30.76 (* end of lemma zenon_L2504_ *) % 30.68/30.76 assert (zenon_L2505_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H14b zenon_H108 zenon_H1d2 zenon_H16c zenon_Hbd zenon_H20 zenon_H1e zenon_H1dc zenon_H4c zenon_Hdc zenon_H1b1 zenon_H1a5 zenon_H20e zenon_H2f8 zenon_H1a2 zenon_H2d zenon_H3d zenon_H1ab zenon_Hee zenon_H100 zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_Hda zenon_H10d zenon_H23b zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.76 apply (zenon_L192_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.76 apply (zenon_L2409_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.76 apply (zenon_L2503_); trivial. % 30.68/30.76 apply (zenon_L2504_); trivial. % 30.68/30.76 (* end of lemma zenon_L2505_ *) % 30.68/30.76 assert (zenon_L2506_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H42 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He7 zenon_Hb8 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H56 zenon_H100 zenon_H4c zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H2d zenon_H15e zenon_Hee zenon_Hf9 zenon_Hcd zenon_Hda zenon_H23b zenon_H10d zenon_H1ab zenon_H1a2 zenon_He1 zenon_H9d. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.76 apply (zenon_L4_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2500_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L1184_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L2490_); trivial. % 30.68/30.76 apply (zenon_L1354_); trivial. % 30.68/30.76 (* end of lemma zenon_L2506_ *) % 30.68/30.76 assert (zenon_L2507_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1a2 zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H2f8 zenon_H20e zenon_H142 zenon_H1a5 zenon_H1b1 zenon_Hdc zenon_Hee zenon_H1d5 zenon_Hc8 zenon_H1db zenon_He1 zenon_H1dc zenon_H3f zenon_H1e zenon_H23b zenon_H20 zenon_H10d zenon_H1ab zenon_Hbd zenon_H9d zenon_H4c zenon_H100 zenon_H56 zenon_Hb8 zenon_He7 zenon_H89 zenon_H222 zenon_H3d zenon_H6f zenon_H14e zenon_H4e zenon_H16c. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2488_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L1184_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L877_); trivial. % 30.68/30.76 (* end of lemma zenon_L2507_ *) % 30.68/30.76 assert (zenon_L2508_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1a2 zenon_H2d zenon_H9c zenon_H3d zenon_H23b zenon_H10d zenon_H1ab zenon_H9d zenon_H4c zenon_H100 zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2484_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L1184_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L2490_); trivial. % 30.68/30.76 (* end of lemma zenon_L2508_ *) % 30.68/30.76 assert (zenon_L2509_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H14b zenon_Hda zenon_H108 zenon_H1d2 zenon_H16c zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H1dc zenon_Hee zenon_Hdc zenon_H1b1 zenon_H1a5 zenon_H20e zenon_H2f8 zenon_H1a2 zenon_H2d zenon_H3d zenon_H23b zenon_H10d zenon_H1ab zenon_H9d zenon_H4c zenon_H100 zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.76 apply (zenon_L192_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.76 apply (zenon_L2409_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.76 apply (zenon_L2507_); trivial. % 30.68/30.76 apply (zenon_L2508_); trivial. % 30.68/30.76 (* end of lemma zenon_L2509_ *) % 30.68/30.76 assert (zenon_L2510_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H16f zenon_H48 zenon_Hcd zenon_Hf9 zenon_H42 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He7 zenon_Hb8 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H56 zenon_H100 zenon_H4c zenon_H1ab zenon_H10d zenon_H23b zenon_H2d zenon_H1a2 zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1b1 zenon_Hdc zenon_Hee zenon_H1dc zenon_H3f zenon_H1e zenon_H20 zenon_Hbd zenon_H1d2 zenon_H108 zenon_Hda zenon_H14b zenon_He1 zenon_H9d. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.76 apply (zenon_L2384_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.76 apply (zenon_L2506_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.76 apply (zenon_L4_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_L2509_); trivial. % 30.68/30.76 apply (zenon_L1354_); trivial. % 30.68/30.76 (* end of lemma zenon_L2510_ *) % 30.68/30.76 assert (zenon_L2511_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1fd zenon_H10d zenon_H26 zenon_Hb8 zenon_H4c zenon_Hda zenon_He1 zenon_Hf9 zenon_Hee zenon_H256 zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_Hde zenon_H222 zenon_H3d zenon_H2d zenon_H3f zenon_H1e zenon_H20 zenon_Hbd zenon_H1db zenon_H23b zenon_Hcd zenon_He2 zenon_Hd2 zenon_H4a zenon_H100 zenon_H6f zenon_H1ab. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.76 apply (zenon_L598_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.76 apply (zenon_L2500_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.76 exact (zenon_H1db zenon_H1b9). % 30.68/30.76 apply (zenon_L2494_); trivial. % 30.68/30.76 (* end of lemma zenon_L2511_ *) % 30.68/30.76 assert (zenon_L2512_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.68/30.76 do 0 intro. intros zenon_H42 zenon_H16c zenon_H4e zenon_H14e zenon_H6f zenon_He7 zenon_Hb8 zenon_H56 zenon_H23b zenon_H10d zenon_Hda zenon_H3f zenon_He9 zenon_Hcd zenon_Hf9 zenon_Hd2 zenon_H4a zenon_H100 zenon_Hee zenon_H1ab zenon_H1fd zenon_H4c zenon_H256 zenon_H159 zenon_H156 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_H2d zenon_H1e zenon_H20 zenon_Hbd zenon_He2 zenon_H1a2 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.76 apply (zenon_L4_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2511_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L2501_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L877_); trivial. % 30.68/30.76 apply (zenon_L2387_); trivial. % 30.68/30.76 (* end of lemma zenon_L2512_ *) % 30.68/30.76 assert (zenon_L2513_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.68/30.76 do 0 intro. intros zenon_H16f zenon_H48 zenon_H42 zenon_H4e zenon_H14e zenon_H6f zenon_He7 zenon_Hb8 zenon_H56 zenon_H23b zenon_H10d zenon_Hda zenon_H3f zenon_He9 zenon_Hcd zenon_Hf9 zenon_Hd2 zenon_H4a zenon_H100 zenon_Hee zenon_H1ab zenon_H1fd zenon_H4c zenon_H256 zenon_H159 zenon_H156 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_H2d zenon_H1e zenon_H20 zenon_Hbd zenon_He2 zenon_H1a2 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_Hf5 zenon_He1. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.76 apply (zenon_L2384_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.76 apply (zenon_L2502_); trivial. % 30.68/30.76 apply (zenon_L2512_); trivial. % 30.68/30.76 (* end of lemma zenon_L2513_ *) % 30.68/30.76 assert (zenon_L2514_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 30.68/30.76 do 0 intro. intros zenon_H92 zenon_H6f zenon_Hde zenon_H20d zenon_Hcd zenon_He1 zenon_He4 zenon_H15a zenon_H89 zenon_H4e zenon_H1d2 zenon_H20e zenon_H56 zenon_H108 zenon_Hf5 zenon_H1db zenon_H18c zenon_H4a zenon_Had zenon_H48 zenon_H172 zenon_H8b zenon_H20. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.76 apply (zenon_L734_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.76 apply (zenon_L1312_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.76 apply (zenon_L749_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.76 apply (zenon_L763_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.76 apply (zenon_L2409_); trivial. % 30.68/30.76 apply (zenon_L744_); trivial. % 30.68/30.76 apply (zenon_L27_); trivial. % 30.68/30.76 (* end of lemma zenon_L2514_ *) % 30.68/30.76 assert (zenon_L2515_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_Hb8 zenon_He2 zenon_H9d zenon_He1 zenon_H1a0 zenon_H6f zenon_H256 zenon_Hb1 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.68/30.76 apply (zenon_L50_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.68/30.76 apply (zenon_L1354_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.68/30.76 apply (zenon_L540_); trivial. % 30.68/30.76 apply (zenon_L2483_); trivial. % 30.68/30.76 (* end of lemma zenon_L2515_ *) % 30.68/30.76 assert (zenon_L2516_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1a2 zenon_H1ab zenon_H100 zenon_H23b zenon_H2d zenon_H3d zenon_H222 zenon_H30a zenon_H2b4 zenon_Hee zenon_Hf9 zenon_Hda zenon_H4c zenon_H10d zenon_H1fd zenon_H15e zenon_Hbd zenon_H20 zenon_H172 zenon_H48 zenon_Had zenon_H18c zenon_H1db zenon_H108 zenon_H56 zenon_H20e zenon_H1d2 zenon_H89 zenon_H15a zenon_He4 zenon_Hcd zenon_H20d zenon_Hde zenon_H92 zenon_H1e zenon_H3f zenon_H142 zenon_H1dc zenon_Hb8 zenon_He2 zenon_H9d zenon_He1 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2511_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L235_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.76 apply (zenon_L2514_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.76 apply (zenon_L29_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.76 apply (zenon_L177_); trivial. % 30.68/30.76 apply (zenon_L2515_); trivial. % 30.68/30.76 (* end of lemma zenon_L2516_ *) % 30.68/30.76 assert (zenon_L2517_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H42 zenon_H16c zenon_H4e zenon_H14e zenon_H6f zenon_H222 zenon_H89 zenon_He7 zenon_Hb8 zenon_H56 zenon_H100 zenon_H4c zenon_H1fd zenon_H10d zenon_Hda zenon_Hf9 zenon_Hee zenon_H256 zenon_H159 zenon_H156 zenon_Hf5 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_H2d zenon_H3f zenon_H1e zenon_H20 zenon_Hbd zenon_H1db zenon_H23b zenon_Hcd zenon_He2 zenon_Hd2 zenon_H4a zenon_H1ab zenon_H1a2 zenon_He1 zenon_H9d. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.76 apply (zenon_L4_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2511_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L1184_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L877_); trivial. % 30.68/30.76 apply (zenon_L1354_); trivial. % 30.68/30.76 (* end of lemma zenon_L2517_ *) % 30.68/30.76 assert (zenon_L2518_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H16f zenon_H14b zenon_H1dc zenon_H92 zenon_H20d zenon_He4 zenon_H1d2 zenon_H20e zenon_H108 zenon_H18c zenon_Had zenon_H48 zenon_H172 zenon_Hc8 zenon_H1d5 zenon_Hfc zenon_H42 zenon_H4e zenon_H14e zenon_H6f zenon_H222 zenon_H89 zenon_He7 zenon_Hb8 zenon_H56 zenon_H100 zenon_H4c zenon_H1fd zenon_H10d zenon_Hda zenon_Hf9 zenon_Hee zenon_H256 zenon_H159 zenon_H156 zenon_Hf5 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_H2d zenon_H3f zenon_H1e zenon_H20 zenon_Hbd zenon_H1db zenon_H23b zenon_Hcd zenon_He2 zenon_Hd2 zenon_H4a zenon_H1ab zenon_H1a2 zenon_He1 zenon_H9d. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.76 apply (zenon_L2384_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.76 apply (zenon_L4_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.76 apply (zenon_L203_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.76 apply (zenon_L192_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.76 apply (zenon_L742_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.76 apply (zenon_L2516_); trivial. % 30.68/30.76 apply (zenon_L2491_); trivial. % 30.68/30.76 apply (zenon_L1354_); trivial. % 30.68/30.76 apply (zenon_L2517_); trivial. % 30.68/30.76 (* end of lemma zenon_L2518_ *) % 30.68/30.76 assert (zenon_L2519_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.76 do 0 intro. intros zenon_Hd9 zenon_Hd1 zenon_H173 zenon_H1b1 zenon_H2f8 zenon_H1a5 zenon_H26 zenon_He1 zenon_H1a2 zenon_H1ab zenon_H4a zenon_Hd2 zenon_Hcd zenon_H23b zenon_H1db zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H2d zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H159 zenon_H256 zenon_Hee zenon_Hf9 zenon_Hda zenon_H10d zenon_H1fd zenon_H4c zenon_H100 zenon_H56 zenon_Hb8 zenon_He7 zenon_H89 zenon_H222 zenon_H6f zenon_H14e zenon_H4e zenon_H42 zenon_Hfc zenon_H1d5 zenon_Hc8 zenon_H172 zenon_H48 zenon_Had zenon_H18c zenon_H108 zenon_H20e zenon_H1d2 zenon_He4 zenon_H20d zenon_H92 zenon_H1dc zenon_H14b zenon_H16f zenon_H1c7 zenon_H101 zenon_Hf5 zenon_H156. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.76 apply (zenon_L47_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.76 apply (zenon_L2384_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.76 apply (zenon_L2502_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.76 apply (zenon_L4_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_L2505_); trivial. % 30.68/30.76 apply (zenon_L2387_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.76 apply (zenon_L154_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.76 apply (zenon_L1253_); trivial. % 30.68/30.76 apply (zenon_L2510_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.76 apply (zenon_L627_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.76 apply (zenon_L2513_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.76 apply (zenon_L122_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.76 apply (zenon_L1253_); trivial. % 30.68/30.76 apply (zenon_L2510_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.76 apply (zenon_L748_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.76 apply (zenon_L2513_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.76 apply (zenon_L58_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.76 apply (zenon_L1253_); trivial. % 30.68/30.76 apply (zenon_L2518_); trivial. % 30.68/30.76 apply (zenon_L90_); trivial. % 30.68/30.76 (* end of lemma zenon_L2519_ *) % 30.68/30.76 assert (zenon_L2520_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_Hb8 zenon_H90 zenon_H222 zenon_H3d zenon_H1a0 zenon_H6f zenon_H256 zenon_Hb1 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.68/30.76 apply (zenon_L39_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.68/30.76 apply (zenon_L775_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.68/30.76 apply (zenon_L540_); trivial. % 30.68/30.76 apply (zenon_L2483_); trivial. % 30.68/30.76 (* end of lemma zenon_L2520_ *) % 30.68/30.76 assert (zenon_L2521_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_Hde zenon_Hb8 zenon_H90 zenon_H222 zenon_H3d zenon_H1a0 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.76 exact (zenon_H30a zenon_H185). % 30.68/30.76 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.76 apply (zenon_L744_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.76 apply (zenon_L294_); trivial. % 30.68/30.76 apply (zenon_L2520_); trivial. % 30.68/30.76 (* end of lemma zenon_L2521_ *) % 30.68/30.76 assert (zenon_L2522_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H142 zenon_H1dc zenon_Hb8 zenon_H90 zenon_H222 zenon_H3d zenon_H1a0 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.76 apply (zenon_L27_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.76 apply (zenon_L29_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.76 apply (zenon_L177_); trivial. % 30.68/30.76 apply (zenon_L2520_); trivial. % 30.68/30.76 (* end of lemma zenon_L2522_ *) % 30.68/30.76 assert (zenon_L2523_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1a2 zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1b1 zenon_Hdc zenon_H4c zenon_Hee zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H1db zenon_He1 zenon_He7 zenon_H23b zenon_H100 zenon_H10d zenon_H1ab zenon_H15e zenon_H56 zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H142 zenon_H1dc zenon_Hb8 zenon_H90 zenon_H222 zenon_H3d zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2488_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L235_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L2522_); trivial. % 30.68/30.76 (* end of lemma zenon_L2523_ *) % 30.68/30.76 assert (zenon_L2524_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1a2 zenon_H2d zenon_H9c zenon_H23b zenon_H100 zenon_H10d zenon_H1ab zenon_H15e zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_Hde zenon_Hb8 zenon_H90 zenon_H222 zenon_H3d zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2484_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L235_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L2521_); trivial. % 30.68/30.76 (* end of lemma zenon_L2524_ *) % 30.68/30.76 assert (zenon_L2525_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_Hde zenon_Hb8 zenon_H1ab zenon_H26 zenon_H100 zenon_H6f zenon_H23b zenon_H4c zenon_H10d zenon_Hda zenon_He1 zenon_H90 zenon_Hcd zenon_Hf9 zenon_Hee zenon_H15e zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.76 exact (zenon_H30a zenon_H185). % 30.68/30.76 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.76 apply (zenon_L744_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.76 apply (zenon_L294_); trivial. % 30.68/30.76 apply (zenon_L2498_); trivial. % 30.68/30.76 (* end of lemma zenon_L2525_ *) % 30.68/30.76 assert (zenon_L2526_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1fd zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_Hf9 zenon_Hcd zenon_H90 zenon_He1 zenon_Hda zenon_H10d zenon_H23b zenon_H6f zenon_H100 zenon_H1ab zenon_Hb8 zenon_Hde zenon_H89 zenon_H15a zenon_H30a zenon_H2b4 zenon_H1db zenon_H2f8 zenon_H20e zenon_H142 zenon_H1a5 zenon_H26 zenon_H1b1 zenon_Hdc zenon_H4c zenon_Hee. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.76 apply (zenon_L598_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.76 apply (zenon_L2525_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.76 exact (zenon_H1db zenon_H1b9). % 30.68/30.76 apply (zenon_L2476_); trivial. % 30.68/30.76 (* end of lemma zenon_L2526_ *) % 30.68/30.76 assert (zenon_L2527_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1a2 zenon_Hee zenon_Hdc zenon_H1b1 zenon_H1a5 zenon_H20e zenon_H2f8 zenon_H1db zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_Hde zenon_H1ab zenon_H23b zenon_H10d zenon_Hda zenon_He1 zenon_Hcd zenon_Hf9 zenon_H1fd zenon_H9d zenon_H4c zenon_H100 zenon_H56 zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H142 zenon_H1dc zenon_Hb8 zenon_H90 zenon_H222 zenon_H3d zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2526_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L1184_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L2522_); trivial. % 30.68/30.76 (* end of lemma zenon_L2527_ *) % 30.68/30.76 assert (zenon_L2528_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1fd zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_Hee zenon_Hf9 zenon_Hcd zenon_H90 zenon_He1 zenon_Hda zenon_H10d zenon_H4c zenon_H23b zenon_H6f zenon_H100 zenon_H26 zenon_H1ab zenon_Hb8 zenon_Hde zenon_H89 zenon_H15a zenon_H30a zenon_H2b4 zenon_H1db zenon_H2d zenon_H9c. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.76 apply (zenon_L598_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.76 apply (zenon_L2525_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.76 exact (zenon_H1db zenon_H1b9). % 30.68/30.76 apply (zenon_L304_); trivial. % 30.68/30.76 (* end of lemma zenon_L2528_ *) % 30.68/30.76 assert (zenon_L2529_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> False). % 30.68/30.76 do 0 intro. intros zenon_H101 zenon_H1c7 zenon_H42 zenon_H16a zenon_H33 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H6f zenon_H222 zenon_H90 zenon_Hb8 zenon_Hde zenon_H89 zenon_H15a zenon_H30a zenon_H2b4 zenon_H56 zenon_H100 zenon_H4c zenon_H1fd zenon_Hee zenon_Hf9 zenon_Hcd zenon_Hda zenon_H10d zenon_H23b zenon_H1ab zenon_H1db zenon_H2d zenon_H1a2 zenon_Hdc zenon_H1b1 zenon_H1a5 zenon_H20e zenon_H2f8 zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H1dc zenon_H1d2 zenon_H108 zenon_H14b zenon_He1. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.76 apply (zenon_L1627_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.76 apply (zenon_L122_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.76 apply (zenon_L1253_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.76 apply (zenon_L4_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.76 apply (zenon_L839_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.76 apply (zenon_L192_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.76 apply (zenon_L2409_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.76 apply (zenon_L2527_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2528_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L1184_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L2521_); trivial. % 30.68/30.76 apply (zenon_L1354_); trivial. % 30.68/30.76 (* end of lemma zenon_L2529_ *) % 30.68/30.76 assert (zenon_L2530_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.68/30.76 do 0 intro. intros zenon_He4 zenon_Hd9 zenon_He1 zenon_H14b zenon_H108 zenon_H1d2 zenon_H1dc zenon_H3f zenon_H1e zenon_H20 zenon_Hbd zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1b1 zenon_H1a2 zenon_H2d zenon_H1db zenon_H1ab zenon_H23b zenon_H10d zenon_Hda zenon_Hf9 zenon_Hee zenon_H1fd zenon_H4c zenon_H100 zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_Hde zenon_Hb8 zenon_H222 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_H14e zenon_H4e zenon_H33 zenon_H16a zenon_H42 zenon_H1c7 zenon_H101 zenon_Hf5 zenon_H20d zenon_H90 zenon_Hcd. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.76 apply (zenon_L47_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.76 apply (zenon_L2529_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.76 apply (zenon_L627_); trivial. % 30.68/30.76 apply (zenon_L386_); trivial. % 30.68/30.76 (* end of lemma zenon_L2530_ *) % 30.68/30.76 assert (zenon_L2531_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.76 do 0 intro. intros zenon_H23b zenon_H8a zenon_H6f zenon_Hd2 zenon_H4a zenon_H100 zenon_H19a zenon_Hee zenon_H1ab. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.76 apply (zenon_L39_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.76 apply (zenon_L880_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.76 apply (zenon_L337_); trivial. % 30.68/30.76 exact (zenon_H1ab zenon_H112). % 30.68/30.76 (* end of lemma zenon_L2531_ *) % 30.68/30.76 assert (zenon_L2532_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_Hb8 zenon_H1ab zenon_Hee zenon_H19a zenon_H100 zenon_H4a zenon_Hd2 zenon_H6f zenon_H23b zenon_H222 zenon_H3d zenon_Heb zenon_He1 zenon_H14e zenon_H4e zenon_H16c. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.68/30.76 apply (zenon_L2531_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.68/30.76 apply (zenon_L775_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.68/30.76 apply (zenon_L204_); trivial. % 30.68/30.76 apply (zenon_L875_); trivial. % 30.68/30.76 (* end of lemma zenon_L2532_ *) % 30.68/30.76 assert (zenon_L2533_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H125 zenon_Hcd zenon_H90 zenon_H20d zenon_H101 zenon_H1c7 zenon_H42 zenon_H16a zenon_H33 zenon_H156 zenon_H159 zenon_H256 zenon_Hde zenon_H89 zenon_H15a zenon_H30a zenon_H2b4 zenon_H56 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H1db zenon_H2d zenon_H1a2 zenon_H1a5 zenon_H20e zenon_H2f8 zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H1dc zenon_H1d2 zenon_H14b zenon_Hd9 zenon_He4 zenon_H1b1 zenon_Hdc zenon_H4c zenon_H108 zenon_Hf5 zenon_Hb8 zenon_H1ab zenon_Hee zenon_H19a zenon_H100 zenon_H4a zenon_Hd2 zenon_H6f zenon_H23b zenon_H222 zenon_H3d zenon_He1 zenon_H14e zenon_H4e zenon_H16c. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.68/30.76 apply (zenon_L2530_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.68/30.76 apply (zenon_L2436_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.68/30.76 apply (zenon_L62_); trivial. % 30.68/30.76 apply (zenon_L2532_); trivial. % 30.68/30.76 (* end of lemma zenon_L2533_ *) % 30.68/30.76 assert (zenon_L2534_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.68/30.76 do 0 intro. intros zenon_H1d5 zenon_Hc8 zenon_He1 zenon_H23b zenon_Hd2 zenon_H4a zenon_H100 zenon_Hee zenon_H1ab zenon_H142 zenon_Hde zenon_H4c zenon_Hdc zenon_H1b1 zenon_H101 zenon_H1c7 zenon_H42 zenon_H16a zenon_H33 zenon_Hf5 zenon_H156 zenon_H159 zenon_H256 zenon_H90 zenon_H15a zenon_H30a zenon_H2b4 zenon_H1fd zenon_Hf9 zenon_Hcd zenon_H10d zenon_H1db zenon_H2d zenon_H1a2 zenon_H1a5 zenon_H20e zenon_H2f8 zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H1dc zenon_H1d2 zenon_H108 zenon_H14b zenon_H125 zenon_H56 zenon_Hb8 zenon_He7 zenon_H89 zenon_H222 zenon_H3d zenon_H6f zenon_H14e zenon_H4e zenon_H16c. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2488_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.68/30.76 apply (zenon_L2529_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.68/30.76 apply (zenon_L2436_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.68/30.76 apply (zenon_L89_); trivial. % 30.68/30.76 apply (zenon_L2532_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L877_); trivial. % 30.68/30.76 (* end of lemma zenon_L2534_ *) % 30.68/30.76 assert (zenon_L2535_ : (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 30.68/30.76 do 0 intro. intros zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_He7 zenon_H23b zenon_H100 zenon_Hee zenon_H1ab zenon_H108 zenon_H4c zenon_H1b1 zenon_He4 zenon_Hd9 zenon_H14b zenon_H1d2 zenon_H1dc zenon_H3f zenon_H1e zenon_H20 zenon_Hbd zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1a2 zenon_H2d zenon_H10d zenon_Hf9 zenon_H1fd zenon_H33 zenon_H16a zenon_H42 zenon_H1c7 zenon_H101 zenon_H125 zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_H14e zenon_H4e zenon_H48 zenon_H16f zenon_Hf5 zenon_H20d zenon_H90 zenon_Hcd. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.76 apply (zenon_L232_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.76 apply (zenon_L2384_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.76 apply (zenon_L839_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.76 apply (zenon_L4_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.76 apply (zenon_L839_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2486_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L235_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L2521_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.76 apply (zenon_L2409_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.76 apply (zenon_L2523_); trivial. % 30.68/30.76 apply (zenon_L2524_); trivial. % 30.68/30.76 apply (zenon_L2387_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.76 apply (zenon_L4_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2486_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L2533_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L877_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.76 apply (zenon_L2409_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.76 apply (zenon_L2534_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.76 apply (zenon_L2484_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.76 apply (zenon_L2533_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.76 exact (zenon_H56 zenon_H25). % 30.68/30.76 apply (zenon_L2521_); trivial. % 30.68/30.76 apply (zenon_L2387_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.76 apply (zenon_L627_); trivial. % 30.68/30.76 apply (zenon_L386_); trivial. % 30.68/30.76 (* end of lemma zenon_L2535_ *) % 30.68/30.76 assert (zenon_L2536_ : (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.76 do 0 intro. intros zenon_Hcd zenon_H20d zenon_H16f zenon_H48 zenon_Hde zenon_H15a zenon_H30a zenon_H2b4 zenon_H56 zenon_H125 zenon_H101 zenon_H1c7 zenon_H42 zenon_H16a zenon_H33 zenon_H1fd zenon_Hf9 zenon_H10d zenon_H2d zenon_H1a2 zenon_H1a5 zenon_H20e zenon_H2f8 zenon_Hbd zenon_H20 zenon_H1e zenon_H3f zenon_H1dc zenon_H1d2 zenon_H14b zenon_Hd9 zenon_He4 zenon_H1b1 zenon_H4c zenon_H108 zenon_Hee zenon_H23b zenon_H100 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_Hb1 zenon_H256 zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He1 zenon_He7 zenon_Hb8 zenon_H1ab. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.76 apply (zenon_L2535_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.76 apply (zenon_L880_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.76 apply (zenon_L2489_); trivial. % 30.68/30.76 exact (zenon_H1ab zenon_H112). % 30.68/30.76 (* end of lemma zenon_L2536_ *) % 30.68/30.76 assert (zenon_L2537_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 30.68/30.76 do 0 intro. intros zenon_H53 zenon_H6f zenon_H89 zenon_H35 zenon_H4a zenon_Hd2 zenon_He1 zenon_H42 zenon_H172 zenon_H4e zenon_H15a zenon_H4c zenon_Had zenon_H20 zenon_H48 zenon_H18c zenon_H14b zenon_Hd6 zenon_H20e zenon_H56 zenon_H1d2 zenon_Hde zenon_H1b1 zenon_H108 zenon_Hbd zenon_H1d5 zenon_H1db zenon_Hc8 zenon_H30a zenon_Hb8 zenon_H14e zenon_H159 zenon_H156 zenon_H256 zenon_H222 zenon_H2b4 zenon_H3f zenon_H100 zenon_H10d zenon_H23b zenon_H125 zenon_He7 zenon_H2f8 zenon_Hee zenon_H1a5 zenon_H1dc zenon_H200 zenon_H1e zenon_H2d zenon_H1fd zenon_H1a2 zenon_He4 zenon_H173 zenon_Hf5 zenon_H20d zenon_Hcd zenon_H92 zenon_Hfc zenon_H16f zenon_Hf9 zenon_Hd1 zenon_H1c7 zenon_H101 zenon_H218 zenon_H225 zenon_Hd9 zenon_H16a zenon_Hc0. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.76 apply (zenon_L734_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.76 apply (zenon_L868_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.76 apply (zenon_L797_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.76 apply (zenon_L232_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.76 apply (zenon_L232_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.76 apply (zenon_L48_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.76 apply (zenon_L627_); trivial. % 30.68/30.76 apply (zenon_L2497_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.76 apply (zenon_L2519_); trivial. % 30.68/30.76 apply (zenon_L405_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.76 apply (zenon_L232_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.76 apply (zenon_L232_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.76 apply (zenon_L4_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.76 apply (zenon_L125_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.76 apply (zenon_L2433_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.76 apply (zenon_L2487_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.76 apply (zenon_L2488_); trivial. % 30.68/30.76 apply (zenon_L294_); trivial. % 30.68/30.76 apply (zenon_L2387_); trivial. % 30.68/30.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.77 apply (zenon_L627_); trivial. % 30.68/30.77 apply (zenon_L2497_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.77 apply (zenon_L2519_); trivial. % 30.68/30.77 apply (zenon_L405_); trivial. % 30.68/30.77 apply (zenon_L2493_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.77 exact (zenon_H30a zenon_H185). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.77 apply (zenon_L744_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.77 apply (zenon_L294_); trivial. % 30.68/30.77 apply (zenon_L2536_); trivial. % 30.68/30.77 apply (zenon_L2387_); trivial. % 30.68/30.77 (* end of lemma zenon_L2537_ *) % 30.68/30.77 assert (zenon_L2538_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 30.68/30.77 do 0 intro. intros zenon_H52 zenon_H20 zenon_Hbd zenon_H1dc zenon_H53 zenon_H6f zenon_H89 zenon_H92 zenon_H125 zenon_Hf9 zenon_H18c zenon_H1c7 zenon_H101 zenon_H100 zenon_Hd1 zenon_H1a8 zenon_He1 zenon_He4 zenon_H35 zenon_H16f zenon_H14b zenon_H10d zenon_Hee zenon_H4c zenon_H1b1 zenon_H1fd zenon_H3f zenon_H23b zenon_He7 zenon_H2d zenon_H1e zenon_Hfc zenon_H1a2 zenon_Hb8 zenon_H256 zenon_H159 zenon_H42 zenon_H222 zenon_H1a5 zenon_H4a zenon_H102 zenon_Hc8 zenon_H19e zenon_H1db zenon_H1d5 zenon_H30a zenon_H15a zenon_H4e zenon_Hde zenon_H14e zenon_H48 zenon_H2b4 zenon_H156 zenon_H173 zenon_Hf5 zenon_H20d zenon_Hcd zenon_H1d2 zenon_H108 zenon_H20e zenon_Hd9 zenon_H218 zenon_H225 zenon_H2f8 zenon_Hd6 zenon_H16a zenon_H200 zenon_H172 zenon_Had zenon_H2c1 zenon_Hc0 zenon_H54. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.77 apply (zenon_L734_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.77 apply (zenon_L734_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.77 apply (zenon_L48_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.77 apply (zenon_L627_); trivial. % 30.68/30.77 apply (zenon_L2397_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.77 apply (zenon_L2454_); trivial. % 30.68/30.77 apply (zenon_L405_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.77 apply (zenon_L2426_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.77 apply (zenon_L2446_); trivial. % 30.68/30.77 apply (zenon_L405_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.77 apply (zenon_L48_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.77 exact (zenon_H18f zenon_Hd2). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.77 apply (zenon_L2439_); trivial. % 30.68/30.77 apply (zenon_L2430_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.77 apply (zenon_L627_); trivial. % 30.68/30.77 apply (zenon_L386_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.77 apply (zenon_L2441_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.77 apply (zenon_L940_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.77 apply (zenon_L2449_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.77 apply (zenon_L47_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.77 apply (zenon_L48_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.77 apply (zenon_L627_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.77 apply (zenon_L2384_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.77 apply (zenon_L839_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.77 apply (zenon_L2391_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.77 apply (zenon_L4_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.77 apply (zenon_L839_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.77 apply (zenon_L386_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.77 apply (zenon_L2466_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.77 apply (zenon_L877_); trivial. % 30.68/30.77 exact (zenon_H1ab zenon_H112). % 30.68/30.77 apply (zenon_L2387_); trivial. % 30.68/30.77 apply (zenon_L405_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.77 apply (zenon_L2467_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.77 apply (zenon_L47_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.77 apply (zenon_L48_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.77 exact (zenon_H18f zenon_Hd2). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.77 apply (zenon_L2467_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.77 apply (zenon_L154_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.77 apply (zenon_L1253_); trivial. % 30.68/30.77 apply (zenon_L1184_); trivial. % 30.68/30.77 apply (zenon_L2468_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.77 apply (zenon_L627_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.77 apply (zenon_L48_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.77 apply (zenon_L2384_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.77 apply (zenon_L839_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.77 apply (zenon_L4_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.77 apply (zenon_L839_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.77 apply (zenon_L2469_); trivial. % 30.68/30.77 apply (zenon_L2387_); trivial. % 30.68/30.77 apply (zenon_L2425_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.77 apply (zenon_L2467_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.77 apply (zenon_L58_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.77 apply (zenon_L1253_); trivial. % 30.68/30.77 apply (zenon_L2427_); trivial. % 30.68/30.77 apply (zenon_L90_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.77 exact (zenon_H18f zenon_Hd2). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.77 apply (zenon_L2467_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.77 apply (zenon_L2472_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.77 apply (zenon_L1253_); trivial. % 30.68/30.77 apply (zenon_L1184_); trivial. % 30.68/30.77 apply (zenon_L2468_); trivial. % 30.68/30.77 apply (zenon_L405_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.77 apply (zenon_L48_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.77 exact (zenon_H18f zenon_Hd2). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.77 apply (zenon_L2384_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.77 apply (zenon_L839_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.77 apply (zenon_L235_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.68/30.77 apply (zenon_L2481_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.68/30.77 apply (zenon_L2436_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.68/30.77 apply (zenon_L62_); trivial. % 30.68/30.77 apply (zenon_L2437_); trivial. % 30.68/30.77 apply (zenon_L2468_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.77 apply (zenon_L627_); trivial. % 30.68/30.77 apply (zenon_L386_); trivial. % 30.68/30.77 apply (zenon_L2387_); trivial. % 30.68/30.77 apply (zenon_L1253_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.68/30.77 apply (zenon_L2537_); trivial. % 30.68/30.77 apply (zenon_L1253_); trivial. % 30.68/30.77 (* end of lemma zenon_L2538_ *) % 30.68/30.77 assert (zenon_L2539_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> False). % 30.68/30.77 do 0 intro. intros zenon_H246 zenon_H1a8 zenon_H18f zenon_Hb8 zenon_H10d zenon_H14e zenon_H1fd zenon_H4c zenon_H1b1 zenon_H101 zenon_H3f zenon_Hf9 zenon_H1c7 zenon_H100 zenon_H125 zenon_H2b4 zenon_H30a zenon_H16f zenon_Hd1 zenon_H222 zenon_Hc8 zenon_H1d5 zenon_H19e zenon_Hfc zenon_H35 zenon_H42 zenon_H225 zenon_H102 zenon_H10e zenon_H218 zenon_H156 zenon_H16a zenon_H200 zenon_H173 zenon_H310 zenon_H1d8 zenon_H2d zenon_H296 zenon_H84 zenon_H1a5 zenon_H1ab zenon_H2b1 zenon_H159 zenon_H256 zenon_He7 zenon_Hee zenon_H23b zenon_H1a2 zenon_H14b zenon_Hc0 zenon_H6b zenon_H92 zenon_H6f zenon_Hde zenon_H20d zenon_Hcd zenon_He1 zenon_He4 zenon_H15a zenon_H89 zenon_H4e zenon_H1d2 zenon_H20e zenon_H56 zenon_H108 zenon_Hf5 zenon_H1db zenon_H18c zenon_H4a zenon_Had zenon_H48 zenon_H172 zenon_H20. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.77 exact (zenon_H84 zenon_H88). % 30.68/30.77 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.77 exact (zenon_H84 zenon_H88). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.77 apply (zenon_L2408_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.77 apply (zenon_L192_); trivial. % 30.68/30.77 apply (zenon_L405_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.77 apply (zenon_L2455_); trivial. % 30.68/30.77 apply (zenon_L2440_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.77 exact (zenon_H84 zenon_H88). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.77 apply (zenon_L1209_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.77 apply (zenon_L2444_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.77 apply (zenon_L192_); trivial. % 30.68/30.77 apply (zenon_L405_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.77 apply (zenon_L2455_); trivial. % 30.68/30.77 apply (zenon_L2440_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.77 exact (zenon_H84 zenon_H88). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.77 apply (zenon_L2453_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.77 apply (zenon_L192_); trivial. % 30.68/30.77 apply (zenon_L405_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.77 apply (zenon_L2455_); trivial. % 30.68/30.77 apply (zenon_L2440_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.77 exact (zenon_H84 zenon_H88). % 30.68/30.77 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.77 exact (zenon_H84 zenon_H88). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.77 apply (zenon_L48_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.77 apply (zenon_L627_); trivial. % 30.68/30.77 apply (zenon_L2406_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.77 apply (zenon_L192_); trivial. % 30.68/30.77 apply (zenon_L405_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.77 apply (zenon_L2455_); trivial. % 30.68/30.77 apply (zenon_L2440_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.77 exact (zenon_H84 zenon_H88). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.77 apply (zenon_L48_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.77 apply (zenon_L627_); trivial. % 30.68/30.77 apply (zenon_L2443_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.77 apply (zenon_L192_); trivial. % 30.68/30.77 apply (zenon_L405_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.77 apply (zenon_L2455_); trivial. % 30.68/30.77 apply (zenon_L2440_); trivial. % 30.68/30.77 apply (zenon_L2456_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.77 apply (zenon_L2403_); trivial. % 30.68/30.77 apply (zenon_L2514_); trivial. % 30.68/30.77 (* end of lemma zenon_L2539_ *) % 30.68/30.77 assert (zenon_L2540_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.77 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H6f zenon_H23b zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_Heb zenon_He1 zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.77 exact (zenon_H30a zenon_H185). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.77 apply (zenon_L744_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.77 apply (zenon_L294_); trivial. % 30.68/30.77 apply (zenon_L2485_); trivial. % 30.68/30.77 (* end of lemma zenon_L2540_ *) % 30.68/30.77 assert (zenon_L2541_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.77 do 0 intro. intros zenon_H125 zenon_H10e zenon_H1b1 zenon_Hdc zenon_H4c zenon_H108 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H6f zenon_H23b zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_He1 zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.68/30.77 apply (zenon_L192_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.68/30.77 apply (zenon_L2436_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.68/30.77 apply (zenon_L62_); trivial. % 30.68/30.77 apply (zenon_L2540_); trivial. % 30.68/30.77 (* end of lemma zenon_L2541_ *) % 30.68/30.77 assert (zenon_L2542_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.77 do 0 intro. intros zenon_H1a2 zenon_H23b zenon_H100 zenon_H10d zenon_H1ab zenon_H108 zenon_H4c zenon_Hdc zenon_H1b1 zenon_H10e zenon_H125 zenon_H15e zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.77 apply (zenon_L2541_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.77 apply (zenon_L235_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.77 exact (zenon_H56 zenon_H25). % 30.68/30.77 apply (zenon_L2490_); trivial. % 30.68/30.77 (* end of lemma zenon_L2542_ *) % 30.68/30.77 assert (zenon_L2543_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.68/30.77 do 0 intro. intros zenon_H125 zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_H10d zenon_H1b1 zenon_Hdc zenon_H4c zenon_H108 zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H16c zenon_H4e zenon_H14e zenon_H222 zenon_H23b zenon_H6f zenon_Hd2 zenon_H4a zenon_H100 zenon_H19a zenon_Hee zenon_H1ab zenon_Hb8 zenon_H1db zenon_Hf5 zenon_He1. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.68/30.77 apply (zenon_L2501_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.68/30.77 apply (zenon_L2436_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.68/30.77 apply (zenon_L62_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.77 apply (zenon_L332_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.77 apply (zenon_L2532_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.77 exact (zenon_H1db zenon_H1b9). % 30.68/30.77 apply (zenon_L221_); trivial. % 30.68/30.77 (* end of lemma zenon_L2543_ *) % 30.68/30.77 assert (zenon_L2544_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.77 do 0 intro. intros zenon_H16f zenon_H48 zenon_H19e zenon_H1a2 zenon_H10e zenon_H1ab zenon_Hee zenon_H100 zenon_H23b zenon_H108 zenon_H4c zenon_Hdc zenon_H1b1 zenon_H10d zenon_H3f zenon_He9 zenon_Hcd zenon_Hf9 zenon_H125 zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.77 apply (zenon_L2384_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.77 apply (zenon_L2385_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.77 apply (zenon_L2542_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.77 apply (zenon_L2541_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.77 apply (zenon_L2543_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.77 exact (zenon_H56 zenon_H25). % 30.68/30.77 apply (zenon_L2490_); trivial. % 30.68/30.77 (* end of lemma zenon_L2544_ *) % 30.68/30.77 assert (zenon_L2545_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.77 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H15a zenon_H89 zenon_H142 zenon_H108 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H256 zenon_H15e zenon_Hee zenon_Hf9 zenon_Hcd zenon_He1 zenon_Hda zenon_H4c zenon_H23b zenon_H6f zenon_Hb8 zenon_Hd2 zenon_H4a zenon_H100 zenon_H26 zenon_H10d zenon_H1ab. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.77 exact (zenon_H30a zenon_H185). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.77 apply (zenon_L744_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.77 apply (zenon_L296_); trivial. % 30.68/30.77 apply (zenon_L2499_); trivial. % 30.68/30.77 (* end of lemma zenon_L2545_ *) % 30.68/30.77 assert (zenon_L2546_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 30.68/30.77 do 0 intro. intros zenon_H1fd zenon_H1ab zenon_H10d zenon_H100 zenon_H4a zenon_Hd2 zenon_Hb8 zenon_H6f zenon_H23b zenon_Hda zenon_He1 zenon_Hcd zenon_Hf9 zenon_H256 zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e zenon_H108 zenon_H89 zenon_H15a zenon_H30a zenon_H2b4 zenon_H1db zenon_H2f8 zenon_H20e zenon_H142 zenon_H1a5 zenon_H26 zenon_H1b1 zenon_Hdc zenon_H4c zenon_Hee. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.77 apply (zenon_L598_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.77 apply (zenon_L2545_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.77 exact (zenon_H1db zenon_H1b9). % 30.68/30.77 apply (zenon_L2476_); trivial. % 30.68/30.77 (* end of lemma zenon_L2546_ *) % 30.68/30.77 assert (zenon_L2547_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.77 do 0 intro. intros zenon_H125 zenon_Hee zenon_H1a5 zenon_H20e zenon_H2f8 zenon_H108 zenon_Hf9 zenon_Hcd zenon_H1fd zenon_H1b1 zenon_Hdc zenon_H4c zenon_H142 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_H1ab zenon_H10d zenon_H26 zenon_H100 zenon_H6f zenon_H23b zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_He1 zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.68/30.77 apply (zenon_L2546_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.68/30.77 apply (zenon_L2436_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.68/30.77 apply (zenon_L89_); trivial. % 30.68/30.77 apply (zenon_L2540_); trivial. % 30.68/30.77 (* end of lemma zenon_L2547_ *) % 30.68/30.77 assert (zenon_L2548_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.77 do 0 intro. intros zenon_H1a2 zenon_H23b zenon_H100 zenon_H10d zenon_H1ab zenon_H142 zenon_H4c zenon_Hdc zenon_H1b1 zenon_H1fd zenon_Hcd zenon_Hf9 zenon_H108 zenon_H2f8 zenon_H20e zenon_H1a5 zenon_Hee zenon_H125 zenon_H15e zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.77 apply (zenon_L2547_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.77 apply (zenon_L235_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.77 exact (zenon_H56 zenon_H25). % 30.68/30.77 apply (zenon_L2490_); trivial. % 30.68/30.77 (* end of lemma zenon_L2548_ *) % 30.68/30.77 assert (zenon_L2549_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.68/30.77 do 0 intro. intros zenon_H1d5 zenon_Hc8 zenon_H4e zenon_H14e zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H2d zenon_H9c zenon_H222 zenon_H23b zenon_H6f zenon_H100 zenon_H26 zenon_H10d zenon_H1ab zenon_Hb8 zenon_Hde zenon_H89 zenon_H15a zenon_H30a zenon_H2b4 zenon_H1db zenon_Hf5 zenon_He1. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.77 apply (zenon_L332_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.77 apply (zenon_L2484_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.77 exact (zenon_H1db zenon_H1b9). % 30.68/30.77 apply (zenon_L221_); trivial. % 30.68/30.77 (* end of lemma zenon_L2549_ *) % 30.68/30.77 assert (zenon_L2550_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.77 do 0 intro. intros zenon_H1a2 zenon_H1ab zenon_H10d zenon_H100 zenon_H23b zenon_H9c zenon_H2d zenon_H15e zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.77 apply (zenon_L2549_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.77 apply (zenon_L235_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.77 exact (zenon_H56 zenon_H25). % 30.68/30.77 apply (zenon_L2490_); trivial. % 30.68/30.77 (* end of lemma zenon_L2550_ *) % 30.68/30.77 assert (zenon_L2551_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.77 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_H100 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_Hb1 zenon_H256 zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He1 zenon_He7 zenon_Hb8 zenon_H1ab. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.77 apply (zenon_L386_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.77 apply (zenon_L880_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.77 apply (zenon_L2489_); trivial. % 30.68/30.77 exact (zenon_H1ab zenon_H112). % 30.68/30.77 (* end of lemma zenon_L2551_ *) % 30.68/30.77 assert (zenon_L2552_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.77 do 0 intro. intros zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_H23b zenon_Hcd zenon_He2 zenon_H100 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He1 zenon_He7 zenon_Hb8 zenon_H1ab. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.77 exact (zenon_H30a zenon_H185). % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.77 apply (zenon_L744_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.77 apply (zenon_L294_); trivial. % 30.68/30.77 apply (zenon_L2551_); trivial. % 30.68/30.77 (* end of lemma zenon_L2552_ *) % 30.68/30.77 assert (zenon_L2553_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.77 do 0 intro. intros zenon_He4 zenon_H56 zenon_H125 zenon_Hf9 zenon_He9 zenon_H3f zenon_H10d zenon_H1b1 zenon_H4c zenon_H108 zenon_Hee zenon_H10e zenon_H1a2 zenon_H19e zenon_H48 zenon_H16f zenon_H20d zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_H23b zenon_Hcd zenon_H100 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He1 zenon_He7 zenon_Hb8 zenon_H1ab. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.77 apply (zenon_L232_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.77 apply (zenon_L2544_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.77 apply (zenon_L627_); trivial. % 30.68/30.77 apply (zenon_L2552_); trivial. % 30.68/30.77 (* end of lemma zenon_L2553_ *) % 30.68/30.77 assert (zenon_L2554_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.68/30.77 do 0 intro. intros zenon_H125 zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_H10d zenon_H89 zenon_H1b1 zenon_Hdc zenon_H4c zenon_Hde zenon_H142 zenon_Hb8 zenon_H1ab zenon_Hee zenon_H19a zenon_H100 zenon_H4a zenon_Hd2 zenon_H6f zenon_H23b zenon_H222 zenon_H3d zenon_He1 zenon_H14e zenon_H4e zenon_H16c. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.68/30.77 apply (zenon_L2501_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.68/30.77 apply (zenon_L2436_); trivial. % 30.68/30.77 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.68/30.77 apply (zenon_L89_); trivial. % 30.68/30.77 apply (zenon_L2532_); trivial. % 30.68/30.77 (* end of lemma zenon_L2554_ *) % 30.68/30.77 assert (zenon_L2555_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1d5 zenon_Hc8 zenon_H14e zenon_He1 zenon_H222 zenon_H23b zenon_H6f zenon_Hd2 zenon_H4a zenon_H100 zenon_H19a zenon_Hee zenon_H1ab zenon_Hb8 zenon_H142 zenon_Hde zenon_H4c zenon_Hdc zenon_H1b1 zenon_H89 zenon_H10d zenon_H3f zenon_He9 zenon_Hcd zenon_Hf9 zenon_H125 zenon_H1db zenon_H156 zenon_H4e zenon_H16c. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.78 apply (zenon_L332_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.78 apply (zenon_L2554_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 apply (zenon_L779_); trivial. % 30.68/30.78 (* end of lemma zenon_L2555_ *) % 30.68/30.78 assert (zenon_L2556_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1a2 zenon_H1fd zenon_H108 zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H16c zenon_H125 zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_H10d zenon_H1b1 zenon_Hdc zenon_H4c zenon_H142 zenon_H1ab zenon_Hee zenon_H100 zenon_H23b zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.78 apply (zenon_L2547_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.78 apply (zenon_L2555_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.78 exact (zenon_H56 zenon_H25). % 30.68/30.78 apply (zenon_L2490_); trivial. % 30.68/30.78 (* end of lemma zenon_L2556_ *) % 30.68/30.78 assert (zenon_L2557_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1a2 zenon_H9c zenon_H2d zenon_H1ab zenon_Hee zenon_H100 zenon_H23b zenon_H16c zenon_H108 zenon_H4c zenon_Hdc zenon_H1b1 zenon_H10d zenon_H3f zenon_He9 zenon_Hcd zenon_Hf9 zenon_H125 zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.78 apply (zenon_L2549_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.78 apply (zenon_L2543_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.78 exact (zenon_H56 zenon_H25). % 30.68/30.78 apply (zenon_L2490_); trivial. % 30.68/30.78 (* end of lemma zenon_L2557_ *) % 30.68/30.78 assert (zenon_L2558_ : ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H64 zenon_H56 zenon_H125 zenon_Hf9 zenon_He9 zenon_H3f zenon_H10d zenon_H1b1 zenon_H4c zenon_H108 zenon_Hee zenon_H2d zenon_H1a2 zenon_H1fd zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1d2 zenon_He4 zenon_H19e zenon_H48 zenon_H16f zenon_H14b zenon_H20d zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_H23b zenon_Hcd zenon_H100 zenon_H4e zenon_H14e zenon_Hf5 zenon_H156 zenon_H159 zenon_H4a zenon_Hd2 zenon_H256 zenon_H6f zenon_H1d5 zenon_H89 zenon_Hc8 zenon_H222 zenon_H1db zenon_He1 zenon_He7 zenon_Hb8 zenon_H1ab. % 30.68/30.78 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.78 apply (zenon_L1209_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.78 apply (zenon_L2384_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.78 apply (zenon_L2385_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.78 apply (zenon_L2544_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.78 apply (zenon_L2409_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.78 apply (zenon_L2548_); trivial. % 30.68/30.78 apply (zenon_L2550_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.78 apply (zenon_L2553_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.78 apply (zenon_L2409_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.78 apply (zenon_L2556_); trivial. % 30.68/30.78 apply (zenon_L2557_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.78 apply (zenon_L627_); trivial. % 30.68/30.78 apply (zenon_L2552_); trivial. % 30.68/30.78 (* end of lemma zenon_L2558_ *) % 30.68/30.78 assert (zenon_L2559_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1a2 zenon_H4c zenon_H15e zenon_H108 zenon_H142 zenon_H1ab zenon_Hee zenon_H100 zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_Hda zenon_H10d zenon_H23b zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.78 apply (zenon_L2545_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.78 apply (zenon_L2501_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.78 exact (zenon_H56 zenon_H25). % 30.68/30.78 apply (zenon_L2490_); trivial. % 30.68/30.78 (* end of lemma zenon_L2559_ *) % 30.68/30.78 assert (zenon_L2560_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1a2 zenon_H1a5 zenon_H20e zenon_H2f8 zenon_H108 zenon_Hda zenon_H1fd zenon_H16c zenon_H125 zenon_Hf9 zenon_Hcd zenon_He9 zenon_H3f zenon_H10d zenon_H1b1 zenon_Hdc zenon_H4c zenon_H142 zenon_H1ab zenon_Hee zenon_H100 zenon_H23b zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.78 apply (zenon_L2546_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.78 apply (zenon_L2555_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.78 exact (zenon_H56 zenon_H25). % 30.68/30.78 apply (zenon_L2490_); trivial. % 30.68/30.78 (* end of lemma zenon_L2560_ *) % 30.68/30.78 assert (zenon_L2561_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (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 (e0) (e2)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_Had zenon_H14b zenon_H20d zenon_H16f zenon_H48 zenon_H19e zenon_He4 zenon_H1d2 zenon_H1fd zenon_Hda zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1a2 zenon_H2d zenon_H1ab zenon_Hee zenon_H100 zenon_H23b zenon_H108 zenon_H4c zenon_Hdc zenon_H1b1 zenon_H10d zenon_H3f zenon_He9 zenon_Hcd zenon_Hf9 zenon_H125 zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.78 apply (zenon_L2384_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.78 apply (zenon_L2385_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.78 apply (zenon_L2542_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.78 apply (zenon_L1662_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.78 apply (zenon_L2559_); trivial. % 30.68/30.78 apply (zenon_L2550_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.78 apply (zenon_L2553_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.78 apply (zenon_L2409_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.78 apply (zenon_L2560_); trivial. % 30.68/30.78 apply (zenon_L2557_); trivial. % 30.68/30.78 (* end of lemma zenon_L2561_ *) % 30.68/30.78 assert (zenon_L2562_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1a2 zenon_Hee zenon_Hdc zenon_H1b1 zenon_H1a5 zenon_H142 zenon_H20e zenon_H2f8 zenon_H108 zenon_Hf9 zenon_Hcd zenon_Hda zenon_H23b zenon_H10d zenon_H1ab zenon_H1fd zenon_H9d zenon_H4c zenon_H100 zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.78 apply (zenon_L2546_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.78 apply (zenon_L1184_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.78 exact (zenon_H56 zenon_H25). % 30.68/30.78 apply (zenon_L2490_); trivial. % 30.68/30.78 (* end of lemma zenon_L2562_ *) % 30.68/30.78 assert (zenon_L2563_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H14b zenon_H125 zenon_H1d2 zenon_H4c zenon_H9d zenon_H1fd zenon_Hda zenon_Hcd zenon_Hf9 zenon_H108 zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1b1 zenon_Hdc zenon_Hee zenon_H1a2 zenon_H1ab zenon_H10d zenon_H100 zenon_H23b zenon_H2d zenon_H15e zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.78 apply (zenon_L2542_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.78 apply (zenon_L2409_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.78 apply (zenon_L2562_); trivial. % 30.68/30.78 apply (zenon_L2550_); trivial. % 30.68/30.78 (* end of lemma zenon_L2563_ *) % 30.68/30.78 assert (zenon_L2564_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H225 zenon_H1ab zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_H14e zenon_H4e zenon_H100 zenon_Hcd zenon_H23b zenon_H15a zenon_H30a zenon_H2b4 zenon_H20d zenon_H16f zenon_H48 zenon_H19e zenon_H1a2 zenon_Hee zenon_H108 zenon_H4c zenon_H1b1 zenon_H10d zenon_H3f zenon_Hf9 zenon_H125 zenon_H56 zenon_He4 zenon_Hde zenon_H10e zenon_Hf5 zenon_H218. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.78 apply (zenon_L232_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.78 apply (zenon_L2553_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.78 apply (zenon_L192_); trivial. % 30.68/30.78 apply (zenon_L405_); trivial. % 30.68/30.78 (* end of lemma zenon_L2564_ *) % 30.68/30.78 assert (zenon_L2565_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H14b zenon_H218 zenon_He4 zenon_H125 zenon_H3f zenon_H19e zenon_H48 zenon_H16f zenon_H20d zenon_H225 zenon_H1d2 zenon_H1fd zenon_Hda zenon_Hcd zenon_Hf9 zenon_H108 zenon_H2f8 zenon_H20e zenon_H1a5 zenon_H1b1 zenon_Hdc zenon_Hee zenon_H1a2 zenon_H16c zenon_H1ab zenon_H10d zenon_H23b zenon_H2d zenon_H9d zenon_H4c zenon_H100 zenon_H56 zenon_H2b4 zenon_H30a zenon_H15a zenon_Hde zenon_Hb8 zenon_He7 zenon_He1 zenon_H1db zenon_H222 zenon_Hc8 zenon_H89 zenon_H1d5 zenon_H6f zenon_H256 zenon_Hd2 zenon_H4a zenon_H159 zenon_H156 zenon_Hf5 zenon_H14e zenon_H4e. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.78 apply (zenon_L2564_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.78 apply (zenon_L2409_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.78 apply (zenon_L2562_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.78 apply (zenon_L332_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.78 apply (zenon_L2484_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 apply (zenon_L779_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.78 apply (zenon_L1184_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.78 exact (zenon_H56 zenon_H25). % 30.68/30.78 apply (zenon_L2490_); trivial. % 30.68/30.78 (* end of lemma zenon_L2565_ *) % 30.68/30.78 assert (zenon_L2566_ : (((op (e2) (op (e2) (e0))) = (e0))/\(((op (e2) (op (e2) (e1))) = (e1))/\(((op (e2) (op (e2) (e2))) = (e2))/\(((op (e2) (op (e2) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0)))/\(((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3)))))))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H5a zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H1db zenon_Hf5 zenon_He1. % 30.68/30.78 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.68/30.78 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.68/30.78 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.68/30.78 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.78 apply (zenon_L193_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.78 apply (zenon_L144_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 apply (zenon_L221_); trivial. % 30.68/30.78 (* end of lemma zenon_L2566_ *) % 30.68/30.78 assert (zenon_L2567_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H20e zenon_H19a zenon_H108 zenon_Hf5 zenon_H1db. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.68/30.78 exact (zenon_H260 zenon_H142). % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.68/30.78 apply (zenon_L225_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.68/30.78 apply (zenon_L62_); trivial. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 (* end of lemma zenon_L2567_ *) % 30.68/30.78 assert (zenon_L2568_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H1a0 zenon_H1dc zenon_H108 zenon_Hf5 zenon_H1db. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.68/30.78 exact (zenon_H260 zenon_H142). % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.68/30.78 apply (zenon_L1834_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.68/30.78 apply (zenon_L62_); trivial. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 (* end of lemma zenon_L2568_ *) % 30.68/30.78 assert (zenon_L2569_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H173 zenon_H15a zenon_He1 zenon_H37 zenon_H1db zenon_H108 zenon_H1dc zenon_H260 zenon_H1d2 zenon_H76 zenon_H73 zenon_H20e zenon_H3f zenon_H198 zenon_H1a2 zenon_H1c7 zenon_Hfc zenon_H65 zenon_H10e zenon_H101 zenon_Hf5 zenon_H156. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.78 apply (zenon_L725_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.78 apply (zenon_L158_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.78 apply (zenon_L818_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.78 apply (zenon_L58_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.78 apply (zenon_L1253_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.78 apply (zenon_L129_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.78 apply (zenon_L2567_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.78 apply (zenon_L23_); trivial. % 30.68/30.78 apply (zenon_L2568_); trivial. % 30.68/30.78 apply (zenon_L90_); trivial. % 30.68/30.78 (* end of lemma zenon_L2569_ *) % 30.68/30.78 assert (zenon_L2570_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H1db zenon_H218 zenon_H36 zenon_H16b. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.78 apply (zenon_L174_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.78 apply (zenon_L131_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 apply (zenon_L1038_); trivial. % 30.68/30.78 (* end of lemma zenon_L2570_ *) % 30.68/30.78 assert (zenon_L2571_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H8d zenon_H6f zenon_H68 zenon_H156 zenon_Hf5 zenon_H101 zenon_H10e zenon_H65 zenon_Hfc zenon_H1c7 zenon_H1a2 zenon_H198 zenon_H3f zenon_H20e zenon_H73 zenon_H1d2 zenon_H260 zenon_H1dc zenon_H108 zenon_He1 zenon_H15a zenon_H173 zenon_H1d5 zenon_H1d8 zenon_H37 zenon_H19e zenon_H1db zenon_H218 zenon_H36 zenon_H16b. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.78 apply (zenon_L232_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.78 apply (zenon_L18_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.78 apply (zenon_L2569_); trivial. % 30.68/30.78 apply (zenon_L2570_); trivial. % 30.68/30.78 (* end of lemma zenon_L2571_ *) % 30.68/30.78 assert (zenon_L2572_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1d5 zenon_H185 zenon_H36 zenon_Hc8 zenon_H37 zenon_H19e zenon_H1db zenon_Hf5 zenon_He1. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.78 apply (zenon_L1001_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.78 apply (zenon_L131_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 apply (zenon_L221_); trivial. % 30.68/30.78 (* end of lemma zenon_L2572_ *) % 30.68/30.78 assert (zenon_L2573_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H2f7 zenon_H20d zenon_H1b3 zenon_H15a zenon_H188 zenon_H68 zenon_H225 zenon_Hde zenon_He1 zenon_H35 zenon_H37 zenon_H2d zenon_H8d zenon_H1d8 zenon_H19e zenon_H218 zenon_H36 zenon_H1d5 zenon_H198 zenon_H101 zenon_H3f zenon_H1d2 zenon_H1db zenon_H108 zenon_H20e zenon_H1dc zenon_H1a2 zenon_Hf5 zenon_H1c7 zenon_Hfc zenon_H65 zenon_H156 zenon_H173 zenon_H6f zenon_H174 zenon_Hc8 zenon_H301. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H260 | zenon_intro zenon_Hc9 ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.68/30.78 exact (zenon_H1b3 zenon_H64). % 30.68/30.78 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.68/30.78 apply (zenon_L119_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.78 apply (zenon_L232_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.78 apply (zenon_L1002_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.78 apply (zenon_L87_); trivial. % 30.68/30.78 apply (zenon_L2571_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.78 apply (zenon_L818_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.78 apply (zenon_L192_); trivial. % 30.68/30.78 apply (zenon_L405_); trivial. % 30.68/30.78 apply (zenon_L2572_); trivial. % 30.68/30.78 apply (zenon_L627_); trivial. % 30.68/30.78 (* end of lemma zenon_L2573_ *) % 30.68/30.78 assert (zenon_L2574_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1a8 zenon_Hcd zenon_Hdc zenon_H37 zenon_H6f zenon_H1db zenon_Hf5 zenon_H108 zenon_H20e zenon_H260 zenon_H1d2 zenon_H2cc. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.78 apply (zenon_L48_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.78 apply (zenon_L125_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.78 apply (zenon_L2567_); trivial. % 30.68/30.78 exact (zenon_H2cc zenon_H182). % 30.68/30.78 (* end of lemma zenon_L2574_ *) % 30.68/30.78 assert (zenon_L2575_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1d2 zenon_H260 zenon_H27 zenon_H26 zenon_H108 zenon_Hf5 zenon_H1db. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H142 | zenon_intro zenon_H1d3 ]. % 30.68/30.78 exact (zenon_H260 zenon_H142). % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H25 | zenon_intro zenon_H1d4 ]. % 30.68/30.78 apply (zenon_L3_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H1b9 ]. % 30.68/30.78 apply (zenon_L62_); trivial. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 (* end of lemma zenon_L2575_ *) % 30.68/30.78 assert (zenon_L2576_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H8a zenon_H37 zenon_H19e zenon_H1db zenon_Hf5 zenon_He1. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.78 apply (zenon_L174_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.78 apply (zenon_L131_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 apply (zenon_L221_); trivial. % 30.68/30.78 (* end of lemma zenon_L2576_ *) % 30.68/30.78 assert (zenon_L2577_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_Hb8 zenon_He1 zenon_Hf5 zenon_H1db zenon_H19e zenon_H1d8 zenon_H1d5 zenon_H100 zenon_H37 zenon_H10d zenon_H117 zenon_Ha4 zenon_H36 zenon_H16b. % 30.68/30.78 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H8a | zenon_intro zenon_Hba ]. % 30.68/30.78 apply (zenon_L2576_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H40 | zenon_intro zenon_Hbb ]. % 30.68/30.78 apply (zenon_L150_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbc ]. % 30.68/30.78 apply (zenon_L151_); trivial. % 30.68/30.78 apply (zenon_L1142_); trivial. % 30.68/30.78 (* end of lemma zenon_L2577_ *) % 30.68/30.78 assert (zenon_L2578_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H11e zenon_He9 zenon_H65 zenon_H27 zenon_H25 zenon_Hed zenon_H198 zenon_H1a5 zenon_Hb6 zenon_H10d. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H10e | zenon_intro zenon_H11f ]. % 30.68/30.78 apply (zenon_L818_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H26 | zenon_intro zenon_H120 ]. % 30.68/30.78 apply (zenon_L3_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hda | zenon_intro zenon_H117 ]. % 30.68/30.78 apply (zenon_L1030_); trivial. % 30.68/30.78 apply (zenon_L151_); trivial. % 30.68/30.78 (* end of lemma zenon_L2578_ *) % 30.68/30.78 assert (zenon_L2579_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1fd zenon_H16b zenon_H36 zenon_Ha4 zenon_H100 zenon_H1d5 zenon_H1d8 zenon_H19e zenon_Hf5 zenon_He1 zenon_Hb8 zenon_H37 zenon_Hfc zenon_H1db zenon_H11e zenon_He9 zenon_H65 zenon_H27 zenon_H25 zenon_Hed zenon_H198 zenon_H1a5 zenon_H10d. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.78 apply (zenon_L2577_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.78 apply (zenon_L203_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 apply (zenon_L2578_); trivial. % 30.68/30.78 (* end of lemma zenon_L2579_ *) % 30.68/30.78 assert (zenon_L2580_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (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) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1a2 zenon_H138 zenon_Hfe zenon_H6f zenon_H10d zenon_H1a5 zenon_H198 zenon_Hed zenon_H27 zenon_H65 zenon_He9 zenon_H11e zenon_Hfc zenon_H37 zenon_Hb8 zenon_He1 zenon_H19e zenon_H1d8 zenon_H1d5 zenon_H100 zenon_Ha4 zenon_H36 zenon_H16b zenon_H1fd zenon_H1d2 zenon_H260 zenon_H1dc zenon_H108 zenon_Hf5 zenon_H1db. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.78 apply (zenon_L2575_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.78 apply (zenon_L2577_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.78 apply (zenon_L235_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 apply (zenon_L1436_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.78 apply (zenon_L2579_); trivial. % 30.68/30.78 apply (zenon_L2568_); trivial. % 30.68/30.78 (* end of lemma zenon_L2580_ *) % 30.68/30.78 assert (zenon_L2581_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1fd zenon_H16b zenon_H36 zenon_Ha4 zenon_H10d zenon_H100 zenon_H1d5 zenon_H1d8 zenon_H19e zenon_Hf5 zenon_He1 zenon_Hb8 zenon_H37 zenon_Hfc zenon_H1db zenon_H2d zenon_H9c. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.78 apply (zenon_L2577_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.78 apply (zenon_L203_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.78 exact (zenon_H1db zenon_H1b9). % 30.68/30.78 apply (zenon_L304_); trivial. % 30.68/30.78 (* end of lemma zenon_L2581_ *) % 30.68/30.78 assert (zenon_L2582_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H173 zenon_Hcd zenon_H68 zenon_H2d zenon_H1db zenon_Hfc zenon_H37 zenon_Hb8 zenon_He1 zenon_H19e zenon_H1d8 zenon_H1d5 zenon_H100 zenon_H10d zenon_Ha4 zenon_H36 zenon_H16b zenon_H1fd zenon_H260 zenon_H1a2 zenon_H138 zenon_H6f zenon_H1a5 zenon_H198 zenon_H27 zenon_H65 zenon_He9 zenon_H11e zenon_H1d2 zenon_H1dc zenon_H108 zenon_He7 zenon_He2 zenon_H14b zenon_Hf5 zenon_H156. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.78 apply (zenon_L48_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.78 apply (zenon_L158_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.68/30.78 apply (zenon_L727_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.68/30.78 apply (zenon_L2580_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.68/30.78 exact (zenon_H260 zenon_H142). % 30.68/30.78 apply (zenon_L2581_); trivial. % 30.68/30.78 apply (zenon_L90_); trivial. % 30.68/30.78 (* end of lemma zenon_L2582_ *) % 30.68/30.78 assert (zenon_L2583_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H174 zenon_H122 zenon_H16a zenon_H2b4 zenon_H218 zenon_H35 zenon_H2c1 zenon_H2d6 zenon_H64 zenon_H2bd zenon_H173 zenon_Hcd zenon_H68 zenon_H2d zenon_H1db zenon_Hfc zenon_H37 zenon_Hb8 zenon_He1 zenon_H19e zenon_H1d8 zenon_H1d5 zenon_H100 zenon_H10d zenon_Ha4 zenon_H36 zenon_H1fd zenon_H260 zenon_H1a2 zenon_H138 zenon_H6f zenon_H1a5 zenon_H198 zenon_H27 zenon_H65 zenon_He9 zenon_H11e zenon_H1d2 zenon_H1dc zenon_H108 zenon_He7 zenon_He2 zenon_H14b zenon_Hf5 zenon_H156. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.78 apply (zenon_L1564_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.78 apply (zenon_L1002_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.78 apply (zenon_L2372_); trivial. % 30.68/30.78 apply (zenon_L2582_); trivial. % 30.68/30.78 (* end of lemma zenon_L2583_ *) % 30.68/30.78 assert (zenon_L2584_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H173 zenon_Hcd zenon_H68 zenon_He1 zenon_H37 zenon_Hda zenon_H198 zenon_H1a5 zenon_Hf5 zenon_H156. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.78 apply (zenon_L48_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.78 apply (zenon_L158_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.78 apply (zenon_L1030_); trivial. % 30.68/30.78 apply (zenon_L90_); trivial. % 30.68/30.78 (* end of lemma zenon_L2584_ *) % 30.68/30.78 assert (zenon_L2585_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1a8 zenon_H156 zenon_H1a5 zenon_H198 zenon_Hda zenon_He1 zenon_Hcd zenon_H173 zenon_H37 zenon_H6f zenon_H1db zenon_Hf5 zenon_H108 zenon_H20e zenon_H260 zenon_H1d2 zenon_H2cc. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.78 apply (zenon_L2584_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.78 apply (zenon_L125_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.78 apply (zenon_L2567_); trivial. % 30.68/30.78 exact (zenon_H2cc zenon_H182). % 30.68/30.78 (* end of lemma zenon_L2585_ *) % 30.68/30.78 assert (zenon_L2586_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e0)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1a8 zenon_H313 zenon_H18f zenon_H1ab zenon_Hee zenon_H3f zenon_H1f zenon_H6f zenon_H8a zenon_H23b zenon_H28f zenon_H4a zenon_Hc3. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.78 exact (zenon_H313 zenon_H68). % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.78 exact (zenon_H18f zenon_Hd2). % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.78 apply (zenon_L1187_); trivial. % 30.68/30.78 apply (zenon_L761_); trivial. % 30.68/30.78 (* end of lemma zenon_L2586_ *) % 30.68/30.78 assert (zenon_L2587_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e0)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H92 zenon_Hd9 zenon_H26 zenon_H313 zenon_H18c zenon_Had zenon_H4a zenon_Hc3. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.78 apply (zenon_L797_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.78 exact (zenon_H313 zenon_H68). % 30.68/30.78 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.78 apply (zenon_L763_); trivial. % 30.68/30.78 apply (zenon_L769_); trivial. % 30.68/30.78 (* end of lemma zenon_L2587_ *) % 30.68/30.78 assert (zenon_L2588_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> ((op (e1) (e1)) = (e0)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H92 zenon_H33 zenon_H2c1 zenon_H313 zenon_H18c zenon_Had zenon_H4a zenon_Hc3. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.78 apply (zenon_L940_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.78 exact (zenon_H313 zenon_H68). % 30.68/30.78 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.78 apply (zenon_L763_); trivial. % 30.68/30.78 apply (zenon_L769_); trivial. % 30.68/30.78 (* end of lemma zenon_L2588_ *) % 30.68/30.78 assert (zenon_L2589_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H2b4 zenon_H20 zenon_H33 zenon_Hc3 zenon_H159 zenon_H8a zenon_H1af zenon_H1d8 zenon_H122. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.78 apply (zenon_L117_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.78 apply (zenon_L1458_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.78 apply (zenon_L186_); trivial. % 30.68/30.78 exact (zenon_H122 zenon_Hb1). % 30.68/30.78 (* end of lemma zenon_L2589_ *) % 30.68/30.78 assert (zenon_L2590_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H16f zenon_Had zenon_H8a zenon_H2d zenon_Hc3 zenon_H20e zenon_H1af zenon_Hd0 zenon_He9 zenon_H3c zenon_Hde zenon_Hdf zenon_H135 zenon_H182 zenon_H6f. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.78 apply (zenon_L34_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.78 apply (zenon_L364_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.78 apply (zenon_L363_); trivial. % 30.68/30.78 apply (zenon_L758_); trivial. % 30.68/30.78 (* end of lemma zenon_L2590_ *) % 30.68/30.78 assert (zenon_L2591_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H11b zenon_H122 zenon_H1e5 zenon_Hf6 zenon_H231 zenon_H17d zenon_H8a. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.78 exact (zenon_H122 zenon_Hb1). % 30.68/30.78 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.78 apply (zenon_L187_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.78 exact (zenon_H231 zenon_Hf4). % 30.68/30.78 apply (zenon_L110_); trivial. % 30.68/30.78 (* end of lemma zenon_L2591_ *) % 30.68/30.78 assert (zenon_L2592_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H2b1 zenon_H1d8 zenon_H159 zenon_H20 zenon_H2b4 zenon_H6f zenon_H135 zenon_Hdf zenon_Hde zenon_H3c zenon_He9 zenon_Hd0 zenon_H1af zenon_H20e zenon_Hc3 zenon_H2d zenon_Had zenon_H16f zenon_H8a zenon_H17d zenon_H231 zenon_Hf6 zenon_H122 zenon_H11b zenon_H9c zenon_H1b9. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.68/30.78 apply (zenon_L2589_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.68/30.78 apply (zenon_L2590_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.68/30.78 apply (zenon_L2591_); trivial. % 30.68/30.78 apply (zenon_L198_); trivial. % 30.68/30.78 (* end of lemma zenon_L2592_ *) % 30.68/30.78 assert (zenon_L2593_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.78 do 0 intro. intros zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H122 zenon_H2b1 zenon_H1d8 zenon_H159 zenon_H20 zenon_H2b4 zenon_H6f zenon_H135 zenon_Hdf zenon_Hde zenon_H3c zenon_He9 zenon_Hd0 zenon_H20e zenon_Hc3 zenon_H2d zenon_Had zenon_H16f zenon_H8a zenon_H17d zenon_H231 zenon_Hf6 zenon_H11b zenon_H100 zenon_H5c zenon_Hbd zenon_H1af zenon_H156. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.78 apply (zenon_L34_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.78 apply (zenon_L364_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.78 apply (zenon_L363_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.68/30.78 apply (zenon_L49_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.68/30.78 apply (zenon_L88_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.68/30.78 exact (zenon_Hd0 zenon_Hcc). % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.78 apply (zenon_L193_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.78 apply (zenon_L144_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.78 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.78 apply (zenon_L194_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.78 apply (zenon_L1497_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.78 apply (zenon_L2592_); trivial. % 30.68/30.78 exact (zenon_H122 zenon_Hb1). % 30.68/30.78 apply (zenon_L290_); trivial. % 30.68/30.78 (* end of lemma zenon_L2593_ *) % 30.68/30.78 assert (zenon_L2594_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.78 do 0 intro. intros zenon_Hbd zenon_H8a zenon_H2d zenon_Hc3 zenon_H100 zenon_H142 zenon_H1dc zenon_H122. % 30.68/30.78 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.78 apply (zenon_L25_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.78 apply (zenon_L1497_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.78 apply (zenon_L177_); trivial. % 30.68/30.78 exact (zenon_H122 zenon_Hb1). % 30.68/30.78 (* end of lemma zenon_L2594_ *) % 30.68/30.78 assert (zenon_L2595_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.78 do 0 intro. intros zenon_H200 zenon_H156 zenon_H5c zenon_H11b zenon_Hf6 zenon_H231 zenon_H17d zenon_H16f zenon_Had zenon_H20e zenon_Hd0 zenon_He9 zenon_H3c zenon_Hde zenon_H135 zenon_H6f zenon_H2b4 zenon_H20 zenon_H159 zenon_H2b1 zenon_Hd6 zenon_H6b zenon_H1d5 zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.78 apply (zenon_L2593_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.78 apply (zenon_L347_); trivial. % 30.68/30.78 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.78 apply (zenon_L2594_); trivial. % 30.68/30.78 apply (zenon_L186_); trivial. % 30.68/30.78 (* end of lemma zenon_L2595_ *) % 30.68/30.78 assert (zenon_L2596_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.68/30.78 do 0 intro. intros zenon_Hf9 zenon_H8a zenon_He1 zenon_H20e zenon_H15e zenon_H1af zenon_Hd0 zenon_H222 zenon_Hde zenon_Hdf zenon_H135 zenon_Hda zenon_H10d zenon_H231. % 30.68/30.78 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.68/30.79 apply (zenon_L50_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.68/30.79 apply (zenon_L359_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.68/30.79 apply (zenon_L64_); trivial. % 30.68/30.79 exact (zenon_H231 zenon_Hf4). % 30.68/30.79 (* end of lemma zenon_L2596_ *) % 30.68/30.79 assert (zenon_L2597_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H200 zenon_H231 zenon_H10d zenon_Hda zenon_H135 zenon_Hde zenon_H222 zenon_Hd0 zenon_H15e zenon_H20e zenon_He1 zenon_Hf9 zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.79 apply (zenon_L2596_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.79 apply (zenon_L347_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.79 apply (zenon_L2594_); trivial. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 (* end of lemma zenon_L2597_ *) % 30.68/30.79 assert (zenon_L2598_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H16f zenon_Had zenon_H2d zenon_Hc3 zenon_H231 zenon_H10d zenon_Hda zenon_H135 zenon_Hdf zenon_Hde zenon_H222 zenon_Hd0 zenon_H20e zenon_Hf9 zenon_H1d5 zenon_H1d8 zenon_H8a zenon_He1 zenon_H1c7 zenon_H55 zenon_H60 zenon_H1af zenon_H156. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L2596_); trivial. % 30.68/30.79 apply (zenon_L365_); trivial. % 30.68/30.79 (* end of lemma zenon_L2598_ *) % 30.68/30.79 assert (zenon_L2599_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H16f zenon_Had zenon_H8a zenon_H2d zenon_Hc3 zenon_H20e zenon_H1af zenon_Hd0 zenon_H222 zenon_H9d zenon_Hde zenon_Hdf zenon_H135 zenon_H182 zenon_H6f. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L359_); trivial. % 30.68/30.79 apply (zenon_L758_); trivial. % 30.68/30.79 (* end of lemma zenon_L2599_ *) % 30.68/30.79 assert (zenon_L2600_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H2b1 zenon_H88 zenon_H2c1 zenon_H6f zenon_H135 zenon_Hdf zenon_Hde zenon_H9d zenon_H222 zenon_Hd0 zenon_H1af zenon_H20e zenon_Hc3 zenon_H2d zenon_Had zenon_H16f zenon_H8a zenon_H17d zenon_H231 zenon_Hf6 zenon_H122 zenon_H11b zenon_H9c zenon_H1b9. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.68/30.79 apply (zenon_L940_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.68/30.79 apply (zenon_L2599_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.68/30.79 apply (zenon_L2591_); trivial. % 30.68/30.79 apply (zenon_L198_); trivial. % 30.68/30.79 (* end of lemma zenon_L2600_ *) % 30.68/30.79 assert (zenon_L2601_ : ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H60 zenon_H1c7 zenon_He1 zenon_H1d8 zenon_Hf9 zenon_Hda zenon_H10d zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H122 zenon_H2b1 zenon_H88 zenon_H2c1 zenon_H6f zenon_H135 zenon_Hdf zenon_Hde zenon_H9d zenon_H222 zenon_Hd0 zenon_H20e zenon_Hc3 zenon_H2d zenon_Had zenon_H16f zenon_H8a zenon_H17d zenon_H231 zenon_Hf6 zenon_H11b zenon_H100 zenon_Hbd zenon_H1af zenon_H16c zenon_H156. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.68/30.79 apply (zenon_L49_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.68/30.79 apply (zenon_L2598_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.68/30.79 exact (zenon_Hd0 zenon_Hcc). % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.79 apply (zenon_L193_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.79 apply (zenon_L144_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.79 apply (zenon_L25_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.79 apply (zenon_L1497_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.79 apply (zenon_L2600_); trivial. % 30.68/30.79 exact (zenon_H122 zenon_Hb1). % 30.68/30.79 apply (zenon_L290_); trivial. % 30.68/30.79 (* end of lemma zenon_L2601_ *) % 30.68/30.79 assert (zenon_L2602_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H101 zenon_H159 zenon_H20 zenon_H2b4 zenon_H3c zenon_H5c zenon_H13b zenon_H200 zenon_H156 zenon_H11b zenon_Hf6 zenon_H231 zenon_H17d zenon_H16f zenon_Had zenon_H20e zenon_Hd0 zenon_H222 zenon_Hde zenon_H135 zenon_H6f zenon_H2c1 zenon_H88 zenon_H2b1 zenon_Hd6 zenon_H6b zenon_H1d5 zenon_H10d zenon_Hda zenon_Hf9 zenon_He1 zenon_H1c7 zenon_H60 zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.79 apply (zenon_L2595_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.79 exact (zenon_H13b zenon_Hfd). % 30.68/30.79 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L2597_); trivial. % 30.68/30.79 apply (zenon_L365_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L2597_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.79 apply (zenon_L2601_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.79 apply (zenon_L347_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.79 apply (zenon_L2594_); trivial. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 (* end of lemma zenon_L2602_ *) % 30.68/30.79 assert (zenon_L2603_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H2b4 zenon_Hde zenon_H17b zenon_Hc3 zenon_H159 zenon_H8a zenon_H1af zenon_H1d8 zenon_H122. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.79 apply (zenon_L817_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.79 apply (zenon_L1458_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 exact (zenon_H122 zenon_Hb1). % 30.68/30.79 (* end of lemma zenon_L2603_ *) % 30.68/30.79 assert (zenon_L2604_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H200 zenon_H20e zenon_H15e zenon_Hd0 zenon_He9 zenon_H3c zenon_Hde zenon_H135 zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.79 apply (zenon_L363_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.79 apply (zenon_L347_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.79 apply (zenon_L2594_); trivial. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 (* end of lemma zenon_L2604_ *) % 30.68/30.79 assert (zenon_L2605_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H267 zenon_H122 zenon_H1d8 zenon_H1af zenon_H8a zenon_H159 zenon_Hc3 zenon_Hde zenon_H2b4 zenon_H156 zenon_H60 zenon_Hd0 zenon_H6b zenon_H6c zenon_H1dc zenon_H9c zenon_H1d2 zenon_H55 zenon_H1c7 zenon_H231. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.68/30.79 apply (zenon_L2603_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.68/30.79 apply (zenon_L180_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.68/30.79 apply (zenon_L1253_); trivial. % 30.68/30.79 exact (zenon_H231 zenon_Hf4). % 30.68/30.79 (* end of lemma zenon_L2605_ *) % 30.68/30.79 assert (zenon_L2606_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.79 do 0 intro. intros zenon_Hbd zenon_Hdf zenon_H5c zenon_H100 zenon_H231 zenon_H1c7 zenon_H55 zenon_H1d2 zenon_H1dc zenon_H6c zenon_H6b zenon_Hd0 zenon_H60 zenon_H156 zenon_H2b4 zenon_Hde zenon_Hc3 zenon_H159 zenon_H8a zenon_H1af zenon_H1d8 zenon_H267 zenon_H122. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.79 apply (zenon_L194_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.79 apply (zenon_L1497_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.79 apply (zenon_L2605_); trivial. % 30.68/30.79 exact (zenon_H122 zenon_Hb1). % 30.68/30.79 (* end of lemma zenon_L2606_ *) % 30.68/30.79 assert (zenon_L2607_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H135 zenon_H122 zenon_H267 zenon_H1d8 zenon_H8a zenon_H159 zenon_Hde zenon_H2b4 zenon_H1dc zenon_H1d2 zenon_H231 zenon_H100 zenon_H5c zenon_Hdf zenon_Hbd zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H60 zenon_H1c7 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H1af zenon_H16c zenon_H156. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.68/30.79 apply (zenon_L49_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.68/30.79 apply (zenon_L2606_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.68/30.79 exact (zenon_Hd0 zenon_Hcc). % 30.68/30.79 apply (zenon_L367_); trivial. % 30.68/30.79 (* end of lemma zenon_L2607_ *) % 30.68/30.79 assert (zenon_L2608_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H1e6 zenon_H1d8 zenon_H8a zenon_H17d zenon_H231 zenon_Hf6 zenon_H122 zenon_H11b zenon_H20e zenon_H15e zenon_H1af zenon_H16c zenon_H156. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.68/30.79 apply (zenon_L2591_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.68/30.79 apply (zenon_L358_); trivial. % 30.68/30.79 apply (zenon_L290_); trivial. % 30.68/30.79 (* end of lemma zenon_L2608_ *) % 30.68/30.79 assert (zenon_L2609_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H30d zenon_H2d zenon_H185 zenon_H156 zenon_H15e zenon_H20e zenon_H11b zenon_H122 zenon_Hf6 zenon_H231 zenon_H1d8 zenon_H1e6 zenon_H1c7 zenon_H3d zenon_H1af zenon_H17d zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H30d); [ zenon_intro zenon_H16b | zenon_intro zenon_H30e ]. % 30.68/30.79 apply (zenon_L848_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H16c | zenon_intro zenon_H30f ]. % 30.68/30.79 apply (zenon_L2608_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H1c5 | zenon_intro zenon_Hbc ]. % 30.68/30.79 apply (zenon_L167_); trivial. % 30.68/30.79 apply (zenon_L110_); trivial. % 30.68/30.79 (* end of lemma zenon_L2609_ *) % 30.68/30.79 assert (zenon_L2610_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H1ca zenon_Hc3 zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H9d zenon_H222 zenon_H30d zenon_H2d zenon_H185 zenon_H156 zenon_H15e zenon_H20e zenon_H11b zenon_H122 zenon_Hf6 zenon_H231 zenon_H1d8 zenon_H1e6 zenon_H1c7 zenon_H1af zenon_H17d zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1cb ]. % 30.68/30.79 apply (zenon_L347_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H1cc ]. % 30.68/30.79 apply (zenon_L163_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H55 | zenon_intro zenon_H3d ]. % 30.68/30.79 apply (zenon_L264_); trivial. % 30.68/30.79 apply (zenon_L2609_); trivial. % 30.68/30.79 (* end of lemma zenon_L2610_ *) % 30.68/30.79 assert (zenon_L2611_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H2b4 zenon_H17d zenon_H1c7 zenon_H1e6 zenon_H231 zenon_Hf6 zenon_H11b zenon_H20e zenon_H15e zenon_H156 zenon_H2d zenon_H30d zenon_H222 zenon_H9d zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_Hc3 zenon_H159 zenon_H8a zenon_H1af zenon_H1d8 zenon_H122. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.79 apply (zenon_L2610_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.79 apply (zenon_L1458_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 exact (zenon_H122 zenon_Hb1). % 30.68/30.79 (* end of lemma zenon_L2611_ *) % 30.68/30.79 assert (zenon_L2612_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H101 zenon_H3c zenon_H13b zenon_H16f zenon_Had zenon_H222 zenon_H30d zenon_H2d zenon_H20e zenon_H11b zenon_Hf6 zenon_H1e6 zenon_H17d zenon_H135 zenon_H122 zenon_H267 zenon_H1d8 zenon_H8a zenon_H159 zenon_Hde zenon_H2b4 zenon_H1dc zenon_H1d2 zenon_H231 zenon_H100 zenon_H5c zenon_Hdf zenon_Hbd zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H60 zenon_H1c7 zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_Hc3 zenon_H1ca zenon_H1af zenon_H156. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L363_); trivial. % 30.68/30.79 apply (zenon_L2607_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.79 exact (zenon_H13b zenon_Hfd). % 30.68/30.79 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.79 apply (zenon_L2606_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L2611_); trivial. % 30.68/30.79 apply (zenon_L2607_); trivial. % 30.68/30.79 (* end of lemma zenon_L2612_ *) % 30.68/30.79 assert (zenon_L2613_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H1d5 zenon_H6b zenon_Hd6 zenon_Hf5 zenon_H6f zenon_H25 zenon_H1af zenon_H16c zenon_H156. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.79 apply (zenon_L193_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.79 apply (zenon_L144_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.79 apply (zenon_L1138_); trivial. % 30.68/30.79 apply (zenon_L290_); trivial. % 30.68/30.79 (* end of lemma zenon_L2613_ *) % 30.68/30.79 assert (zenon_L2614_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H135 zenon_Hdf zenon_Hde zenon_H60 zenon_H1c7 zenon_He1 zenon_H8a zenon_H1d8 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H6f zenon_H25 zenon_H1af zenon_H16c zenon_H156. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.68/30.79 apply (zenon_L49_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.68/30.79 apply (zenon_L365_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.68/30.79 exact (zenon_Hd0 zenon_Hcc). % 30.68/30.79 apply (zenon_L2613_); trivial. % 30.68/30.79 (* end of lemma zenon_L2614_ *) % 30.68/30.79 assert (zenon_L2615_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H208 zenon_H1ca zenon_Hc3 zenon_H19e zenon_H1bd zenon_Hbd zenon_H5c zenon_H100 zenon_H1d2 zenon_H1dc zenon_H2b4 zenon_H159 zenon_H267 zenon_H1e6 zenon_H20e zenon_H2d zenon_H30d zenon_H222 zenon_Had zenon_H16f zenon_H13b zenon_H101 zenon_H3c zenon_H1f zenon_H5e zenon_H156 zenon_H16c zenon_H1af zenon_H6f zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H1d8 zenon_He1 zenon_H1c7 zenon_H60 zenon_Hde zenon_Hdf zenon_H135 zenon_H11b zenon_H122 zenon_Hf6 zenon_H231 zenon_H17d zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.68/30.79 apply (zenon_L2612_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.68/30.79 apply (zenon_L218_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.68/30.79 apply (zenon_L2614_); trivial. % 30.68/30.79 apply (zenon_L2591_); trivial. % 30.68/30.79 (* end of lemma zenon_L2615_ *) % 30.68/30.79 assert (zenon_L2616_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((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)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H200 zenon_H17d zenon_H231 zenon_Hf6 zenon_H11b zenon_H135 zenon_Hde zenon_H60 zenon_H1c7 zenon_He1 zenon_Hd0 zenon_H1d5 zenon_H6b zenon_Hd6 zenon_H6f zenon_H16c zenon_H156 zenon_H5e zenon_H1f zenon_H3c zenon_H101 zenon_H13b zenon_H16f zenon_Had zenon_H222 zenon_H30d zenon_H20e zenon_H1e6 zenon_H267 zenon_H159 zenon_H2b4 zenon_H1d2 zenon_H5c zenon_H1bd zenon_H1ca zenon_H208 zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.79 apply (zenon_L2615_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.79 apply (zenon_L347_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.79 apply (zenon_L2594_); trivial. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 (* end of lemma zenon_L2616_ *) % 30.68/30.79 assert (zenon_L2617_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H225 zenon_H74 zenon_Hbd zenon_H2d zenon_H100 zenon_H1dc zenon_H19e zenon_H208 zenon_H1ca zenon_H1bd zenon_H5c zenon_H1d2 zenon_H267 zenon_H1e6 zenon_H20e zenon_H30d zenon_H222 zenon_Had zenon_H16f zenon_H13b zenon_H101 zenon_H3c zenon_H1f zenon_H5e zenon_H156 zenon_H6f zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_He1 zenon_H1c7 zenon_H60 zenon_H135 zenon_H11b zenon_Hf6 zenon_H231 zenon_H17d zenon_H200 zenon_H10d zenon_Hf9 zenon_H2b4 zenon_Hde zenon_Hc3 zenon_H159 zenon_H8a zenon_H1af zenon_H1d8 zenon_H122. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.79 exact (zenon_H74 zenon_H73). % 30.68/30.79 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L2604_); trivial. % 30.68/30.79 apply (zenon_L2616_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L2597_); trivial. % 30.68/30.79 apply (zenon_L2616_); trivial. % 30.68/30.79 apply (zenon_L2603_); trivial. % 30.68/30.79 (* end of lemma zenon_L2617_ *) % 30.68/30.79 assert (zenon_L2618_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H200 zenon_H156 zenon_H16c zenon_H1ca zenon_H1bd zenon_H6c zenon_H5e zenon_H1c7 zenon_H60 zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H5c zenon_H231 zenon_H1d2 zenon_H2b4 zenon_Hde zenon_H159 zenon_H267 zenon_H135 zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.79 apply (zenon_L2607_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.79 apply (zenon_L347_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.79 apply (zenon_L2594_); trivial. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 (* end of lemma zenon_L2618_ *) % 30.68/30.79 assert (zenon_L2619_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H16f zenon_Had zenon_H3c zenon_He9 zenon_H20e zenon_H200 zenon_H156 zenon_H1ca zenon_H1bd zenon_H6c zenon_H5e zenon_H1c7 zenon_H60 zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H5c zenon_H231 zenon_H1d2 zenon_H2b4 zenon_Hde zenon_H159 zenon_H267 zenon_H135 zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L2604_); trivial. % 30.68/30.79 apply (zenon_L2618_); trivial. % 30.68/30.79 (* end of lemma zenon_L2619_ *) % 30.68/30.79 assert (zenon_L2620_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H16f zenon_Had zenon_Hf9 zenon_He1 zenon_H20e zenon_H222 zenon_Hda zenon_H10d zenon_H200 zenon_H156 zenon_H1ca zenon_H1bd zenon_H6c zenon_H5e zenon_H1c7 zenon_H60 zenon_Hd6 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H5c zenon_H231 zenon_H1d2 zenon_H2b4 zenon_Hde zenon_H159 zenon_H267 zenon_H135 zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L2597_); trivial. % 30.68/30.79 apply (zenon_L2618_); trivial. % 30.68/30.79 (* end of lemma zenon_L2620_ *) % 30.68/30.79 assert (zenon_L2621_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H1ca zenon_Hc3 zenon_H19e zenon_H98 zenon_H5e zenon_H222 zenon_H1c7 zenon_H1b9 zenon_H60 zenon_H1af zenon_Hf5 zenon_Hd6. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1cb ]. % 30.68/30.79 apply (zenon_L347_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H1cc ]. % 30.68/30.79 apply (zenon_L514_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H55 | zenon_intro zenon_H3d ]. % 30.68/30.79 apply (zenon_L216_); trivial. % 30.68/30.79 apply (zenon_L144_); trivial. % 30.68/30.79 (* end of lemma zenon_L2621_ *) % 30.68/30.79 assert (zenon_L2622_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H23b zenon_H8a zenon_H6f zenon_Hd6 zenon_Hf5 zenon_H1af zenon_H60 zenon_H1c7 zenon_H222 zenon_H5e zenon_H19e zenon_Hc3 zenon_H1ca zenon_H19a zenon_Hee zenon_H9c zenon_H1b9. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.79 apply (zenon_L39_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.79 apply (zenon_L2621_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.79 apply (zenon_L337_); trivial. % 30.68/30.79 apply (zenon_L198_); trivial. % 30.68/30.79 (* end of lemma zenon_L2622_ *) % 30.68/30.79 assert (zenon_L2623_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H135 zenon_Hde zenon_He1 zenon_H2d zenon_Had zenon_H16f zenon_Hd0 zenon_H1d5 zenon_H6b zenon_H122 zenon_H23b zenon_H8a zenon_H6f zenon_Hd6 zenon_H60 zenon_H1c7 zenon_H222 zenon_H5e zenon_H19e zenon_Hc3 zenon_H1ca zenon_H19a zenon_Hee zenon_H100 zenon_H1d8 zenon_H5c zenon_Hdf zenon_Hbd zenon_H1af zenon_H16c zenon_H156. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.68/30.79 apply (zenon_L49_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.68/30.79 apply (zenon_L366_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.68/30.79 exact (zenon_Hd0 zenon_Hcc). % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.79 apply (zenon_L193_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.79 apply (zenon_L144_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.79 apply (zenon_L194_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.79 apply (zenon_L1497_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.79 apply (zenon_L2622_); trivial. % 30.68/30.79 exact (zenon_H122 zenon_Hb1). % 30.68/30.79 apply (zenon_L290_); trivial. % 30.68/30.79 (* end of lemma zenon_L2623_ *) % 30.68/30.79 assert (zenon_L2624_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H200 zenon_H156 zenon_H16c zenon_H5c zenon_Hee zenon_H19a zenon_H1ca zenon_H5e zenon_H222 zenon_H1c7 zenon_H60 zenon_Hd6 zenon_H6f zenon_H23b zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H16f zenon_Had zenon_He1 zenon_Hde zenon_H135 zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.79 apply (zenon_L2623_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.79 apply (zenon_L347_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.79 apply (zenon_L2594_); trivial. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 (* end of lemma zenon_L2624_ *) % 30.68/30.79 assert (zenon_L2625_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.79 do 0 intro. intros zenon_H200 zenon_H156 zenon_H5c zenon_Hee zenon_H19a zenon_H1ca zenon_H5e zenon_H222 zenon_H1c7 zenon_H60 zenon_Hd6 zenon_H6f zenon_H23b zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H16f zenon_Had zenon_He1 zenon_Hde zenon_H135 zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L235_); trivial. % 30.68/30.79 apply (zenon_L2624_); trivial. % 30.68/30.79 (* end of lemma zenon_L2625_ *) % 30.68/30.79 assert (zenon_L2626_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H2b4 zenon_H17d zenon_H3d zenon_H1c7 zenon_H1e6 zenon_H231 zenon_Hf6 zenon_H11b zenon_H20e zenon_H15e zenon_H156 zenon_H2d zenon_H30d zenon_Hc3 zenon_H159 zenon_H8a zenon_H1af zenon_H1d8 zenon_H122. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.79 apply (zenon_L2609_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.79 apply (zenon_L1458_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 exact (zenon_H122 zenon_Hb1). % 30.68/30.79 (* end of lemma zenon_L2626_ *) % 30.68/30.79 assert (zenon_L2627_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H267 zenon_Hde zenon_H185 zenon_H156 zenon_H1b9 zenon_Hcc zenon_H60 zenon_H108 zenon_H231. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.68/30.79 apply (zenon_L817_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.68/30.79 apply (zenon_L179_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.68/30.79 apply (zenon_L550_); trivial. % 30.68/30.79 exact (zenon_H231 zenon_Hf4). % 30.68/30.79 (* end of lemma zenon_L2627_ *) % 30.68/30.79 assert (zenon_L2628_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H2b4 zenon_H231 zenon_H108 zenon_H60 zenon_Hcc zenon_H1b9 zenon_H156 zenon_Hde zenon_H267 zenon_Hc3 zenon_H159 zenon_H8a zenon_H1af zenon_H1d8 zenon_H122. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.79 apply (zenon_L2627_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.79 apply (zenon_L1458_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.79 apply (zenon_L186_); trivial. % 30.68/30.79 exact (zenon_H122 zenon_Hb1). % 30.68/30.79 (* end of lemma zenon_L2628_ *) % 30.68/30.79 assert (zenon_L2629_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H1d5 zenon_H30d zenon_H2d zenon_H15e zenon_H20e zenon_H11b zenon_Hf6 zenon_H1e6 zenon_H17d zenon_H122 zenon_H1d8 zenon_H8a zenon_H159 zenon_H267 zenon_Hde zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H231 zenon_H2b4 zenon_H1ca zenon_Hc3 zenon_H19e zenon_H1bd zenon_H6c zenon_H5e zenon_H3c zenon_He9 zenon_H1af zenon_H1c7. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.79 apply (zenon_L174_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.79 apply (zenon_L2626_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.79 apply (zenon_L2628_); trivial. % 30.68/30.79 apply (zenon_L1885_); trivial. % 30.68/30.79 (* end of lemma zenon_L2629_ *) % 30.68/30.79 assert (zenon_L2630_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H2b1 zenon_H159 zenon_Hc3 zenon_H20 zenon_H2b4 zenon_H6f zenon_H16c zenon_H17d zenon_H231 zenon_H122 zenon_H11b zenon_H1e6 zenon_H8a zenon_H1d8 zenon_Hf6 zenon_H27 zenon_H117 zenon_H1af zenon_H3d zenon_H1c7. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.68/30.79 apply (zenon_L2589_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.68/30.79 apply (zenon_L758_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.68/30.79 apply (zenon_L2591_); trivial. % 30.68/30.79 apply (zenon_L188_); trivial. % 30.68/30.79 (* end of lemma zenon_L2630_ *) % 30.68/30.79 assert (zenon_L2631_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.79 do 0 intro. intros zenon_H225 zenon_H74 zenon_H1c7 zenon_H3c zenon_H5e zenon_H6c zenon_H1bd zenon_H19e zenon_H1ca zenon_H231 zenon_H108 zenon_H156 zenon_H267 zenon_H1fd zenon_H6f zenon_H20 zenon_H2b1 zenon_H30d zenon_H2d zenon_H20e zenon_H11b zenon_Hf6 zenon_H1e6 zenon_H17d zenon_Hb5 zenon_H1d5 zenon_Had zenon_H16f zenon_H27 zenon_Hcc zenon_H60 zenon_H2b4 zenon_Hde zenon_Hc3 zenon_H159 zenon_H8a zenon_H1af zenon_H1d8 zenon_H122. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.79 exact (zenon_H74 zenon_H73). % 30.68/30.79 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.79 apply (zenon_L34_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.79 apply (zenon_L364_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.79 apply (zenon_L2629_); trivial. % 30.68/30.79 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.80 apply (zenon_L174_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.80 apply (zenon_L2630_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.80 apply (zenon_L2626_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.80 apply (zenon_L2628_); trivial. % 30.68/30.80 apply (zenon_L461_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.80 apply (zenon_L2628_); trivial. % 30.68/30.80 apply (zenon_L1885_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.80 apply (zenon_L554_); trivial. % 30.68/30.80 apply (zenon_L2603_); trivial. % 30.68/30.80 (* end of lemma zenon_L2631_ *) % 30.68/30.80 assert (zenon_L2632_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H90 zenon_H231 zenon_H17d zenon_H8a. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 apply (zenon_L139_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 exact (zenon_H231 zenon_Hf4). % 30.68/30.80 apply (zenon_L110_); trivial. % 30.68/30.80 (* end of lemma zenon_L2632_ *) % 30.68/30.80 assert (zenon_L2633_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H1e6 zenon_H1d8 zenon_H8a zenon_H17d zenon_H231 zenon_Hf6 zenon_H122 zenon_H11b zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.68/30.80 apply (zenon_L186_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.68/30.80 apply (zenon_L2591_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.68/30.80 apply (zenon_L550_); trivial. % 30.68/30.80 apply (zenon_L245_); trivial. % 30.68/30.80 (* end of lemma zenon_L2633_ *) % 30.68/30.80 assert (zenon_L2634_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H25b zenon_H2d zenon_H10e zenon_H2b7 zenon_Hcc zenon_H60 zenon_H1dc zenon_H19a zenon_Hee zenon_H10d zenon_H2b4 zenon_H122 zenon_H8a zenon_H1af zenon_H1d8 zenon_Hc3 zenon_H159 zenon_Hde zenon_H156 zenon_H108 zenon_H267 zenon_Hb5 zenon_H1fd. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.80 apply (zenon_L87_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.80 apply (zenon_L2003_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.80 apply (zenon_L2628_); trivial. % 30.68/30.80 apply (zenon_L461_); trivial. % 30.68/30.80 apply (zenon_L461_); trivial. % 30.68/30.80 (* end of lemma zenon_L2634_ *) % 30.68/30.80 assert (zenon_L2635_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H2b4 zenon_H2d zenon_H16b zenon_Hc3 zenon_H159 zenon_H8a zenon_H1af zenon_H1d8 zenon_H122. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.68/30.80 apply (zenon_L848_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.68/30.80 apply (zenon_L1458_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.68/30.80 apply (zenon_L186_); trivial. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 (* end of lemma zenon_L2635_ *) % 30.68/30.80 assert (zenon_L2636_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H30d zenon_H122 zenon_H1d8 zenon_H159 zenon_Hc3 zenon_H2d zenon_H2b4 zenon_H6f zenon_H182 zenon_H1c7 zenon_H3d zenon_H1af zenon_H17d zenon_H8a. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H30d); [ zenon_intro zenon_H16b | zenon_intro zenon_H30e ]. % 30.68/30.80 apply (zenon_L2635_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H16c | zenon_intro zenon_H30f ]. % 30.68/30.80 apply (zenon_L758_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H1c5 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L167_); trivial. % 30.68/30.80 apply (zenon_L110_); trivial. % 30.68/30.80 (* end of lemma zenon_L2636_ *) % 30.68/30.80 assert (zenon_L2637_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H2b1 zenon_H20 zenon_H185 zenon_H6f zenon_H2b4 zenon_H2d zenon_Hc3 zenon_H159 zenon_H30d zenon_H17d zenon_H231 zenon_H122 zenon_H11b zenon_H1e6 zenon_H8a zenon_H1d8 zenon_Hf6 zenon_H27 zenon_H117 zenon_H1af zenon_H3d zenon_H1c7. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.68/30.80 apply (zenon_L117_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.68/30.80 apply (zenon_L2636_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.68/30.80 apply (zenon_L2591_); trivial. % 30.68/30.80 apply (zenon_L188_); trivial. % 30.68/30.80 (* end of lemma zenon_L2637_ *) % 30.68/30.80 assert (zenon_L2638_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H1fd zenon_H27 zenon_H6f zenon_H185 zenon_H20 zenon_H2b1 zenon_H30d zenon_H2d zenon_H20e zenon_H11b zenon_Hf6 zenon_H1e6 zenon_H1c7 zenon_H3d zenon_H17d zenon_H122 zenon_H1d8 zenon_H1af zenon_H159 zenon_Hc3 zenon_H267 zenon_Hde zenon_H156 zenon_Hcc zenon_H60 zenon_H108 zenon_H231 zenon_H2b4 zenon_H8a zenon_Hb5. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.80 apply (zenon_L2637_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.80 apply (zenon_L2626_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.80 apply (zenon_L2628_); trivial. % 30.68/30.80 apply (zenon_L461_); trivial. % 30.68/30.80 (* end of lemma zenon_L2638_ *) % 30.68/30.80 assert (zenon_L2639_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H1d5 zenon_Hb5 zenon_H17d zenon_H1c7 zenon_H1e6 zenon_Hf6 zenon_H11b zenon_H20e zenon_H2d zenon_H30d zenon_H2b1 zenon_H20 zenon_H185 zenon_H6f zenon_H27 zenon_H1fd zenon_H122 zenon_H1d8 zenon_H8a zenon_H159 zenon_Hc3 zenon_H267 zenon_Hde zenon_Hcc zenon_H60 zenon_H108 zenon_H231 zenon_H2b4 zenon_H1af zenon_H16c zenon_H156. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.80 apply (zenon_L174_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.80 apply (zenon_L2638_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.80 apply (zenon_L2628_); trivial. % 30.68/30.80 apply (zenon_L290_); trivial. % 30.68/30.80 (* end of lemma zenon_L2639_ *) % 30.68/30.80 assert (zenon_L2640_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H16f zenon_Had zenon_H19a zenon_H1d5 zenon_Hb5 zenon_H17d zenon_H1c7 zenon_H1e6 zenon_Hf6 zenon_H11b zenon_H20e zenon_H2d zenon_H30d zenon_H2b1 zenon_H20 zenon_H185 zenon_H6f zenon_H27 zenon_H1fd zenon_H122 zenon_H1d8 zenon_H8a zenon_H159 zenon_Hc3 zenon_H267 zenon_Hde zenon_Hcc zenon_H60 zenon_H108 zenon_H231 zenon_H2b4 zenon_H1af zenon_H156. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.80 apply (zenon_L34_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.80 apply (zenon_L364_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.80 apply (zenon_L235_); trivial. % 30.68/30.80 apply (zenon_L2639_); trivial. % 30.68/30.80 (* end of lemma zenon_L2640_ *) % 30.68/30.80 assert (zenon_L2641_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (op (e2) (e1))) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H25c zenon_H301 zenon_H10d zenon_H2b7 zenon_H25b zenon_He7 zenon_H97 zenon_H42 zenon_H218 zenon_H174 zenon_H20 zenon_H313 zenon_H225 zenon_H1bd zenon_H3c zenon_H267 zenon_H108 zenon_H30d zenon_H11b zenon_H17d zenon_Hf6 zenon_H20e zenon_H1e6 zenon_H159 zenon_H2b4 zenon_H2b1 zenon_H27 zenon_Hb5 zenon_H1fd zenon_H74 zenon_H92 zenon_Had zenon_H8a zenon_H2d zenon_Hc3 zenon_H6f zenon_H19a zenon_H200 zenon_H1dc zenon_Hde zenon_H16f zenon_H1d8 zenon_He1 zenon_H1c7 zenon_H60 zenon_H156 zenon_H1af zenon_H1d5 zenon_H5c zenon_H100 zenon_H23b zenon_Hee zenon_H19e zenon_H222 zenon_H5e zenon_H1ca zenon_H122 zenon_Hbd zenon_Hd6 zenon_H6b zenon_H135. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.68/30.80 apply (zenon_L2625_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.80 apply (zenon_L912_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.80 exact (zenon_H313 zenon_H68). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.80 apply (zenon_L2631_); trivial. % 30.68/30.80 apply (zenon_L2632_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.80 apply (zenon_L199_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.80 apply (zenon_L4_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.80 apply (zenon_L34_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.80 apply (zenon_L364_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.80 apply (zenon_L235_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.80 apply (zenon_L4_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.80 apply (zenon_L364_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.80 apply (zenon_L2630_); trivial. % 30.68/30.80 apply (zenon_L862_); trivial. % 30.68/30.80 apply (zenon_L2633_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.68/30.80 apply (zenon_L2634_); trivial. % 30.68/30.80 apply (zenon_L2640_); trivial. % 30.68/30.80 apply (zenon_L461_); trivial. % 30.68/30.80 (* end of lemma zenon_L2641_ *) % 30.68/30.80 assert (zenon_L2642_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.80 do 0 intro. intros zenon_Hbd zenon_Hdf zenon_H5c zenon_H1d8 zenon_Hc3 zenon_H100 zenon_H10e zenon_H10d zenon_H122. % 30.68/30.80 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.80 apply (zenon_L194_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.80 apply (zenon_L1497_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.80 apply (zenon_L63_); trivial. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 (* end of lemma zenon_L2642_ *) % 30.68/30.80 assert (zenon_L2643_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (op (e2) (e0))) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H200 zenon_H10d zenon_H10e zenon_H5c zenon_H19e zenon_H122 zenon_H1dc zenon_H100 zenon_Hc3 zenon_H2d zenon_Hbd zenon_H1d8 zenon_H1af zenon_H8a. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.80 apply (zenon_L2642_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.80 apply (zenon_L347_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.80 apply (zenon_L2594_); trivial. % 30.68/30.80 apply (zenon_L186_); trivial. % 30.68/30.80 (* end of lemma zenon_L2643_ *) % 30.68/30.80 assert (zenon_L2644_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H3f zenon_H2c zenon_H10d zenon_H117 zenon_Hb3 zenon_Hb9. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 apply (zenon_L720_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L68_); trivial. % 30.68/30.80 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.80 (* end of lemma zenon_L2644_ *) % 30.68/30.80 assert (zenon_L2645_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H3f zenon_H2c zenon_Hee zenon_H15e zenon_Hb3 zenon_Hb9. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 apply (zenon_L720_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L995_); trivial. % 30.68/30.80 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.80 (* end of lemma zenon_L2645_ *) % 30.68/30.80 assert (zenon_L2646_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H3f zenon_H2c zenon_H1dc zenon_H1b9 zenon_Hb3 zenon_Hb9. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 apply (zenon_L720_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L996_); trivial. % 30.68/30.80 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.80 (* end of lemma zenon_L2646_ *) % 30.68/30.80 assert (zenon_L2647_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H1fd zenon_H10d zenon_Hee zenon_Hb9 zenon_Hb3 zenon_H1dc zenon_H2c zenon_H3f zenon_H122 zenon_H11b zenon_H8a zenon_Hb5. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.80 apply (zenon_L2644_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.80 apply (zenon_L2645_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.80 apply (zenon_L2646_); trivial. % 30.68/30.80 apply (zenon_L461_); trivial. % 30.68/30.80 (* end of lemma zenon_L2647_ *) % 30.68/30.80 assert (zenon_L2648_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H100 zenon_H37 zenon_H10d zenon_H117 zenon_Hb3 zenon_Hb9. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 apply (zenon_L721_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L68_); trivial. % 30.68/30.80 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.80 (* end of lemma zenon_L2648_ *) % 30.68/30.80 assert (zenon_L2649_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H100 zenon_H37 zenon_Hee zenon_H15e zenon_Hb3 zenon_Hb9. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 apply (zenon_L721_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L995_); trivial. % 30.68/30.80 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.80 (* end of lemma zenon_L2649_ *) % 30.68/30.80 assert (zenon_L2650_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H100 zenon_H37 zenon_H1dc zenon_H1b9 zenon_Hb3 zenon_Hb9. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 apply (zenon_L721_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L996_); trivial. % 30.68/30.80 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.80 (* end of lemma zenon_L2650_ *) % 30.68/30.80 assert (zenon_L2651_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H1fd zenon_H10d zenon_Hee zenon_Hb9 zenon_Hb3 zenon_H1dc zenon_H37 zenon_H100 zenon_H122 zenon_H11b zenon_H8a zenon_Hb5. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.80 apply (zenon_L2648_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.80 apply (zenon_L2649_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.80 apply (zenon_L2650_); trivial. % 30.68/30.80 apply (zenon_L461_); trivial. % 30.68/30.80 (* end of lemma zenon_L2651_ *) % 30.68/30.80 assert (zenon_L2652_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H222 zenon_H3d zenon_H10d zenon_H117 zenon_Hb3 zenon_Hb9. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 apply (zenon_L722_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L68_); trivial. % 30.68/30.80 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.80 (* end of lemma zenon_L2652_ *) % 30.68/30.80 assert (zenon_L2653_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H222 zenon_H3d zenon_Hee zenon_H15e zenon_Hb3 zenon_Hb9. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 apply (zenon_L722_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L995_); trivial. % 30.68/30.80 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.80 (* end of lemma zenon_L2653_ *) % 30.68/30.80 assert (zenon_L2654_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H222 zenon_H3d zenon_H1dc zenon_H1b9 zenon_Hb3 zenon_Hb9. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 apply (zenon_L722_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L996_); trivial. % 30.68/30.80 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.80 (* end of lemma zenon_L2654_ *) % 30.68/30.80 assert (zenon_L2655_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H1fd zenon_H10d zenon_Hee zenon_Hb9 zenon_Hb3 zenon_H1dc zenon_H3d zenon_H222 zenon_H122 zenon_H11b zenon_H8a zenon_Hb5. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.80 apply (zenon_L2652_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.80 apply (zenon_L2653_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.80 apply (zenon_L2654_); trivial. % 30.68/30.80 apply (zenon_L461_); trivial. % 30.68/30.80 (* end of lemma zenon_L2655_ *) % 30.68/30.80 assert (zenon_L2656_ : (((op (e3) (op (e3) (e0))) = (e0))/\(((op (e3) (op (e3) (e1))) = (e1))/\(((op (e3) (op (e3) (e2))) = (e2))/\(((op (e3) (op (e3) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0)))/\(((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1)))/\(((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3)))))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H270 zenon_H17d zenon_H1fd zenon_H8a zenon_Hb5 zenon_H1dc zenon_Hee zenon_H122 zenon_H3f zenon_H10d zenon_H11b zenon_H100 zenon_H222 zenon_H97 zenon_H42. % 30.68/30.80 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.68/30.80 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.68/30.80 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.68/30.80 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.68/30.80 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.68/30.80 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.68/30.80 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.80 apply (zenon_L2647_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.80 apply (zenon_L2651_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.80 apply (zenon_L2655_); trivial. % 30.68/30.80 apply (zenon_L862_); trivial. % 30.68/30.80 apply (zenon_L110_); trivial. % 30.68/30.80 (* end of lemma zenon_L2656_ *) % 30.68/30.80 assert (zenon_L2657_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H1ab zenon_H15e zenon_H4c zenon_H14e zenon_H17d zenon_H8a. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 exact (zenon_H1ab zenon_H112). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L752_); trivial. % 30.68/30.80 apply (zenon_L110_); trivial. % 30.68/30.80 (* end of lemma zenon_L2657_ *) % 30.68/30.80 assert (zenon_L2658_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H2f8 zenon_H20e zenon_H9d zenon_H100 zenon_Hb5 zenon_Hee zenon_H10d zenon_H26 zenon_H1dc zenon_H142 zenon_H2b7 zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.80 apply (zenon_L350_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.80 apply (zenon_L1184_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.80 apply (zenon_L1208_); trivial. % 30.68/30.80 apply (zenon_L2657_); trivial. % 30.68/30.80 (* end of lemma zenon_L2658_ *) % 30.68/30.80 assert (zenon_L2659_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H2f8 zenon_H20e zenon_H142 zenon_H1a0 zenon_Hee zenon_H1b1 zenon_Hdc zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.80 apply (zenon_L350_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.80 apply (zenon_L337_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.80 apply (zenon_L2436_); trivial. % 30.68/30.80 apply (zenon_L2657_); trivial. % 30.68/30.80 (* end of lemma zenon_L2659_ *) % 30.68/30.80 assert (zenon_L2660_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H1a2 zenon_H2b7 zenon_H1dc zenon_H10d zenon_Hb5 zenon_H9d zenon_H100 zenon_H56 zenon_H2f8 zenon_H20e zenon_H142 zenon_Hee zenon_H1b1 zenon_Hdc zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.80 apply (zenon_L2658_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.80 apply (zenon_L1184_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.80 exact (zenon_H56 zenon_H25). % 30.68/30.80 apply (zenon_L2659_); trivial. % 30.68/30.80 (* end of lemma zenon_L2660_ *) % 30.68/30.80 assert (zenon_L2661_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H256 zenon_H8a zenon_Had zenon_H35 zenon_H2c zenon_H1a5 zenon_H117 zenon_H156 zenon_H4e zenon_H1c5. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H14f | zenon_intro zenon_H257 ]. % 30.68/30.80 apply (zenon_L913_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H182 | zenon_intro zenon_H258 ]. % 30.68/30.80 apply (zenon_L730_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H155 | zenon_intro zenon_H16c ]. % 30.68/30.80 apply (zenon_L828_); trivial. % 30.68/30.80 apply (zenon_L779_); trivial. % 30.68/30.80 (* end of lemma zenon_L2661_ *) % 30.68/30.80 assert (zenon_L2662_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H1fd zenon_H1c5 zenon_H4e zenon_H156 zenon_H1a5 zenon_H2c zenon_H35 zenon_Had zenon_H256 zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H2d zenon_H142 zenon_H8a zenon_Hb5. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.80 apply (zenon_L2661_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.80 apply (zenon_L2657_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.80 apply (zenon_L175_); trivial. % 30.68/30.80 apply (zenon_L461_); trivial. % 30.68/30.80 (* end of lemma zenon_L2662_ *) % 30.68/30.80 assert (zenon_L2663_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H102 zenon_H6c zenon_H18c zenon_H18f zenon_He9 zenon_H4a zenon_H19e zenon_H185 zenon_H20 zenon_H2b1 zenon_H1fd zenon_H4e zenon_H156 zenon_H1a5 zenon_H2c zenon_H35 zenon_Had zenon_H256 zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H2d zenon_H142 zenon_H8a zenon_Hb5. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.80 apply (zenon_L174_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.80 apply (zenon_L1773_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.80 apply (zenon_L175_); trivial. % 30.68/30.80 apply (zenon_L2662_); trivial. % 30.68/30.80 (* end of lemma zenon_L2663_ *) % 30.68/30.80 assert (zenon_L2664_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H11b zenon_H122 zenon_H1ab zenon_H37 zenon_H95 zenon_H17d zenon_H8a. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.80 exact (zenon_H122 zenon_Hb1). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.80 exact (zenon_H1ab zenon_H112). % 30.68/30.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.80 apply (zenon_L513_); trivial. % 30.68/30.80 apply (zenon_L110_); trivial. % 30.68/30.80 (* end of lemma zenon_L2664_ *) % 30.68/30.80 assert (zenon_L2665_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.68/30.80 do 0 intro. intros zenon_H42 zenon_Hb5 zenon_H142 zenon_H2d zenon_H4c zenon_H14e zenon_H256 zenon_Had zenon_H1a5 zenon_H1fd zenon_H1d8 zenon_H1d5 zenon_H17d zenon_H95 zenon_H122 zenon_H11b zenon_H1ab zenon_H102 zenon_H6c zenon_H18c zenon_H18f zenon_H35 zenon_He9 zenon_H156 zenon_H4a zenon_H19e zenon_H4e zenon_H185 zenon_H20 zenon_H2b1 zenon_H8a zenon_H97. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.80 apply (zenon_L2663_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.80 apply (zenon_L2664_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.80 apply (zenon_L1773_); trivial. % 30.68/30.80 apply (zenon_L862_); trivial. % 30.68/30.80 (* end of lemma zenon_L2665_ *) % 30.68/30.80 assert (zenon_L2666_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H101 zenon_H97 zenon_H2b1 zenon_H20 zenon_H185 zenon_H4e zenon_H4a zenon_H156 zenon_H35 zenon_H18f zenon_H18c zenon_H6c zenon_H102 zenon_H95 zenon_H1d5 zenon_H1d8 zenon_H1fd zenon_H1a5 zenon_Had zenon_H256 zenon_H2d zenon_H42 zenon_Hdc zenon_Hd1 zenon_H19a zenon_H19e zenon_H2f8 zenon_H20e zenon_H100 zenon_Hb5 zenon_Hee zenon_H10d zenon_H26 zenon_H1dc zenon_H142 zenon_H2b7 zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.80 apply (zenon_L2665_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.80 apply (zenon_L154_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.80 apply (zenon_L824_); trivial. % 30.68/30.80 apply (zenon_L2658_); trivial. % 30.68/30.80 (* end of lemma zenon_L2666_ *) % 30.68/30.80 assert (zenon_L2667_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e2)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H1fd zenon_H1a5 zenon_H8a zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H2d zenon_H142 zenon_Hee zenon_H4e zenon_H155. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.80 apply (zenon_L828_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.80 apply (zenon_L2657_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.80 apply (zenon_L175_); trivial. % 30.68/30.80 apply (zenon_L1468_); trivial. % 30.68/30.80 (* end of lemma zenon_L2667_ *) % 30.68/30.80 assert (zenon_L2668_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.80 do 0 intro. intros zenon_H173 zenon_H100 zenon_H20e zenon_H2f8 zenon_H19e zenon_H19a zenon_Hd1 zenon_H42 zenon_H256 zenon_Had zenon_H1d8 zenon_H1d5 zenon_H95 zenon_H102 zenon_H6c zenon_H18c zenon_H18f zenon_H35 zenon_H156 zenon_H185 zenon_H20 zenon_H2b1 zenon_H97 zenon_H101 zenon_H4a zenon_Hb5 zenon_H10d zenon_H26 zenon_H1dc zenon_H2b7 zenon_H1fd zenon_H1a5 zenon_H8a zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H2d zenon_H142 zenon_Hee zenon_H4e. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.80 apply (zenon_L2666_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.80 apply (zenon_L748_); trivial. % 30.68/30.80 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.80 apply (zenon_L1208_); trivial. % 30.68/30.80 apply (zenon_L2667_); trivial. % 30.68/30.80 (* end of lemma zenon_L2668_ *) % 30.68/30.80 assert (zenon_L2669_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 30.68/30.81 do 0 intro. intros zenon_H310 zenon_H6b zenon_H4e zenon_Hee zenon_H142 zenon_H2d zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H1a5 zenon_H1fd zenon_H2b7 zenon_H1dc zenon_H26 zenon_H10d zenon_Hb5 zenon_H4a zenon_H101 zenon_H97 zenon_H2b1 zenon_H20 zenon_H185 zenon_H156 zenon_H35 zenon_H18f zenon_H18c zenon_H102 zenon_H95 zenon_H1d5 zenon_Had zenon_H256 zenon_H42 zenon_Hd1 zenon_H19a zenon_H19e zenon_H2f8 zenon_H20e zenon_H100 zenon_H173 zenon_H2ed zenon_H8a zenon_H1d8. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_Hdf | zenon_intro zenon_H311 ]. % 30.68/30.81 apply (zenon_L303_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H6c | zenon_intro zenon_H312 ]. % 30.68/30.81 apply (zenon_L2668_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H76 ]. % 30.68/30.81 exact (zenon_H2ed zenon_Hc9). % 30.68/30.81 apply (zenon_L174_); trivial. % 30.68/30.81 (* end of lemma zenon_L2669_ *) % 30.68/30.81 assert (zenon_L2670_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.81 do 0 intro. intros zenon_Hbd zenon_H4c zenon_H14e zenon_Hdc zenon_H1b1 zenon_H310 zenon_H6b zenon_H4e zenon_Hee zenon_H2d zenon_H11b zenon_H1ab zenon_H17d zenon_H1a5 zenon_H1fd zenon_H2b7 zenon_H26 zenon_H10d zenon_Hb5 zenon_H4a zenon_H101 zenon_H97 zenon_H2b1 zenon_H20 zenon_H185 zenon_H156 zenon_H35 zenon_H18f zenon_H18c zenon_H102 zenon_H1d5 zenon_Had zenon_H256 zenon_H42 zenon_Hd1 zenon_H19e zenon_H2f8 zenon_H20e zenon_H100 zenon_H173 zenon_H2ed zenon_H8a zenon_H1d8 zenon_H1a2 zenon_H56 zenon_He1 zenon_Hf9 zenon_H142 zenon_H1dc zenon_H122. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.81 apply (zenon_L25_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.68/30.81 apply (zenon_L50_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.68/30.81 apply (zenon_L2660_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.81 apply (zenon_L350_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.81 apply (zenon_L2669_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.81 apply (zenon_L1207_); trivial. % 30.68/30.81 apply (zenon_L2657_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.81 apply (zenon_L350_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.81 apply (zenon_L2669_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.81 apply (zenon_L2436_); trivial. % 30.68/30.81 apply (zenon_L752_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.81 apply (zenon_L177_); trivial. % 30.68/30.81 exact (zenon_H122 zenon_Hb1). % 30.68/30.81 (* end of lemma zenon_L2670_ *) % 30.68/30.81 assert (zenon_L2671_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_H2f8 zenon_H20e zenon_H142 zenon_H55 zenon_H19e zenon_Heb zenon_Hee zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.81 apply (zenon_L350_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.81 apply (zenon_L824_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.81 apply (zenon_L1207_); trivial. % 30.68/30.81 apply (zenon_L2657_); trivial. % 30.68/30.81 (* end of lemma zenon_L2671_ *) % 30.68/30.81 assert (zenon_L2672_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 30.68/30.81 do 0 intro. intros zenon_H2f8 zenon_H20e zenon_H142 zenon_H55 zenon_H19e zenon_H1b1 zenon_Hdc zenon_H14e zenon_H4c zenon_Hf4. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.81 apply (zenon_L350_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.81 apply (zenon_L824_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.81 apply (zenon_L2436_); trivial. % 30.68/30.81 apply (zenon_L752_); trivial. % 30.68/30.81 (* end of lemma zenon_L2672_ *) % 30.68/30.81 assert (zenon_L2673_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> False). % 30.68/30.81 do 0 intro. intros zenon_Hf9 zenon_He1 zenon_H222 zenon_H8a zenon_H17d zenon_H1ab zenon_H122 zenon_H11b zenon_Hee zenon_H2f8 zenon_H20e zenon_H142 zenon_H55 zenon_H19e zenon_H1b1 zenon_Hdc zenon_H14e zenon_H4c. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.68/30.81 apply (zenon_L50_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.68/30.81 apply (zenon_L264_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.68/30.81 apply (zenon_L2671_); trivial. % 30.68/30.81 apply (zenon_L2672_); trivial. % 30.68/30.81 (* end of lemma zenon_L2673_ *) % 30.68/30.81 assert (zenon_L2674_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_He4 zenon_H64 zenon_Hde zenon_H4c zenon_H14e zenon_H1b1 zenon_H19e zenon_H55 zenon_H142 zenon_H20e zenon_H2f8 zenon_Hee zenon_H11b zenon_H122 zenon_H1ab zenon_H17d zenon_H222 zenon_Hf9 zenon_H2ed zenon_He1 zenon_H8a. % 30.68/30.81 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.81 apply (zenon_L1209_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.81 apply (zenon_L2673_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.81 exact (zenon_H2ed zenon_Hc9). % 30.68/30.81 apply (zenon_L50_); trivial. % 30.68/30.81 (* end of lemma zenon_L2674_ *) % 30.68/30.81 assert (zenon_L2675_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.81 do 0 intro. intros zenon_Hbd zenon_H8a zenon_H2d zenon_H1e zenon_H3f zenon_H142 zenon_H1dc zenon_H122. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.81 apply (zenon_L25_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.81 apply (zenon_L29_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.81 apply (zenon_L177_); trivial. % 30.68/30.81 exact (zenon_H122 zenon_Hb1). % 30.68/30.81 (* end of lemma zenon_L2675_ *) % 30.68/30.81 assert (zenon_L2676_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.68/30.81 do 0 intro. intros zenon_H1fd zenon_H10e zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H2d zenon_H142 zenon_H8a zenon_Hb5. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.81 apply (zenon_L87_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.81 apply (zenon_L2657_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.81 apply (zenon_L175_); trivial. % 30.68/30.81 apply (zenon_L461_); trivial. % 30.68/30.81 (* end of lemma zenon_L2676_ *) % 30.68/30.81 assert (zenon_L2677_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 30.68/30.81 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_He1 zenon_H55 zenon_H1fd zenon_H4e zenon_H156 zenon_H1a5 zenon_H2c zenon_H35 zenon_Had zenon_H256 zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H2d zenon_H142 zenon_H8a zenon_Hb5. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.81 apply (zenon_L174_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.81 apply (zenon_L126_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.81 apply (zenon_L175_); trivial. % 30.68/30.81 apply (zenon_L2662_); trivial. % 30.68/30.81 (* end of lemma zenon_L2677_ *) % 30.68/30.81 assert (zenon_L2678_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_Hf9 zenon_H8a zenon_He1 zenon_H55 zenon_H222 zenon_Hed zenon_H4c zenon_Hee zenon_H95 zenon_H37. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.68/30.81 apply (zenon_L50_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.68/30.81 apply (zenon_L264_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.68/30.81 apply (zenon_L1207_); trivial. % 30.68/30.81 apply (zenon_L513_); trivial. % 30.68/30.81 (* end of lemma zenon_L2678_ *) % 30.68/30.81 assert (zenon_L2679_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_H1d5 zenon_H1d8 zenon_H8a zenon_He1 zenon_H55 zenon_H2d zenon_H142 zenon_H156 zenon_H4e zenon_H16c. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.81 apply (zenon_L174_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.81 apply (zenon_L126_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.81 apply (zenon_L175_); trivial. % 30.68/30.81 apply (zenon_L779_); trivial. % 30.68/30.81 (* end of lemma zenon_L2679_ *) % 30.68/30.81 assert (zenon_L2680_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_H16f zenon_H6f zenon_H68 zenon_H1dc zenon_Hf9 zenon_H222 zenon_Hed zenon_Hee zenon_Hbd zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H1d5 zenon_H1d8 zenon_H8a zenon_He1 zenon_H55 zenon_H2d zenon_H142 zenon_H156 zenon_H4e. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.81 apply (zenon_L18_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.81 apply (zenon_L25_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.81 apply (zenon_L2678_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.81 apply (zenon_L177_); trivial. % 30.68/30.81 exact (zenon_H122 zenon_Hb1). % 30.68/30.81 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.81 apply (zenon_L2657_); trivial. % 30.68/30.81 apply (zenon_L2679_); trivial. % 30.68/30.81 (* end of lemma zenon_L2680_ *) % 30.68/30.81 assert (zenon_L2681_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_He4 zenon_Hda zenon_Hd9 zenon_H4c zenon_H14e zenon_H1b1 zenon_H19e zenon_H55 zenon_H142 zenon_H20e zenon_H2f8 zenon_Hee zenon_H11b zenon_H122 zenon_H1ab zenon_H17d zenon_H222 zenon_Hf9 zenon_H2ed zenon_He1 zenon_H8a. % 30.68/30.81 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.81 apply (zenon_L47_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.81 apply (zenon_L2673_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.81 exact (zenon_H2ed zenon_Hc9). % 30.68/30.81 apply (zenon_L50_); trivial. % 30.68/30.81 (* end of lemma zenon_L2681_ *) % 30.68/30.81 assert (zenon_L2682_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.68/30.81 do 0 intro. intros zenon_H225 zenon_H2d zenon_H173 zenon_H15a zenon_H156 zenon_H1d8 zenon_H1d5 zenon_Hbd zenon_H1dc zenon_H68 zenon_H6f zenon_H16f zenon_H4e zenon_H1a5 zenon_H1fd zenon_H35 zenon_Had zenon_H256 zenon_Hb5 zenon_H174 zenon_H3c zenon_H8a zenon_He1 zenon_H2ed zenon_Hf9 zenon_H222 zenon_H17d zenon_H1ab zenon_H122 zenon_H11b zenon_Hee zenon_H2f8 zenon_H20e zenon_H142 zenon_H55 zenon_H19e zenon_H1b1 zenon_H14e zenon_H4c zenon_Hd9 zenon_He4 zenon_H185 zenon_Hde. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.81 apply (zenon_L232_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.81 apply (zenon_L2677_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.81 apply (zenon_L94_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.81 apply (zenon_L787_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.81 apply (zenon_L2680_); trivial. % 30.68/30.81 apply (zenon_L828_); trivial. % 30.68/30.81 apply (zenon_L848_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.81 apply (zenon_L88_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.81 apply (zenon_L2681_); trivial. % 30.68/30.81 apply (zenon_L817_); trivial. % 30.68/30.81 (* end of lemma zenon_L2682_ *) % 30.68/30.81 assert (zenon_L2683_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 30.68/30.81 do 0 intro. intros zenon_H173 zenon_H1b1 zenon_H142 zenon_H20e zenon_H2f8 zenon_H19e zenon_H182 zenon_H159 zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a zenon_Hf9 zenon_He1 zenon_H55 zenon_H222 zenon_Hee zenon_H95 zenon_Hd1 zenon_H16f zenon_H4e zenon_H117 zenon_H1a5. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.81 apply (zenon_L2673_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.81 apply (zenon_L787_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.81 apply (zenon_L729_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.81 apply (zenon_L2678_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.81 apply (zenon_L2657_); trivial. % 30.68/30.81 apply (zenon_L733_); trivial. % 30.68/30.81 apply (zenon_L828_); trivial. % 30.68/30.81 (* end of lemma zenon_L2683_ *) % 30.68/30.81 assert (zenon_L2684_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 30.68/30.81 do 0 intro. intros zenon_H1a8 zenon_H2d zenon_H1fd zenon_H6f zenon_H1d5 zenon_H1d8 zenon_H156 zenon_H15a zenon_H73 zenon_H18f zenon_H173 zenon_H1b1 zenon_H142 zenon_H20e zenon_H2f8 zenon_H19e zenon_H159 zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a zenon_Hf9 zenon_He1 zenon_H55 zenon_H222 zenon_Hee zenon_H95 zenon_Hd1 zenon_H16f zenon_H4e zenon_H117 zenon_H1a5. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.81 apply (zenon_L94_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.81 apply (zenon_L787_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.81 apply (zenon_L18_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.81 apply (zenon_L2678_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.81 apply (zenon_L2657_); trivial. % 30.68/30.81 apply (zenon_L2679_); trivial. % 30.68/30.81 apply (zenon_L2667_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.81 exact (zenon_H18f zenon_Hd2). % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.81 apply (zenon_L824_); trivial. % 30.68/30.81 apply (zenon_L2683_); trivial. % 30.68/30.81 (* end of lemma zenon_L2684_ *) % 30.68/30.81 assert (zenon_L2685_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 30.68/30.81 do 0 intro. intros zenon_H296 zenon_H1dc zenon_H3f zenon_Hbd zenon_H6c zenon_H4a zenon_H18c zenon_Hd6 zenon_H1a8 zenon_H2d zenon_H1fd zenon_H6f zenon_H1d5 zenon_H1d8 zenon_H156 zenon_H15a zenon_H73 zenon_H18f zenon_H173 zenon_H1b1 zenon_H142 zenon_H20e zenon_H2f8 zenon_H19e zenon_H159 zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a zenon_Hf9 zenon_He1 zenon_H55 zenon_H222 zenon_Hee zenon_Hd1 zenon_H16f zenon_H4e zenon_H117 zenon_H1a5. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.68/30.81 apply (zenon_L2675_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.68/30.81 apply (zenon_L763_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.68/30.81 apply (zenon_L161_); trivial. % 30.68/30.81 apply (zenon_L2684_); trivial. % 30.68/30.81 (* end of lemma zenon_L2685_ *) % 30.68/30.81 assert (zenon_L2686_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 30.68/30.81 do 0 intro. intros zenon_H53 zenon_H97 zenon_He4 zenon_H2ed zenon_He1 zenon_H8a zenon_H222 zenon_H55 zenon_H2f8 zenon_H122 zenon_H14e zenon_H17d zenon_H11b zenon_Hee zenon_H4c zenon_H19e zenon_H142 zenon_H20e zenon_H1b1 zenon_Hf9 zenon_Hde zenon_Hbd zenon_H1dc zenon_H3f zenon_H2d zenon_H1fd zenon_Hb5 zenon_H92 zenon_H18c zenon_H4a zenon_Hd6 zenon_H1a8 zenon_H159 zenon_Hd1 zenon_H18f zenon_H296 zenon_H174 zenon_H15a zenon_H16f zenon_H6f zenon_H173 zenon_H1d8 zenon_Had zenon_H4e zenon_H35 zenon_H1a5 zenon_H156 zenon_H256 zenon_H1d5 zenon_H3c zenon_Hd9 zenon_H225 zenon_H84 zenon_H301. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.68/30.81 apply (zenon_L2674_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.68/30.81 apply (zenon_L2675_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.68/30.81 apply (zenon_L2676_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.81 exact (zenon_H84 zenon_H88). % 30.68/30.81 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.81 apply (zenon_L2682_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.81 apply (zenon_L232_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.81 apply (zenon_L2677_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.81 apply (zenon_L2685_); trivial. % 30.68/30.81 apply (zenon_L848_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.81 apply (zenon_L88_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.81 apply (zenon_L2681_); trivial. % 30.68/30.81 apply (zenon_L817_); trivial. % 30.68/30.81 apply (zenon_L39_); trivial. % 30.68/30.81 apply (zenon_L862_); trivial. % 30.68/30.81 (* end of lemma zenon_L2686_ *) % 30.68/30.81 assert (zenon_L2687_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_H101 zenon_H2b1 zenon_H20 zenon_H185 zenon_H6c zenon_H102 zenon_H95 zenon_H42 zenon_H301 zenon_H84 zenon_H225 zenon_Hd9 zenon_H3c zenon_H1d5 zenon_H256 zenon_H156 zenon_H1a5 zenon_H35 zenon_H4e zenon_Had zenon_H1d8 zenon_H173 zenon_H6f zenon_H16f zenon_H15a zenon_H174 zenon_H296 zenon_H18f zenon_Hd1 zenon_H159 zenon_H1a8 zenon_Hd6 zenon_H4a zenon_H18c zenon_H92 zenon_H1fd zenon_H2d zenon_H3f zenon_Hbd zenon_Hde zenon_Hf9 zenon_H19e zenon_H222 zenon_He1 zenon_H2ed zenon_He4 zenon_H97 zenon_H53 zenon_H1a2 zenon_H2b7 zenon_H1dc zenon_H10d zenon_Hb5 zenon_H100 zenon_H56 zenon_H2f8 zenon_H20e zenon_H142 zenon_Hee zenon_H1b1 zenon_Hdc zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.81 apply (zenon_L2665_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.81 apply (zenon_L154_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.81 apply (zenon_L2686_); trivial. % 30.68/30.81 apply (zenon_L2660_); trivial. % 30.68/30.81 (* end of lemma zenon_L2687_ *) % 30.68/30.81 assert (zenon_L2688_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_H101 zenon_H2b1 zenon_H20 zenon_H185 zenon_H6c zenon_H102 zenon_H42 zenon_Hdc zenon_H301 zenon_H84 zenon_H225 zenon_Hd9 zenon_H3c zenon_H1d5 zenon_H256 zenon_H156 zenon_H1a5 zenon_H35 zenon_H4e zenon_Had zenon_H1d8 zenon_H173 zenon_H6f zenon_H16f zenon_H15a zenon_H174 zenon_H296 zenon_H18f zenon_Hd1 zenon_H159 zenon_H1a8 zenon_Hd6 zenon_H4a zenon_H18c zenon_H92 zenon_H1fd zenon_H2d zenon_H3f zenon_Hbd zenon_Hde zenon_Hf9 zenon_H1b1 zenon_H19e zenon_H222 zenon_He1 zenon_H2ed zenon_He4 zenon_H97 zenon_H53 zenon_H2f8 zenon_H20e zenon_H100 zenon_Hb5 zenon_Hee zenon_H10d zenon_H26 zenon_H1dc zenon_H142 zenon_H2b7 zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.68/30.81 apply (zenon_L2675_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.68/30.81 apply (zenon_L763_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.68/30.81 apply (zenon_L161_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.81 apply (zenon_L2665_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.81 apply (zenon_L154_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.81 apply (zenon_L2686_); trivial. % 30.68/30.81 apply (zenon_L2658_); trivial. % 30.68/30.81 (* end of lemma zenon_L2688_ *) % 30.68/30.81 assert (zenon_L2689_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_H100 zenon_H20e zenon_H2f8 zenon_H53 zenon_H97 zenon_He4 zenon_H2ed zenon_He1 zenon_H222 zenon_H19e zenon_H1b1 zenon_Hf9 zenon_Hde zenon_Hbd zenon_H3f zenon_H92 zenon_H18c zenon_Hd6 zenon_H1a8 zenon_H159 zenon_Hd1 zenon_H18f zenon_H296 zenon_H174 zenon_H15a zenon_H16f zenon_H6f zenon_H173 zenon_H1d8 zenon_Had zenon_H35 zenon_H156 zenon_H256 zenon_H1d5 zenon_H3c zenon_Hd9 zenon_H225 zenon_H84 zenon_H301 zenon_H42 zenon_H102 zenon_H6c zenon_H185 zenon_H20 zenon_H2b1 zenon_H101 zenon_H4a zenon_Hb5 zenon_H10d zenon_H26 zenon_H1dc zenon_H2b7 zenon_H1fd zenon_H1a5 zenon_H8a zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H2d zenon_H142 zenon_Hee zenon_H4e. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.81 apply (zenon_L2688_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.81 apply (zenon_L748_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.81 apply (zenon_L1208_); trivial. % 30.68/30.81 apply (zenon_L2667_); trivial. % 30.68/30.81 (* end of lemma zenon_L2689_ *) % 30.68/30.81 assert (zenon_L2690_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_H125 zenon_H73 zenon_Hd9 zenon_Hfd zenon_Hfc zenon_Hde zenon_H2f8 zenon_H20e zenon_H142 zenon_H1a0 zenon_Hee zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hda | zenon_intro zenon_H128 ]. % 30.68/30.81 apply (zenon_L47_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hed | zenon_intro zenon_H129 ]. % 30.68/30.81 apply (zenon_L58_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_Hcc | zenon_intro zenon_Heb ]. % 30.68/30.81 apply (zenon_L89_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.81 apply (zenon_L350_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.81 apply (zenon_L337_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.81 apply (zenon_L1207_); trivial. % 30.68/30.81 apply (zenon_L2657_); trivial. % 30.68/30.81 (* end of lemma zenon_L2690_ *) % 30.68/30.81 assert (zenon_L2691_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.68/30.81 do 0 intro. intros zenon_H296 zenon_H1dc zenon_H3f zenon_Hbd zenon_Hd6 zenon_H42 zenon_Hb5 zenon_H142 zenon_H2d zenon_H4c zenon_H14e zenon_H256 zenon_Had zenon_H1a5 zenon_H1fd zenon_H1d8 zenon_H1d5 zenon_H17d zenon_H122 zenon_H11b zenon_H1ab zenon_H102 zenon_H6c zenon_H18c zenon_H18f zenon_H35 zenon_He9 zenon_H156 zenon_H4a zenon_H19e zenon_H4e zenon_H185 zenon_H20 zenon_H2b1 zenon_H8a zenon_H97. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.68/30.81 apply (zenon_L2675_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.68/30.81 apply (zenon_L763_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.68/30.81 apply (zenon_L161_); trivial. % 30.68/30.81 apply (zenon_L2665_); trivial. % 30.68/30.81 (* end of lemma zenon_L2691_ *) % 30.68/30.81 assert (zenon_L2692_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.81 do 0 intro. intros zenon_H2b1 zenon_H20 zenon_H185 zenon_H3d zenon_H4e zenon_H19e zenon_H4a zenon_H156 zenon_H100 zenon_H9d zenon_H18f zenon_H18c zenon_H6c zenon_H102 zenon_H1ab. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H33 | zenon_intro zenon_H2b2 ]. % 30.68/30.81 apply (zenon_L117_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H182 | zenon_intro zenon_H2b3 ]. % 30.68/30.81 apply (zenon_L731_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H112 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H106 ]. % 30.68/30.81 apply (zenon_L763_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H107 ]. % 30.68/30.81 exact (zenon_H18f zenon_Hd2). % 30.68/30.81 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfd | zenon_intro zenon_H37 ]. % 30.68/30.81 apply (zenon_L60_); trivial. % 30.68/30.81 apply (zenon_L841_); trivial. % 30.68/30.81 exact (zenon_H1ab zenon_H112). % 30.68/30.81 (* end of lemma zenon_L2692_ *) % 30.68/30.81 assert (zenon_L2693_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> False). % 30.68/30.81 do 0 intro. intros zenon_H1fd zenon_H1c5 zenon_H4e zenon_H156 zenon_H1a5 zenon_H2c zenon_H35 zenon_Had zenon_H256 zenon_H8a zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H2d zenon_H142 zenon_H6f zenon_H1a0. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.81 apply (zenon_L2661_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.81 apply (zenon_L2657_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.81 apply (zenon_L175_); trivial. % 30.68/30.81 apply (zenon_L540_); trivial. % 30.68/30.81 (* end of lemma zenon_L2693_ *) % 30.68/30.81 assert (zenon_L2694_ : (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> False). % 30.68/30.81 do 0 intro. intros zenon_Hde zenon_Hd9 zenon_H73 zenon_H125 zenon_H23b zenon_H1f zenon_H53 zenon_He4 zenon_H2ed zenon_H1b1 zenon_H92 zenon_H1a8 zenon_H159 zenon_Hd1 zenon_H174 zenon_H15a zenon_H173 zenon_H3c zenon_H225 zenon_H84 zenon_H301 zenon_He1 zenon_H2b1 zenon_H20 zenon_H185 zenon_H19e zenon_H4a zenon_H156 zenon_H100 zenon_H18f zenon_H18c zenon_H6c zenon_H102 zenon_H95 zenon_H1a2 zenon_H2b7 zenon_H1dc zenon_H10d zenon_Hb5 zenon_H20e zenon_H2f8 zenon_H56 zenon_H1d5 zenon_H1d8 zenon_H35 zenon_Had zenon_H256 zenon_H6f zenon_H42 zenon_H16f zenon_H68 zenon_Hf9 zenon_H222 zenon_Hbd zenon_Hfc zenon_H296 zenon_H3f zenon_Hd6 zenon_H97 zenon_H101 zenon_H1fd zenon_H1a5 zenon_H8a zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H2d zenon_H142 zenon_Hee zenon_H4e. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.81 apply (zenon_L2687_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.81 apply (zenon_L2689_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.81 apply (zenon_L1187_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.81 exact (zenon_H56 zenon_H25). % 30.68/30.81 apply (zenon_L2690_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.81 apply (zenon_L2691_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.81 apply (zenon_L58_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.81 apply (zenon_L2680_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.81 apply (zenon_L2658_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.81 apply (zenon_L1184_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.81 exact (zenon_H56 zenon_H25). % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.81 apply (zenon_L174_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.81 apply (zenon_L2692_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.81 apply (zenon_L175_); trivial. % 30.68/30.81 apply (zenon_L2693_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.81 apply (zenon_L2664_); trivial. % 30.68/30.81 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.81 apply (zenon_L2692_); trivial. % 30.68/30.81 apply (zenon_L1354_); trivial. % 30.68/30.81 apply (zenon_L2667_); trivial. % 30.68/30.81 (* end of lemma zenon_L2694_ *) % 30.68/30.82 assert (zenon_L2695_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H310 zenon_H6b zenon_H4e zenon_Hee zenon_H142 zenon_H2d zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H1a5 zenon_H1fd zenon_H101 zenon_H97 zenon_Hd6 zenon_H3f zenon_H296 zenon_Hfc zenon_Hbd zenon_H222 zenon_Hf9 zenon_H68 zenon_H16f zenon_H42 zenon_H6f zenon_H256 zenon_Had zenon_H35 zenon_H1d5 zenon_H56 zenon_H2f8 zenon_H20e zenon_Hb5 zenon_H10d zenon_H1dc zenon_H2b7 zenon_H1a2 zenon_H95 zenon_H102 zenon_H18c zenon_H18f zenon_H100 zenon_H156 zenon_H4a zenon_H19e zenon_H185 zenon_H20 zenon_H2b1 zenon_He1 zenon_H301 zenon_H84 zenon_H225 zenon_H3c zenon_H173 zenon_H15a zenon_H174 zenon_Hd1 zenon_H159 zenon_H1a8 zenon_H92 zenon_H1b1 zenon_He4 zenon_H53 zenon_H1f zenon_H23b zenon_H125 zenon_H73 zenon_Hd9 zenon_Hde zenon_H2ed zenon_H8a zenon_H1d8. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_Hdf | zenon_intro zenon_H311 ]. % 30.68/30.82 apply (zenon_L303_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H6c | zenon_intro zenon_H312 ]. % 30.68/30.82 apply (zenon_L2694_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H76 ]. % 30.68/30.82 exact (zenon_H2ed zenon_Hc9). % 30.68/30.82 apply (zenon_L174_); trivial. % 30.68/30.82 (* end of lemma zenon_L2695_ *) % 30.68/30.82 assert (zenon_L2696_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H310 zenon_H69 zenon_H48 zenon_H4e zenon_Hee zenon_H142 zenon_H2d zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H1a5 zenon_H1fd zenon_H2b7 zenon_H1dc zenon_H26 zenon_H10d zenon_Hb5 zenon_H4a zenon_H101 zenon_H97 zenon_H2b1 zenon_H20 zenon_H185 zenon_H156 zenon_H35 zenon_H18f zenon_H18c zenon_H102 zenon_H95 zenon_H1d5 zenon_Had zenon_H256 zenon_H42 zenon_Hd1 zenon_H19a zenon_H19e zenon_H2f8 zenon_H20e zenon_H100 zenon_H173 zenon_H2ed zenon_H8a zenon_H1d8. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_Hdf | zenon_intro zenon_H311 ]. % 30.68/30.82 apply (zenon_L740_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H6c | zenon_intro zenon_H312 ]. % 30.68/30.82 apply (zenon_L2668_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H76 ]. % 30.68/30.82 exact (zenon_H2ed zenon_Hc9). % 30.68/30.82 apply (zenon_L174_); trivial. % 30.68/30.82 (* end of lemma zenon_L2696_ *) % 30.68/30.82 assert (zenon_L2697_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> False). % 30.68/30.82 do 0 intro. intros zenon_Hf9 zenon_He1 zenon_H1d8 zenon_H2ed zenon_H173 zenon_H100 zenon_H20e zenon_H2f8 zenon_H19e zenon_Hd1 zenon_H42 zenon_H256 zenon_Had zenon_H1d5 zenon_H95 zenon_H102 zenon_H18c zenon_H18f zenon_H35 zenon_H156 zenon_H185 zenon_H20 zenon_H2b1 zenon_H97 zenon_H101 zenon_H4a zenon_H1fd zenon_H1a5 zenon_H17d zenon_H1ab zenon_H122 zenon_H11b zenon_H2d zenon_H4e zenon_H48 zenon_H69 zenon_H310 zenon_Hb5 zenon_H8a zenon_Hee zenon_H10d zenon_H26 zenon_H1dc zenon_H142 zenon_H2b7 zenon_H14e zenon_H4c. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.68/30.82 apply (zenon_L50_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.68/30.82 apply (zenon_L2658_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.82 apply (zenon_L350_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.82 apply (zenon_L2696_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.82 apply (zenon_L1207_); trivial. % 30.68/30.82 apply (zenon_L2657_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.82 apply (zenon_L350_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.82 apply (zenon_L2696_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.82 apply (zenon_L1208_); trivial. % 30.68/30.82 apply (zenon_L752_); trivial. % 30.68/30.82 (* end of lemma zenon_L2697_ *) % 30.68/30.82 assert (zenon_L2698_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.82 do 0 intro. intros zenon_Hbd zenon_H4c zenon_H14e zenon_H2b7 zenon_H26 zenon_H10d zenon_Hee zenon_H8a zenon_Hb5 zenon_H310 zenon_H69 zenon_H48 zenon_H4e zenon_H2d zenon_H11b zenon_H1ab zenon_H17d zenon_H1a5 zenon_H1fd zenon_H4a zenon_H101 zenon_H97 zenon_H2b1 zenon_H20 zenon_H185 zenon_H156 zenon_H35 zenon_H18f zenon_H18c zenon_H102 zenon_H1d5 zenon_Had zenon_H256 zenon_H42 zenon_Hd1 zenon_H19e zenon_H2f8 zenon_H20e zenon_H100 zenon_H173 zenon_H2ed zenon_H1d8 zenon_He1 zenon_Hf9 zenon_H142 zenon_H1dc zenon_H122. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.82 apply (zenon_L25_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.82 apply (zenon_L2697_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.82 apply (zenon_L177_); trivial. % 30.68/30.82 exact (zenon_H122 zenon_Hb1). % 30.68/30.82 (* end of lemma zenon_L2698_ *) % 30.68/30.82 assert (zenon_L2699_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H1a2 zenon_H1dc zenon_Hf9 zenon_He1 zenon_H1d8 zenon_H2ed zenon_H173 zenon_H100 zenon_H19e zenon_Hd1 zenon_H42 zenon_H256 zenon_Had zenon_H1d5 zenon_H102 zenon_H18c zenon_H18f zenon_H35 zenon_H156 zenon_H185 zenon_H20 zenon_H2b1 zenon_H97 zenon_H101 zenon_H4a zenon_H1fd zenon_H1a5 zenon_H2d zenon_H4e zenon_H48 zenon_H69 zenon_H310 zenon_Hb5 zenon_H10d zenon_H2b7 zenon_Hbd zenon_H3f zenon_H1f zenon_H6f zenon_H23b zenon_H56 zenon_H2f8 zenon_H20e zenon_H142 zenon_Hee zenon_H1b1 zenon_Hdc zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H8a. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.82 apply (zenon_L2698_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.82 apply (zenon_L1187_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.82 exact (zenon_H56 zenon_H25). % 30.68/30.82 apply (zenon_L2659_); trivial. % 30.68/30.82 (* end of lemma zenon_L2699_ *) % 30.68/30.82 assert (zenon_L2700_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e1) (e3)) = (e1)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H16f zenon_Hd1 zenon_H95 zenon_H8a zenon_H17d zenon_H14e zenon_H4c zenon_H1ab zenon_H122 zenon_H11b zenon_H159 zenon_H4e zenon_H182. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.82 apply (zenon_L729_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.82 apply (zenon_L2664_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.82 apply (zenon_L2657_); trivial. % 30.68/30.82 apply (zenon_L733_); trivial. % 30.68/30.82 (* end of lemma zenon_L2700_ *) % 30.68/30.82 assert (zenon_L2701_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H23b zenon_H1f zenon_H125 zenon_Hfc zenon_H8a zenon_He1 zenon_H2ed zenon_H101 zenon_H2b1 zenon_H20 zenon_H6c zenon_H102 zenon_H42 zenon_H301 zenon_H84 zenon_H225 zenon_Hd9 zenon_H3c zenon_H1d5 zenon_H256 zenon_H156 zenon_H1a5 zenon_H35 zenon_H4e zenon_Had zenon_H1d8 zenon_H173 zenon_H6f zenon_H16f zenon_H15a zenon_H174 zenon_H296 zenon_H18f zenon_Hd1 zenon_H159 zenon_H1a8 zenon_Hd6 zenon_H4a zenon_H18c zenon_H92 zenon_H1fd zenon_H2d zenon_H3f zenon_Hbd zenon_Hf9 zenon_H19e zenon_H222 zenon_He4 zenon_H97 zenon_H53 zenon_H1a2 zenon_H2b7 zenon_H1dc zenon_H10d zenon_Hb5 zenon_H100 zenon_H56 zenon_H2f8 zenon_H20e zenon_H142 zenon_Hee zenon_H1b1 zenon_H11b zenon_H122 zenon_H1ab zenon_H4c zenon_H14e zenon_H17d zenon_H185 zenon_Hde. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.68/30.82 apply (zenon_L2675_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.68/30.82 apply (zenon_L763_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.68/30.82 apply (zenon_L161_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.82 apply (zenon_L2694_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.82 exact (zenon_H18f zenon_Hd2). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.82 apply (zenon_L1187_); trivial. % 30.68/30.82 apply (zenon_L2700_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.82 apply (zenon_L2691_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.82 apply (zenon_L47_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.68/30.82 apply (zenon_L2675_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.68/30.82 apply (zenon_L763_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.68/30.82 apply (zenon_L161_); trivial. % 30.68/30.82 apply (zenon_L2687_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.82 exact (zenon_H2ed zenon_Hc9). % 30.68/30.82 apply (zenon_L50_); trivial. % 30.68/30.82 apply (zenon_L817_); trivial. % 30.68/30.82 (* end of lemma zenon_L2701_ *) % 30.68/30.82 assert (zenon_L2702_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H246 zenon_H20 zenon_H185 zenon_Hbd zenon_H4c zenon_H14e zenon_H2b7 zenon_H10d zenon_Hee zenon_Hb5 zenon_H310 zenon_H48 zenon_H4e zenon_H11b zenon_H1ab zenon_H17d zenon_H1a5 zenon_H1fd zenon_H4a zenon_H101 zenon_H97 zenon_H2b1 zenon_H156 zenon_H35 zenon_H18f zenon_H18c zenon_H102 zenon_H1d5 zenon_Had zenon_H256 zenon_H42 zenon_Hd1 zenon_H19e zenon_H2f8 zenon_H20e zenon_H100 zenon_H173 zenon_H2ed zenon_H1d8 zenon_He1 zenon_Hf9 zenon_H1dc zenon_H122 zenon_Hde zenon_H1b1 zenon_H56 zenon_H1a2 zenon_H53 zenon_He4 zenon_H222 zenon_H3f zenon_H92 zenon_Hd6 zenon_H1a8 zenon_H159 zenon_H296 zenon_H174 zenon_H15a zenon_H16f zenon_H3c zenon_Hd9 zenon_H225 zenon_H84 zenon_H301 zenon_Hfc zenon_H125 zenon_H23b zenon_H6f zenon_Hc0 zenon_H6b zenon_H142 zenon_H2d zenon_H8a. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.82 exact (zenon_H84 zenon_H88). % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.82 apply (zenon_L1209_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.82 apply (zenon_L2670_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.82 apply (zenon_L1187_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.82 exact (zenon_H56 zenon_H25). % 30.68/30.82 apply (zenon_L2659_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.82 exact (zenon_H2ed zenon_Hc9). % 30.68/30.82 apply (zenon_L50_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.82 apply (zenon_L1209_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.82 apply (zenon_L2670_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.82 exact (zenon_H2ed zenon_Hc9). % 30.68/30.82 apply (zenon_L50_); trivial. % 30.68/30.82 apply (zenon_L117_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.82 exact (zenon_H84 zenon_H88). % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.82 exact (zenon_H84 zenon_H88). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.82 apply (zenon_L749_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.82 apply (zenon_L2695_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.82 apply (zenon_L177_); trivial. % 30.68/30.82 exact (zenon_H122 zenon_Hb1). % 30.68/30.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.82 apply (zenon_L2699_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.82 exact (zenon_H2ed zenon_Hc9). % 30.68/30.82 apply (zenon_L50_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.82 apply (zenon_L2701_); trivial. % 30.68/30.82 apply (zenon_L39_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.82 apply (zenon_L2698_); trivial. % 30.68/30.82 apply (zenon_L117_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.82 apply (zenon_L303_); trivial. % 30.68/30.82 apply (zenon_L25_); trivial. % 30.68/30.82 (* end of lemma zenon_L2702_ *) % 30.68/30.82 assert (zenon_L2703_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (op (e1) (e1))) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H23b zenon_H6f zenon_Hd2 zenon_H4a zenon_H100 zenon_H8a zenon_H17d zenon_H14e zenon_H4c zenon_H122 zenon_H11b zenon_Hdc zenon_H1b1 zenon_Hee zenon_H142 zenon_H20e zenon_H2f8 zenon_H1ab. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.82 apply (zenon_L39_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.82 apply (zenon_L880_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.82 apply (zenon_L2659_); trivial. % 30.68/30.82 exact (zenon_H1ab zenon_H112). % 30.68/30.82 (* end of lemma zenon_L2703_ *) % 30.68/30.82 assert (zenon_L2704_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H2d9 zenon_H317 zenon_H88 zenon_H188 zenon_H10e zenon_H198 zenon_H65 zenon_H40 zenon_H3f. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H1e | zenon_intro zenon_H2da ]. % 30.68/30.82 exact (zenon_H317 zenon_H1e). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H1f | zenon_intro zenon_H2db ]. % 30.68/30.82 apply (zenon_L1035_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_He9 | zenon_intro zenon_H2c ]. % 30.68/30.82 apply (zenon_L818_); trivial. % 30.68/30.82 apply (zenon_L746_); trivial. % 30.68/30.82 (* end of lemma zenon_L2704_ *) % 30.68/30.82 assert (zenon_L2705_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H8d zenon_H6f zenon_H88 zenon_H15a zenon_H185 zenon_H36 zenon_Hc8 zenon_H40 zenon_H97. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.82 apply (zenon_L734_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.82 apply (zenon_L1000_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.82 apply (zenon_L1001_); trivial. % 30.68/30.82 apply (zenon_L862_); trivial. % 30.68/30.82 (* end of lemma zenon_L2705_ *) % 30.68/30.82 assert (zenon_L2706_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H11b zenon_H1e1 zenon_Hf6 zenon_H1ab zenon_H231 zenon_H113 zenon_H40. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.82 apply (zenon_L690_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.82 exact (zenon_H1ab zenon_H112). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.82 exact (zenon_H231 zenon_Hf4). % 30.68/30.82 apply (zenon_L753_); trivial. % 30.68/30.82 (* end of lemma zenon_L2706_ *) % 30.68/30.82 assert (zenon_L2707_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H1e6 zenon_H113 zenon_H231 zenon_H1ab zenon_Hf6 zenon_H11b zenon_H40 zenon_H222 zenon_Hc9 zenon_H20d zenon_H1af zenon_H16b zenon_H218. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.68/30.82 apply (zenon_L2706_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.68/30.82 apply (zenon_L1337_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.68/30.82 apply (zenon_L627_); trivial. % 30.68/30.82 apply (zenon_L245_); trivial. % 30.68/30.82 (* end of lemma zenon_L2707_ *) % 30.68/30.82 assert (zenon_L2708_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H1e6 zenon_H113 zenon_H231 zenon_H1ab zenon_Hf6 zenon_H11b zenon_H40 zenon_H222 zenon_H6b zenon_H1af zenon_H76 zenon_H20d. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.68/30.82 apply (zenon_L2706_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.68/30.82 apply (zenon_L1337_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.68/30.82 apply (zenon_L193_); trivial. % 30.68/30.82 apply (zenon_L1343_); trivial. % 30.68/30.82 (* end of lemma zenon_L2708_ *) % 30.68/30.82 assert (zenon_L2709_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H1d5 zenon_H20d zenon_H6b zenon_H11b zenon_Hf6 zenon_H1ab zenon_H231 zenon_H113 zenon_H1e6 zenon_H222 zenon_H40 zenon_H1c7 zenon_H55 zenon_H60 zenon_H1af zenon_H16b zenon_H218. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.82 apply (zenon_L2708_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.82 apply (zenon_L775_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.82 apply (zenon_L216_); trivial. % 30.68/30.82 apply (zenon_L245_); trivial. % 30.68/30.82 (* end of lemma zenon_L2709_ *) % 30.68/30.82 assert (zenon_L2710_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H11b zenon_H1b9 zenon_H1a0 zenon_H1ab zenon_H231 zenon_H113 zenon_H40. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.82 apply (zenon_L751_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.82 exact (zenon_H1ab zenon_H112). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.82 exact (zenon_H231 zenon_Hf4). % 30.68/30.82 apply (zenon_L753_); trivial. % 30.68/30.82 (* end of lemma zenon_L2710_ *) % 30.68/30.82 assert (zenon_L2711_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H1d5 zenon_H6b zenon_Hf5 zenon_H222 zenon_H40 zenon_H113 zenon_H231 zenon_H1ab zenon_H1a0 zenon_H11b zenon_H1af zenon_H16b zenon_H218. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.82 apply (zenon_L193_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.82 apply (zenon_L775_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.82 apply (zenon_L2710_); trivial. % 30.68/30.82 apply (zenon_L245_); trivial. % 30.68/30.82 (* end of lemma zenon_L2711_ *) % 30.68/30.82 assert (zenon_L2712_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H135 zenon_H60 zenon_H1c7 zenon_H1e6 zenon_Hf6 zenon_H20d zenon_Hd0 zenon_H1d5 zenon_H6b zenon_H222 zenon_H40 zenon_H113 zenon_H231 zenon_H1ab zenon_H1a0 zenon_H11b zenon_H1af zenon_H16b zenon_H218. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.68/30.82 apply (zenon_L2707_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.68/30.82 apply (zenon_L2709_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.68/30.82 exact (zenon_Hd0 zenon_Hcc). % 30.68/30.82 apply (zenon_L2711_); trivial. % 30.68/30.82 (* end of lemma zenon_L2712_ *) % 30.68/30.82 assert (zenon_L2713_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H174 zenon_H3f zenon_H2d zenon_H10e zenon_H23b zenon_H88 zenon_He7 zenon_H6f zenon_H218 zenon_H1af zenon_H11b zenon_H231 zenon_H113 zenon_H40 zenon_H222 zenon_H6b zenon_H1d5 zenon_Hd0 zenon_H20d zenon_Hf6 zenon_H1e6 zenon_H1c7 zenon_H60 zenon_H135 zenon_H1ab. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.82 apply (zenon_L734_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.82 apply (zenon_L746_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.82 apply (zenon_L87_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.82 apply (zenon_L1053_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.82 apply (zenon_L80_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.82 apply (zenon_L2712_); trivial. % 30.68/30.82 exact (zenon_H1ab zenon_H112). % 30.68/30.82 (* end of lemma zenon_L2713_ *) % 30.68/30.82 assert (zenon_L2714_ : (((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 (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H11b zenon_H185 zenon_Ha4 zenon_H1ab zenon_H231 zenon_H113 zenon_H40. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.82 apply (zenon_L869_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.82 exact (zenon_H1ab zenon_H112). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.82 exact (zenon_H231 zenon_Hf4). % 30.68/30.82 apply (zenon_L753_); trivial. % 30.68/30.82 (* end of lemma zenon_L2714_ *) % 30.68/30.82 assert (zenon_L2715_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H1e6 zenon_H113 zenon_H231 zenon_H1ab zenon_Hf6 zenon_H11b zenon_H40 zenon_H222 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H16b zenon_H218. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e7 ]. % 30.68/30.82 apply (zenon_L2706_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e8 ]. % 30.68/30.82 apply (zenon_L1337_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H1c5 ]. % 30.68/30.82 apply (zenon_L550_); trivial. % 30.68/30.82 apply (zenon_L245_); trivial. % 30.68/30.82 (* end of lemma zenon_L2715_ *) % 30.68/30.82 assert (zenon_L2716_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (op (e2) (e2))) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (op (e2) (e3))) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H25b zenon_H30b zenon_H6f zenon_H88 zenon_H3f zenon_H40 zenon_H2d zenon_H10e zenon_H1e6 zenon_H218 zenon_Hcc zenon_H60 zenon_H108 zenon_H1af zenon_H222 zenon_Hf6 zenon_H1ab zenon_H113 zenon_H11b zenon_H174. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.82 apply (zenon_L734_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.82 apply (zenon_L746_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.82 apply (zenon_L87_); trivial. % 30.68/30.82 apply (zenon_L2715_); trivial. % 30.68/30.82 apply (zenon_L1806_); trivial. % 30.68/30.82 (* end of lemma zenon_L2716_ *) % 30.68/30.82 assert (zenon_L2717_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H11b zenon_H40 zenon_H97 zenon_H1ab zenon_H10d zenon_H117 zenon_Hb3 zenon_Hb9. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.82 apply (zenon_L36_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.82 exact (zenon_H1ab zenon_H112). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.82 apply (zenon_L68_); trivial. % 30.68/30.82 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.82 (* end of lemma zenon_L2717_ *) % 30.68/30.82 assert (zenon_L2718_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H11b zenon_H40 zenon_H97 zenon_H1ab zenon_Hee zenon_H15e zenon_Hb3 zenon_Hb9. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.82 apply (zenon_L36_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.82 exact (zenon_H1ab zenon_H112). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.82 apply (zenon_L995_); trivial. % 30.68/30.82 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.82 (* end of lemma zenon_L2718_ *) % 30.68/30.82 assert (zenon_L2719_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (op (e3) (e3))) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H11b zenon_H40 zenon_H97 zenon_H1ab zenon_H1dc zenon_H1b9 zenon_Hb3 zenon_Hb9. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.82 apply (zenon_L36_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.82 exact (zenon_H1ab zenon_H112). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.82 apply (zenon_L996_); trivial. % 30.68/30.82 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.82 (* end of lemma zenon_L2719_ *) % 30.68/30.82 assert (zenon_L2720_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 30.68/30.82 do 0 intro. intros zenon_Hbd zenon_H20 zenon_H90 zenon_H40 zenon_H2d zenon_H73 zenon_H2d6 zenon_H10d zenon_H122. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.82 apply (zenon_L27_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.82 apply (zenon_L766_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.82 apply (zenon_L1439_); trivial. % 30.68/30.82 exact (zenon_H122 zenon_Hb1). % 30.68/30.82 (* end of lemma zenon_L2720_ *) % 30.68/30.82 assert (zenon_L2721_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H101 zenon_H138 zenon_Hda zenon_H198 zenon_Hdc zenon_Hd1 zenon_H46 zenon_He1 zenon_H40. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.82 apply (zenon_L1041_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.82 apply (zenon_L154_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.82 exact (zenon_H46 zenon_H55). % 30.68/30.82 apply (zenon_L1354_); trivial. % 30.68/30.82 (* end of lemma zenon_L2721_ *) % 30.68/30.82 assert (zenon_L2722_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H11b zenon_H122 zenon_H1ab zenon_H117 zenon_H198 zenon_Ha4 zenon_H113 zenon_H40. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.82 exact (zenon_H122 zenon_Hb1). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.82 exact (zenon_H1ab zenon_H112). % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.82 apply (zenon_L1006_); trivial. % 30.68/30.82 apply (zenon_L753_); trivial. % 30.68/30.82 (* end of lemma zenon_L2722_ *) % 30.68/30.82 assert (zenon_L2723_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H11e zenon_H15a zenon_H27 zenon_H25 zenon_He1 zenon_H46 zenon_Hd1 zenon_Hdc zenon_H138 zenon_H101 zenon_H11b zenon_H122 zenon_H1ab zenon_H198 zenon_Ha4 zenon_H113 zenon_H40. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H10e | zenon_intro zenon_H11f ]. % 30.68/30.82 apply (zenon_L725_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H26 | zenon_intro zenon_H120 ]. % 30.68/30.82 apply (zenon_L3_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hda | zenon_intro zenon_H117 ]. % 30.68/30.82 apply (zenon_L2721_); trivial. % 30.68/30.82 apply (zenon_L2722_); trivial. % 30.68/30.82 (* end of lemma zenon_L2723_ *) % 30.68/30.82 assert (zenon_L2724_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.82 do 0 intro. intros zenon_H23b zenon_Hcd zenon_He2 zenon_H40 zenon_H6f zenon_H25 zenon_H1dc zenon_H1ab. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.82 apply (zenon_L386_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.82 apply (zenon_L80_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.82 apply (zenon_L1834_); trivial. % 30.68/30.82 exact (zenon_H1ab zenon_H112). % 30.68/30.82 (* end of lemma zenon_L2724_ *) % 30.68/30.82 assert (zenon_L2725_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H1a5 zenon_H36 zenon_H17b zenon_H15e. % 30.68/30.82 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 30.68/30.82 intro zenon_D_pnotp. % 30.68/30.82 apply zenon_H1a5. % 30.68/30.82 rewrite <- zenon_D_pnotp. % 30.68/30.82 exact zenon_H36. % 30.68/30.82 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 30.68/30.82 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e5]. % 30.68/30.82 congruence. % 30.68/30.82 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H10f ]. % 30.68/30.82 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e2)))). % 30.68/30.82 intro zenon_D_pnotp. % 30.68/30.82 apply zenon_H2e5. % 30.68/30.82 rewrite <- zenon_D_pnotp. % 30.68/30.82 exact zenon_H211. % 30.68/30.82 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.68/30.82 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2e4]. % 30.68/30.82 congruence. % 30.68/30.82 apply (zenon_L1140_); trivial. % 30.68/30.82 apply zenon_H10f. apply refl_equal. % 30.68/30.82 apply zenon_H10f. apply refl_equal. % 30.68/30.82 apply zenon_H1fb. apply sym_equal. exact zenon_H15e. % 30.68/30.82 (* end of lemma zenon_L2725_ *) % 30.68/30.82 assert (zenon_L2726_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e2)) -> False). % 30.68/30.82 do 0 intro. intros zenon_H1fd zenon_H40 zenon_H113 zenon_Ha4 zenon_H198 zenon_H1ab zenon_H122 zenon_H11b zenon_H17b zenon_H36 zenon_H1a5 zenon_H6f zenon_H25 zenon_He1 zenon_Heb. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.82 apply (zenon_L2722_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.82 apply (zenon_L2725_); trivial. % 30.68/30.82 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.82 apply (zenon_L1138_); trivial. % 30.68/30.82 apply (zenon_L204_); trivial. % 30.68/30.82 (* end of lemma zenon_L2726_ *) % 30.68/30.83 assert (zenon_L2727_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H101 zenon_H138 zenon_Hda zenon_H198 zenon_H155 zenon_H159 zenon_H46 zenon_He1 zenon_H40. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.83 apply (zenon_L1041_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.83 apply (zenon_L93_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.83 exact (zenon_H46 zenon_H55). % 30.68/30.83 apply (zenon_L1354_); trivial. % 30.68/30.83 (* end of lemma zenon_L2727_ *) % 30.68/30.83 assert (zenon_L2728_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H11e zenon_Hc9 zenon_Hc8 zenon_H27 zenon_H25 zenon_H40 zenon_He1 zenon_H46 zenon_H159 zenon_H138 zenon_H101 zenon_H16a zenon_H198 zenon_H155. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H10e | zenon_intro zenon_H11f ]. % 30.68/30.83 apply (zenon_L726_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H26 | zenon_intro zenon_H120 ]. % 30.68/30.83 apply (zenon_L3_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hda | zenon_intro zenon_H117 ]. % 30.68/30.83 apply (zenon_L2727_); trivial. % 30.68/30.83 apply (zenon_L1004_); trivial. % 30.68/30.83 (* end of lemma zenon_L2728_ *) % 30.68/30.83 assert (zenon_L2729_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H101 zenon_H138 zenon_Hda zenon_H198 zenon_Hed zenon_Hfc zenon_H46 zenon_He1 zenon_H40. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.83 apply (zenon_L1041_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.83 apply (zenon_L58_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.83 exact (zenon_H46 zenon_H55). % 30.68/30.83 apply (zenon_L1354_); trivial. % 30.68/30.83 (* end of lemma zenon_L2729_ *) % 30.68/30.83 assert (zenon_L2730_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H11e zenon_Hc9 zenon_Hc8 zenon_H27 zenon_H25 zenon_H40 zenon_He1 zenon_H46 zenon_Hfc zenon_Hed zenon_H138 zenon_H101 zenon_Ha4 zenon_H198 zenon_Hf4. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H10e | zenon_intro zenon_H11f ]. % 30.68/30.83 apply (zenon_L726_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H26 | zenon_intro zenon_H120 ]. % 30.68/30.83 apply (zenon_L3_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hda | zenon_intro zenon_H117 ]. % 30.68/30.83 apply (zenon_L2729_); trivial. % 30.68/30.83 apply (zenon_L1006_); trivial. % 30.68/30.83 (* end of lemma zenon_L2730_ *) % 30.68/30.83 assert (zenon_L2731_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> False). % 30.68/30.83 do 0 intro. intros zenon_Hf9 zenon_H1dc zenon_Hcd zenon_H23b zenon_H89 zenon_H90 zenon_H20d zenon_H159 zenon_H16a zenon_H1fd zenon_H113 zenon_H1ab zenon_H122 zenon_H11b zenon_H36 zenon_H1a5 zenon_H6f zenon_H267 zenon_H11e zenon_Hc9 zenon_Hc8 zenon_H27 zenon_H25 zenon_H40 zenon_He1 zenon_H46 zenon_Hfc zenon_Hed zenon_H138 zenon_H101 zenon_Ha4 zenon_H198. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.68/30.83 apply (zenon_L2724_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.68/30.83 apply (zenon_L1354_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.68/30.83 apply (zenon_L2726_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.68/30.83 apply (zenon_L2728_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.68/30.83 apply (zenon_L627_); trivial. % 30.68/30.83 apply (zenon_L538_); trivial. % 30.68/30.83 apply (zenon_L2730_); trivial. % 30.68/30.83 (* end of lemma zenon_L2731_ *) % 30.68/30.83 assert (zenon_L2732_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H222 zenon_H40 zenon_H6f zenon_H25 zenon_H218 zenon_H36 zenon_H16b. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.83 apply (zenon_L273_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.83 apply (zenon_L775_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.83 apply (zenon_L1138_); trivial. % 30.68/30.83 apply (zenon_L1038_); trivial. % 30.68/30.83 (* end of lemma zenon_L2732_ *) % 30.68/30.83 assert (zenon_L2733_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H174 zenon_H16a zenon_H101 zenon_H138 zenon_H159 zenon_H46 zenon_H27 zenon_Hc8 zenon_H11e zenon_Hfc zenon_H267 zenon_H1a5 zenon_H1fd zenon_H20d zenon_H23b zenon_Hcd zenon_Hf9 zenon_H1dc zenon_He9 zenon_H35 zenon_H15a zenon_Hd1 zenon_H173 zenon_H3f zenon_H113 zenon_Ha4 zenon_H198 zenon_H1ab zenon_H122 zenon_H11b zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H222 zenon_H40 zenon_H6f zenon_H25 zenon_H218 zenon_H36. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.83 apply (zenon_L2723_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.83 apply (zenon_L95_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.83 apply (zenon_L2731_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.83 apply (zenon_L80_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.83 apply (zenon_L1834_); trivial. % 30.68/30.83 exact (zenon_H1ab zenon_H112). % 30.68/30.83 apply (zenon_L2728_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L746_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L2722_); trivial. % 30.68/30.83 apply (zenon_L2732_); trivial. % 30.68/30.83 (* end of lemma zenon_L2733_ *) % 30.68/30.83 assert (zenon_L2734_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H101 zenon_H138 zenon_Hda zenon_H198 zenon_Hd2 zenon_Hcd zenon_H46 zenon_He1 zenon_H40. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.83 apply (zenon_L1041_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.83 apply (zenon_L122_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.83 exact (zenon_H46 zenon_H55). % 30.68/30.83 apply (zenon_L1354_); trivial. % 30.68/30.83 (* end of lemma zenon_L2734_ *) % 30.68/30.83 assert (zenon_L2735_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H124 zenon_H65 zenon_H88 zenon_H188 zenon_He1 zenon_H46 zenon_Hcd zenon_H198 zenon_Hda zenon_H138 zenon_H101 zenon_Hd6 zenon_H25 zenon_H6f zenon_H40. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.83 apply (zenon_L1035_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.83 apply (zenon_L2734_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.83 apply (zenon_L46_); trivial. % 30.68/30.83 apply (zenon_L80_); trivial. % 30.68/30.83 (* end of lemma zenon_L2735_ *) % 30.68/30.83 assert (zenon_L2736_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H10d zenon_H36 zenon_H17b zenon_Hb6. % 30.68/30.83 cut (((op (e0) (op (e0) (e3))) = (e3)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 30.68/30.83 intro zenon_D_pnotp. % 30.68/30.83 apply zenon_H10d. % 30.68/30.83 rewrite <- zenon_D_pnotp. % 30.68/30.83 exact zenon_H36. % 30.68/30.83 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 30.68/30.83 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e5]. % 30.68/30.83 congruence. % 30.68/30.83 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H211 | zenon_intro zenon_H10f ]. % 30.68/30.83 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (op (e0) (e3))) = (op (e0) (e2)))). % 30.68/30.83 intro zenon_D_pnotp. % 30.68/30.83 apply zenon_H2e5. % 30.68/30.83 rewrite <- zenon_D_pnotp. % 30.68/30.83 exact zenon_H211. % 30.68/30.83 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 30.68/30.83 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2e4]. % 30.68/30.83 congruence. % 30.68/30.83 apply (zenon_L1140_); trivial. % 30.68/30.83 apply zenon_H10f. apply refl_equal. % 30.68/30.83 apply zenon_H10f. apply refl_equal. % 30.68/30.83 apply zenon_Hb7. apply sym_equal. exact zenon_Hb6. % 30.68/30.83 (* end of lemma zenon_L2736_ *) % 30.68/30.83 assert (zenon_L2737_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e2)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H1fd zenon_H40 zenon_H113 zenon_Ha4 zenon_H198 zenon_H1ab zenon_H122 zenon_H11b zenon_H1a5 zenon_H6f zenon_H25 zenon_H10d zenon_H36 zenon_H17b. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.68/30.83 apply (zenon_L2722_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.68/30.83 apply (zenon_L2725_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.68/30.83 apply (zenon_L1138_); trivial. % 30.68/30.83 apply (zenon_L2736_); trivial. % 30.68/30.83 (* end of lemma zenon_L2737_ *) % 30.68/30.83 assert (zenon_L2738_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H225 zenon_H218 zenon_H222 zenon_Hc9 zenon_H1d5 zenon_H3f zenon_H173 zenon_Hd1 zenon_H15a zenon_H35 zenon_H1dc zenon_Hf9 zenon_H23b zenon_H20d zenon_H267 zenon_Hfc zenon_H11e zenon_Hc8 zenon_H27 zenon_H159 zenon_H16a zenon_H174 zenon_Hd6 zenon_H101 zenon_H138 zenon_Hcd zenon_H46 zenon_He1 zenon_H188 zenon_H88 zenon_H65 zenon_H124 zenon_H1fd zenon_H40 zenon_H113 zenon_Ha4 zenon_H198 zenon_H1ab zenon_H122 zenon_H11b zenon_H1a5 zenon_H6f zenon_H25 zenon_H10d zenon_H36. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.83 apply (zenon_L43_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.83 apply (zenon_L2733_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.83 apply (zenon_L2735_); trivial. % 30.68/30.83 apply (zenon_L2737_); trivial. % 30.68/30.83 (* end of lemma zenon_L2738_ *) % 30.68/30.83 assert (zenon_L2739_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.83 do 0 intro. intros zenon_He4 zenon_Hbd zenon_H20 zenon_H2d zenon_H2d6 zenon_H36 zenon_H10d zenon_H1a5 zenon_H11b zenon_H122 zenon_H198 zenon_Ha4 zenon_H113 zenon_H1fd zenon_H124 zenon_H65 zenon_H88 zenon_H188 zenon_He1 zenon_H46 zenon_H138 zenon_H101 zenon_Hd6 zenon_H174 zenon_H16a zenon_H159 zenon_H27 zenon_Hc8 zenon_H11e zenon_Hfc zenon_H267 zenon_H20d zenon_Hf9 zenon_H35 zenon_H15a zenon_Hd1 zenon_H173 zenon_H3f zenon_H1d5 zenon_H222 zenon_H218 zenon_H225 zenon_H23b zenon_Hcd zenon_H40 zenon_H6f zenon_H25 zenon_H1dc zenon_H1ab. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.83 apply (zenon_L2720_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.83 apply (zenon_L80_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.83 apply (zenon_L1834_); trivial. % 30.68/30.83 exact (zenon_H1ab zenon_H112). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L2723_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L2738_); trivial. % 30.68/30.83 apply (zenon_L2724_); trivial. % 30.68/30.83 (* end of lemma zenon_L2739_ *) % 30.68/30.83 assert (zenon_L2740_ : (((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) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.83 do 0 intro. intros zenon_H23b zenon_H68 zenon_Had zenon_H1f zenon_H188 zenon_H3f zenon_H25 zenon_H1dc zenon_H1ab. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.83 apply (zenon_L639_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.83 apply (zenon_L1159_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.83 apply (zenon_L1834_); trivial. % 30.68/30.83 exact (zenon_H1ab zenon_H112). % 30.68/30.83 (* end of lemma zenon_L2740_ *) % 30.68/30.83 assert (zenon_L2741_ : (((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 (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 30.68/30.83 do 0 intro. intros zenon_H23b zenon_H68 zenon_Had zenon_H40 zenon_H6f zenon_H25 zenon_H1dc zenon_H1ab. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H90 | zenon_intro zenon_H23c ]. % 30.68/30.83 apply (zenon_L639_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H98 | zenon_intro zenon_H23d ]. % 30.68/30.83 apply (zenon_L80_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H112 ]. % 30.68/30.83 apply (zenon_L1834_); trivial. % 30.68/30.83 exact (zenon_H1ab zenon_H112). % 30.68/30.83 (* end of lemma zenon_L2741_ *) % 30.68/30.83 assert (zenon_L2742_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H174 zenon_H16a zenon_H101 zenon_H138 zenon_H159 zenon_H46 zenon_H27 zenon_Hc8 zenon_H11e zenon_Hf9 zenon_H1dc zenon_Hcd zenon_H23b zenon_H90 zenon_H20d zenon_H1fd zenon_H1a5 zenon_H267 zenon_Hfc zenon_He9 zenon_H35 zenon_H15a zenon_Hd1 zenon_H173 zenon_H3f zenon_H113 zenon_Ha4 zenon_H198 zenon_H1ab zenon_H122 zenon_H11b zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H222 zenon_H40 zenon_H6f zenon_H25 zenon_H218 zenon_H36. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.83 apply (zenon_L2723_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.83 apply (zenon_L95_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.83 apply (zenon_L2731_); trivial. % 30.68/30.83 apply (zenon_L2728_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L746_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L2722_); trivial. % 30.68/30.83 apply (zenon_L2732_); trivial. % 30.68/30.83 (* end of lemma zenon_L2742_ *) % 30.68/30.83 assert (zenon_L2743_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H174 zenon_H46 zenon_H159 zenon_Hda zenon_H138 zenon_H101 zenon_Hfc zenon_Hf9 zenon_Hcd zenon_H100 zenon_H10d zenon_H90 zenon_H11e zenon_H15a zenon_H27 zenon_Hd1 zenon_H173 zenon_H3f zenon_H113 zenon_Ha4 zenon_H198 zenon_H1ab zenon_H122 zenon_H11b zenon_H1d5 zenon_He1 zenon_Hc9 zenon_H222 zenon_H40 zenon_H6f zenon_H25 zenon_H218 zenon_H36. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.83 apply (zenon_L2723_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.68/30.83 apply (zenon_L386_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.68/30.83 apply (zenon_L60_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.68/30.83 apply (zenon_L1538_); trivial. % 30.68/30.83 apply (zenon_L538_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.83 apply (zenon_L2729_); trivial. % 30.68/30.83 apply (zenon_L2727_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L746_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L2722_); trivial. % 30.68/30.83 apply (zenon_L2732_); trivial. % 30.68/30.83 (* end of lemma zenon_L2743_ *) % 30.68/30.83 assert (zenon_L2744_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H92 zenon_H65 zenon_H1f zenon_H188 zenon_Had zenon_H6b zenon_H225 zenon_H35 zenon_H267 zenon_H20d zenon_H23b zenon_H1dc zenon_Hc8 zenon_H16a zenon_H218 zenon_H222 zenon_Hc9 zenon_He1 zenon_H1d5 zenon_H3f zenon_H173 zenon_Hd1 zenon_H27 zenon_H15a zenon_H11e zenon_H100 zenon_Hcd zenon_Hf9 zenon_Hfc zenon_H101 zenon_H138 zenon_H159 zenon_H46 zenon_H174 zenon_H1fd zenon_H40 zenon_H113 zenon_Ha4 zenon_H198 zenon_H1ab zenon_H122 zenon_H11b zenon_H1a5 zenon_H6f zenon_H25 zenon_H10d zenon_H36. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 apply (zenon_L1035_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_L2741_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_L17_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.83 apply (zenon_L43_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.83 apply (zenon_L2742_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.83 apply (zenon_L2743_); trivial. % 30.68/30.83 apply (zenon_L2737_); trivial. % 30.68/30.83 (* end of lemma zenon_L2744_ *) % 30.68/30.83 assert (zenon_L2745_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H11b zenon_H6e zenon_H48 zenon_H14e zenon_H1ab zenon_H231 zenon_H110 zenon_Hb6. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.83 apply (zenon_L770_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.83 exact (zenon_H1ab zenon_H112). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.83 exact (zenon_H231 zenon_Hf4). % 30.68/30.83 apply (zenon_L1303_); trivial. % 30.68/30.83 (* end of lemma zenon_L2745_ *) % 30.68/30.83 assert (zenon_L2746_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H11b zenon_H37 zenon_H9d zenon_H1ab zenon_H231 zenon_H110 zenon_Hb6. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.83 apply (zenon_L320_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.83 exact (zenon_H1ab zenon_H112). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.83 exact (zenon_H231 zenon_Hf4). % 30.68/30.83 apply (zenon_L1303_); trivial. % 30.68/30.83 (* end of lemma zenon_L2746_ *) % 30.68/30.83 assert (zenon_L2747_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.68/30.83 do 0 intro. intros zenon_H16f zenon_H14e zenon_H48 zenon_H231 zenon_He1 zenon_H11b zenon_H1ab zenon_H110 zenon_He7 zenon_H73 zenon_Hf9 zenon_Hee zenon_Hb6 zenon_H4e zenon_H16b zenon_H16a. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.83 apply (zenon_L2745_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.68/30.83 apply (zenon_L52_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.68/30.83 apply (zenon_L2746_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.68/30.83 apply (zenon_L204_); trivial. % 30.68/30.83 exact (zenon_H231 zenon_Hf4). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.83 apply (zenon_L490_); trivial. % 30.68/30.83 apply (zenon_L859_); trivial. % 30.68/30.83 (* end of lemma zenon_L2747_ *) % 30.68/30.83 assert (zenon_L2748_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (op (e1) (e0))) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (op (e1) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 30.68/30.83 do 0 intro. intros zenon_H174 zenon_H2d zenon_H1e zenon_H10d zenon_H16f zenon_H14e zenon_H48 zenon_H231 zenon_He1 zenon_H11b zenon_H1ab zenon_H110 zenon_He7 zenon_H73 zenon_Hf9 zenon_Hee zenon_Hb6 zenon_H4e zenon_H16a. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L232_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L151_); trivial. % 30.68/30.83 apply (zenon_L2747_); trivial. % 30.68/30.83 (* end of lemma zenon_L2748_ *) % 30.68/30.83 assert (zenon_L2749_ : (((op (e3) (op (e3) (e0))) = (e0))/\(((op (e3) (op (e3) (e1))) = (e1))/\(((op (e3) (op (e3) (e2))) = (e2))/\(((op (e3) (op (e3) (e3))) = (e3))/\(((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0)))/\(((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1)))/\(((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3)))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 30.68/30.83 do 0 intro. intros zenon_H270 zenon_H110 zenon_Hb5 zenon_Hb6 zenon_H30b zenon_H231 zenon_H11b. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.83 apply (zenon_L37_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.83 apply (zenon_L2329_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.83 exact (zenon_H231 zenon_Hf4). % 30.68/30.83 exact (zenon_Hb9 zenon_Hbc). % 30.68/30.83 apply (zenon_L1303_); trivial. % 30.68/30.83 (* end of lemma zenon_L2749_ *) % 30.68/30.83 assert (zenon_L2750_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 30.68/30.83 do 0 intro. intros zenon_Hf9 zenon_Hde zenon_H8b zenon_Hfd zenon_H100 zenon_Hb6 zenon_He1 zenon_H231. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.68/30.83 apply (zenon_L288_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.68/30.83 apply (zenon_L60_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.68/30.83 apply (zenon_L204_); trivial. % 30.68/30.83 exact (zenon_H231 zenon_Hf4). % 30.68/30.83 (* end of lemma zenon_L2750_ *) % 30.68/30.83 assert (zenon_L2751_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (op (e0) (e2))) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H1a2 zenon_Hfd zenon_H198 zenon_H35 zenon_H28c zenon_H6c zenon_H6b zenon_H6f zenon_Hb6. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.68/30.83 apply (zenon_L2024_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.68/30.83 exact (zenon_H28c zenon_H19a). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.68/30.83 apply (zenon_L17_); trivial. % 30.68/30.83 apply (zenon_L540_); trivial. % 30.68/30.83 (* end of lemma zenon_L2751_ *) % 30.68/30.83 assert (zenon_L2752_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H11b zenon_H122 zenon_H90 zenon_H17d zenon_H231 zenon_H110 zenon_Hb6. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.83 exact (zenon_H122 zenon_Hb1). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.83 apply (zenon_L139_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.83 exact (zenon_H231 zenon_Hf4). % 30.68/30.83 apply (zenon_L1303_); trivial. % 30.68/30.83 (* end of lemma zenon_L2752_ *) % 30.68/30.83 assert (zenon_L2753_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e1)) = (e3)) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H11b zenon_H122 zenon_H2c zenon_H188 zenon_Ha4 zenon_H231 zenon_H110 zenon_Hb6. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.83 exact (zenon_H122 zenon_Hb1). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.83 apply (zenon_L124_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.83 exact (zenon_H231 zenon_Hf4). % 30.68/30.83 apply (zenon_L1303_); trivial. % 30.68/30.83 (* end of lemma zenon_L2753_ *) % 30.68/30.83 assert (zenon_L2754_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 30.68/30.83 do 0 intro. intros zenon_H42 zenon_H110 zenon_H231 zenon_Ha4 zenon_H188 zenon_H122 zenon_H11b zenon_He1 zenon_Hfd zenon_H33 zenon_H36 zenon_H3c zenon_Hb6 zenon_H30b. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.83 apply (zenon_L2753_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.83 apply (zenon_L158_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.83 apply (zenon_L7_); trivial. % 30.68/30.83 apply (zenon_L1806_); trivial. % 30.68/30.83 (* end of lemma zenon_L2754_ *) % 30.68/30.83 assert (zenon_L2755_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H11b zenon_H122 zenon_H89 zenon_He2 zenon_H231 zenon_H110 zenon_Hb6. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.68/30.83 exact (zenon_H122 zenon_Hb1). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.68/30.83 exact (zenon_H231 zenon_Hf4). % 30.68/30.83 apply (zenon_L1303_); trivial. % 30.68/30.83 (* end of lemma zenon_L2755_ *) % 30.68/30.83 assert (zenon_L2756_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H16f zenon_H185 zenon_H15a zenon_He1 zenon_Hfd zenon_Hee zenon_Hb6 zenon_H16a zenon_H36 zenon_H16b. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.83 apply (zenon_L1000_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.83 apply (zenon_L158_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.83 apply (zenon_L490_); trivial. % 30.68/30.83 apply (zenon_L1541_); trivial. % 30.68/30.83 (* end of lemma zenon_L2756_ *) % 30.68/30.83 assert (zenon_L2757_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> ((op (e0) (e3)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H16f zenon_H6f zenon_H68 zenon_He1 zenon_Hfd zenon_Hee zenon_Hb6 zenon_H16a zenon_H36 zenon_H16b. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.83 apply (zenon_L18_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.83 apply (zenon_L158_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.83 apply (zenon_L490_); trivial. % 30.68/30.83 apply (zenon_L1541_); trivial. % 30.68/30.83 (* end of lemma zenon_L2757_ *) % 30.68/30.83 assert (zenon_L2758_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (op (e0) (e3))) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H174 zenon_H218 zenon_H2d6 zenon_H2c1 zenon_H64 zenon_H2b4 zenon_H110 zenon_H231 zenon_Ha4 zenon_H188 zenon_H122 zenon_H11b zenon_H10d zenon_H16f zenon_H6f zenon_H68 zenon_He1 zenon_Hfd zenon_Hee zenon_Hb6 zenon_H16a zenon_H36. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L1564_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L2753_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L151_); trivial. % 30.68/30.83 apply (zenon_L2757_); trivial. % 30.68/30.83 (* end of lemma zenon_L2758_ *) % 30.68/30.83 assert (zenon_L2759_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (op (e0) (e3))) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (op (e0) (e1))) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (op (e0) (e0))) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (op (e0) (e2))) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 30.68/30.83 do 0 intro. intros zenon_H92 zenon_H65 zenon_H1f zenon_H36 zenon_H16a zenon_Hee zenon_He1 zenon_H16f zenon_H10d zenon_H188 zenon_Ha4 zenon_H2b4 zenon_H64 zenon_H2c1 zenon_H2d6 zenon_H218 zenon_H174 zenon_H6f zenon_H6b zenon_H28c zenon_H35 zenon_H198 zenon_Hfd zenon_H1a2 zenon_H11b zenon_H122 zenon_H17d zenon_H231 zenon_H110 zenon_Hb6. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 apply (zenon_L1035_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_L2758_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_L2751_); trivial. % 30.68/30.83 apply (zenon_L2752_); trivial. % 30.68/30.83 (* end of lemma zenon_L2759_ *) % 30.68/30.83 assert (zenon_L2760_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (op (e1) (e2))) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 30.68/30.83 do 0 intro. intros zenon_H2f8 zenon_He2 zenon_H4c zenon_Had zenon_H28c zenon_Hfd zenon_Hfc zenon_Hb6 zenon_Hee. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hfe | zenon_intro zenon_H2f9 ]. % 30.68/30.83 apply (zenon_L742_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H19a | zenon_intro zenon_H2fa ]. % 30.68/30.83 exact (zenon_H28c zenon_H19a). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_Hed | zenon_intro zenon_H15e ]. % 30.68/30.83 apply (zenon_L58_); trivial. % 30.68/30.83 apply (zenon_L490_); trivial. % 30.68/30.83 (* end of lemma zenon_L2760_ *) % 30.68/30.83 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H83. zenon_intro zenon_H319. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H319). zenon_intro zenon_H2d9. zenon_intro zenon_H31a. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H31a). zenon_intro zenon_H11e. zenon_intro zenon_H31b. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H31b). zenon_intro zenon_H2bd. zenon_intro zenon_H31c. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H31c). zenon_intro zenon_H31e. zenon_intro zenon_H31d. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H31d). zenon_intro zenon_H102. zenon_intro zenon_H31f. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H31f). zenon_intro zenon_H2f8. zenon_intro zenon_H320. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H320). zenon_intro zenon_H256. zenon_intro zenon_H321. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H321). zenon_intro zenon_H310. zenon_intro zenon_H322. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H322). zenon_intro zenon_H1ca. zenon_intro zenon_H323. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H323). zenon_intro zenon_H1d2. zenon_intro zenon_H324. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H324). zenon_intro zenon_H1e6. zenon_intro zenon_H325. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H325). zenon_intro zenon_H2fc. zenon_intro zenon_H326. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H326). zenon_intro zenon_Haa. zenon_intro zenon_H327. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H327). zenon_intro zenon_H2b7. zenon_intro zenon_H11b. % 30.68/30.83 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H301. zenon_intro zenon_H328. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H328). zenon_intro zenon_H246. zenon_intro zenon_H329. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H329). zenon_intro zenon_Hc0. zenon_intro zenon_H32a. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H32a). zenon_intro zenon_H92. zenon_intro zenon_H32b. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H32b). zenon_intro zenon_H225. zenon_intro zenon_H32c. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_He4. zenon_intro zenon_H32d. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H32d). zenon_intro zenon_H174. zenon_intro zenon_H32e. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H32e). zenon_intro zenon_H8d. zenon_intro zenon_H32f. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H32f). zenon_intro zenon_H172. zenon_intro zenon_H330. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H330). zenon_intro zenon_H296. zenon_intro zenon_H331. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H331). zenon_intro zenon_H1a8. zenon_intro zenon_H332. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H332). zenon_intro zenon_H124. zenon_intro zenon_H333. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H333). zenon_intro zenon_H173. zenon_intro zenon_H334. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H334). zenon_intro zenon_H101. zenon_intro zenon_H335. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H335). zenon_intro zenon_H16f. zenon_intro zenon_H336. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H336). zenon_intro zenon_H42. zenon_intro zenon_H337. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H337). zenon_intro zenon_H200. zenon_intro zenon_H338. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H338). zenon_intro zenon_H14b. zenon_intro zenon_H339. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H339). zenon_intro zenon_H208. zenon_intro zenon_H33a. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H33a). zenon_intro zenon_H1a2. zenon_intro zenon_H33b. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H33b). zenon_intro zenon_H135. zenon_intro zenon_H33c. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H33c). zenon_intro zenon_H125. zenon_intro zenon_H33d. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H33d). zenon_intro zenon_H1d5. zenon_intro zenon_H33e. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H33e). zenon_intro zenon_H1fd. zenon_intro zenon_H33f. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H33f). zenon_intro zenon_Hbd. zenon_intro zenon_H340. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H340). zenon_intro zenon_H2b4. zenon_intro zenon_H341. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H341). zenon_intro zenon_H23b. zenon_intro zenon_H342. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H342). zenon_intro zenon_H2b1. zenon_intro zenon_H343. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H343). zenon_intro zenon_Hf9. zenon_intro zenon_H344. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H344). zenon_intro zenon_H267. zenon_intro zenon_H345. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H345). zenon_intro zenon_Hb8. zenon_intro zenon_H30d. % 30.68/30.83 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H15a. zenon_intro zenon_H346. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H346). zenon_intro zenon_Hc8. zenon_intro zenon_H347. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H347). zenon_intro zenon_He7. zenon_intro zenon_H348. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H348). zenon_intro zenon_H18c. zenon_intro zenon_H349. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H349). zenon_intro zenon_Had. zenon_intro zenon_H34a. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H34a). zenon_intro zenon_H1d8. zenon_intro zenon_H34b. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H34b). zenon_intro zenon_H35. zenon_intro zenon_H34c. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H34c). zenon_intro zenon_H3c. zenon_intro zenon_H34d. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H34d). zenon_intro zenon_H3f. zenon_intro zenon_H34e. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H34e). zenon_intro zenon_H19e. zenon_intro zenon_H34f. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H34f). zenon_intro zenon_H100. zenon_intro zenon_H350. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H350). zenon_intro zenon_H222. zenon_intro zenon_H351. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H351). zenon_intro zenon_H1a5. zenon_intro zenon_H352. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H352). zenon_intro zenon_H27. zenon_intro zenon_H353. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H353). zenon_intro zenon_H10d. zenon_intro zenon_H354. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H354). zenon_intro zenon_H20e. zenon_intro zenon_H355. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H355). zenon_intro zenon_Hee. zenon_intro zenon_H356. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H356). zenon_intro zenon_H1dc. zenon_intro zenon_H357. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H357). zenon_intro zenon_H16a. zenon_intro zenon_H358. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H358). zenon_intro zenon_H218. zenon_intro zenon_H359. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H359). zenon_intro zenon_Ha4. zenon_intro zenon_H35a. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H35a). zenon_intro zenon_H156. zenon_intro zenon_H35b. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H35b). zenon_intro zenon_H14e. zenon_intro zenon_H35c. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H35c). zenon_intro zenon_Hf6. zenon_intro zenon_H35d. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H35d). zenon_intro zenon_H65. zenon_intro zenon_H35e. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H35e). zenon_intro zenon_Hd9. zenon_intro zenon_H35f. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H35f). zenon_intro zenon_H2c1. zenon_intro zenon_H360. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H360). zenon_intro zenon_H138. zenon_intro zenon_H361. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H361). zenon_intro zenon_H309. zenon_intro zenon_H362. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H362). zenon_intro zenon_H364. zenon_intro zenon_H363. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H363). zenon_intro zenon_Hd1. zenon_intro zenon_H365. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H365). zenon_intro zenon_H1b1. zenon_intro zenon_H366. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H366). zenon_intro zenon_H28f. zenon_intro zenon_H367. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H367). zenon_intro zenon_Hfc. zenon_intro zenon_H368. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H368). zenon_intro zenon_H159. zenon_intro zenon_H369. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H369). zenon_intro zenon_H2b0. zenon_intro zenon_H36a. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H36a). zenon_intro zenon_H1bd. zenon_intro zenon_H36b. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H36b). zenon_intro zenon_H6b. zenon_intro zenon_H36c. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H36c). zenon_intro zenon_H20d. zenon_intro zenon_H36d. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H36d). zenon_intro zenon_Hd6. zenon_intro zenon_H36e. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H36e). zenon_intro zenon_H1c7. zenon_intro zenon_H36f. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H36f). zenon_intro zenon_H108. zenon_intro zenon_H370. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H370). zenon_intro zenon_H97. zenon_intro zenon_H371. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H371). zenon_intro zenon_Hb5. zenon_intro zenon_H372. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H372). zenon_intro zenon_H17d. zenon_intro zenon_H373. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H373). zenon_intro zenon_H30b. zenon_intro zenon_H374. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H374). zenon_intro zenon_H113. zenon_intro zenon_H110. % 30.68/30.83 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H20. zenon_intro zenon_H375. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H375). zenon_intro zenon_Hde. zenon_intro zenon_H376. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H376). zenon_intro zenon_H2d. zenon_intro zenon_H377. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H377). zenon_intro zenon_Hcd. zenon_intro zenon_H378. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H378). zenon_intro zenon_H6f. zenon_intro zenon_He1. % 30.68/30.83 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H37a. zenon_intro zenon_H379. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H37a); [ zenon_intro zenon_H37c | zenon_intro zenon_H37b ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H37c). zenon_intro zenon_H64. zenon_intro zenon_H37d. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H37d). zenon_intro zenon_H1b3. zenon_intro zenon_H37e. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_H64. zenon_intro zenon_H1b3. % 30.68/30.83 exact (zenon_H1b3 zenon_H64). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H37b); [ zenon_intro zenon_H380 | zenon_intro zenon_H37f ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H380). zenon_intro zenon_H64. zenon_intro zenon_H381. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H381). zenon_intro zenon_H1b3. zenon_intro zenon_H382. % 30.68/30.83 exact (zenon_H1b3 zenon_H64). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H37f); [ zenon_intro zenon_H384 | zenon_intro zenon_H383 ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H384). zenon_intro zenon_H64. zenon_intro zenon_H385. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H385). zenon_intro zenon_H1b3. zenon_intro zenon_H386. % 30.68/30.83 exact (zenon_H1b3 zenon_H64). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H383); [ zenon_intro zenon_H388 | zenon_intro zenon_H387 ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H388). zenon_intro zenon_H64. zenon_intro zenon_H389. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H389). zenon_intro zenon_H1b3. zenon_intro zenon_H38a. % 30.68/30.83 exact (zenon_H1b3 zenon_H64). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H387); [ zenon_intro zenon_H38c | zenon_intro zenon_H38b ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H38c). zenon_intro zenon_H1e. zenon_intro zenon_H38d. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H38d). zenon_intro zenon_H84. zenon_intro zenon_H38e. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H38e). zenon_intro zenon_H88. zenon_intro zenon_H317. % 30.68/30.83 exact (zenon_H317 zenon_H1e). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H38b); [ zenon_intro zenon_H390 | zenon_intro zenon_H38f ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H390). zenon_intro zenon_H1e. zenon_intro zenon_H391. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H391). zenon_intro zenon_H84. zenon_intro zenon_H392. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_Hd2. zenon_intro zenon_H18f. % 30.68/30.83 exact (zenon_H18f zenon_Hd2). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H38f); [ zenon_intro zenon_H394 | zenon_intro zenon_H393 ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H394). zenon_intro zenon_H1e. zenon_intro zenon_H395. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H395). zenon_intro zenon_H84. zenon_intro zenon_H396. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H396). zenon_intro zenon_H25. zenon_intro zenon_H46. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.83 apply (zenon_L2_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.83 apply (zenon_L3_); trivial. % 30.68/30.83 apply (zenon_L9_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.68/30.83 apply (zenon_L10_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.68/30.83 apply (zenon_L13_); trivial. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H85 | zenon_intro zenon_H185 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H103 | zenon_intro zenon_H182 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.83 apply (zenon_L14_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.83 apply (zenon_L41_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.83 apply (zenon_L2_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.83 apply (zenon_L3_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 exact (zenon_H85 zenon_H89). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 exact (zenon_H85 zenon_H89). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_L18_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_L23_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.83 apply (zenon_L16_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.83 apply (zenon_L42_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.83 apply (zenon_L74_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.83 apply (zenon_L2_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.83 apply (zenon_L45_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.83 apply (zenon_L46_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.83 apply (zenon_L48_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.83 apply (zenon_L83_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.83 apply (zenon_L86_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.83 apply (zenon_L92_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.83 apply (zenon_L93_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.83 exact (zenon_H46 zenon_H55). % 30.68/30.83 apply (zenon_L85_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 exact (zenon_H85 zenon_H89). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_L18_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_L24_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.83 apply (zenon_L41_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.83 apply (zenon_L42_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.83 apply (zenon_L74_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.83 apply (zenon_L2_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.83 apply (zenon_L45_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.83 apply (zenon_L46_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.83 apply (zenon_L94_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.83 apply (zenon_L83_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.83 apply (zenon_L104_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.83 apply (zenon_L58_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.83 exact (zenon_H46 zenon_H55). % 30.68/30.83 apply (zenon_L85_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.83 apply (zenon_L102_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.83 apply (zenon_L93_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.83 exact (zenon_H46 zenon_H55). % 30.68/30.83 apply (zenon_L85_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.83 apply (zenon_L104_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.83 apply (zenon_L105_); trivial. % 30.68/30.83 apply (zenon_L106_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_L17_); trivial. % 30.68/30.83 apply (zenon_L40_); trivial. % 30.68/30.83 apply (zenon_L28_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.83 apply (zenon_L14_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.83 apply (zenon_L109_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.83 apply (zenon_L2_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.83 apply (zenon_L3_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.83 apply (zenon_L111_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.83 apply (zenon_L114_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.83 apply (zenon_L105_); trivial. % 30.68/30.83 apply (zenon_L106_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_L17_); trivial. % 30.68/30.83 apply (zenon_L108_); trivial. % 30.68/30.83 apply (zenon_L28_); trivial. % 30.68/30.83 apply (zenon_L116_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.83 apply (zenon_L2_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.83 apply (zenon_L3_); trivial. % 30.68/30.83 apply (zenon_L117_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H393); [ zenon_intro zenon_H39a | zenon_intro zenon_H399 ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H39a). zenon_intro zenon_H1e. zenon_intro zenon_H39b. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H39b). zenon_intro zenon_H84. zenon_intro zenon_H39c. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H39c). zenon_intro zenon_H112. zenon_intro zenon_H18e. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H19f | zenon_intro zenon_H68 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.83 apply (zenon_L2_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_L119_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_L138_); trivial. % 30.68/30.83 apply (zenon_L139_); trivial. % 30.68/30.83 apply (zenon_L140_); trivial. % 30.68/30.83 apply (zenon_L119_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.68/30.83 apply (zenon_L141_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.68/30.83 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H29b); [ zenon_intro zenon_H74 | zenon_intro zenon_H10e ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H13b | zenon_intro zenon_H19a ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L453_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L583_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L584_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_L18_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.83 apply (zenon_L590_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.83 apply (zenon_L42_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.83 apply (zenon_L596_); trivial. % 30.68/30.83 apply (zenon_L393_); trivial. % 30.68/30.83 apply (zenon_L50_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.83 apply (zenon_L587_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L453_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L580_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L385_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.83 apply (zenon_L588_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.83 apply (zenon_L42_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.83 apply (zenon_L597_); trivial. % 30.68/30.83 apply (zenon_L393_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_L157_); trivial. % 30.68/30.83 apply (zenon_L50_); trivial. % 30.68/30.83 apply (zenon_L589_); trivial. % 30.68/30.83 apply (zenon_L139_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L48_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L148_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L598_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 apply (zenon_L148_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_L18_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_L273_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.83 apply (zenon_L602_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.83 apply (zenon_L42_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.83 apply (zenon_L583_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.83 apply (zenon_L45_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.83 apply (zenon_L607_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.83 apply (zenon_L608_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.83 apply (zenon_L350_); trivial. % 30.68/30.83 apply (zenon_L186_); trivial. % 30.68/30.83 apply (zenon_L609_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.83 apply (zenon_L611_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.83 apply (zenon_L458_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.83 apply (zenon_L372_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.83 apply (zenon_L608_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.83 apply (zenon_L174_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.83 apply (zenon_L455_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.83 apply (zenon_L370_); trivial. % 30.68/30.83 apply (zenon_L245_); trivial. % 30.68/30.83 apply (zenon_L186_); trivial. % 30.68/30.83 apply (zenon_L609_); trivial. % 30.68/30.83 apply (zenon_L614_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L453_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L148_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L598_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 apply (zenon_L148_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_L18_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_L273_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.83 apply (zenon_L615_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.83 apply (zenon_L42_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.83 apply (zenon_L583_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.83 apply (zenon_L45_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.83 apply (zenon_L300_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.83 exact (zenon_H13b zenon_Hfd). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.83 apply (zenon_L212_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.83 apply (zenon_L34_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.83 apply (zenon_L617_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.83 apply (zenon_L618_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.83 apply (zenon_L350_); trivial. % 30.68/30.83 apply (zenon_L186_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.83 apply (zenon_L610_); trivial. % 30.68/30.83 apply (zenon_L101_); trivial. % 30.68/30.83 apply (zenon_L609_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.83 apply (zenon_L583_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.83 apply (zenon_L458_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.83 apply (zenon_L300_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.83 exact (zenon_H13b zenon_Hfd). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.83 apply (zenon_L282_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.83 apply (zenon_L619_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.83 apply (zenon_L608_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.68/30.83 apply (zenon_L595_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.68/30.83 apply (zenon_L455_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.68/30.83 apply (zenon_L370_); trivial. % 30.68/30.83 apply (zenon_L245_); trivial. % 30.68/30.83 apply (zenon_L186_); trivial. % 30.68/30.83 apply (zenon_L609_); trivial. % 30.68/30.83 apply (zenon_L614_); trivial. % 30.68/30.83 apply (zenon_L620_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_L601_); trivial. % 30.68/30.83 apply (zenon_L139_); trivial. % 30.68/30.83 apply (zenon_L140_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.83 apply (zenon_L615_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L48_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L583_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L584_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_L18_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_L606_); trivial. % 30.68/30.83 apply (zenon_L50_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L453_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L580_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L378_); trivial. % 30.68/30.83 apply (zenon_L586_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L453_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L49_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.83 apply (zenon_L120_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.83 apply (zenon_L585_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.83 apply (zenon_L448_); trivial. % 30.68/30.83 apply (zenon_L137_); trivial. % 30.68/30.83 apply (zenon_L589_); trivial. % 30.68/30.83 apply (zenon_L139_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.83 apply (zenon_L607_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L48_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L49_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L598_); trivial. % 30.68/30.83 apply (zenon_L616_); trivial. % 30.68/30.83 apply (zenon_L622_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_L601_); trivial. % 30.68/30.83 apply (zenon_L139_); trivial. % 30.68/30.83 apply (zenon_L140_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L48_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L583_); trivial. % 30.68/30.83 apply (zenon_L288_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.83 apply (zenon_L120_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.83 apply (zenon_L146_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.83 apply (zenon_L451_); trivial. % 30.68/30.83 apply (zenon_L137_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L580_); trivial. % 30.68/30.83 apply (zenon_L288_); trivial. % 30.68/30.83 apply (zenon_L139_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L48_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.83 apply (zenon_L457_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.83 apply (zenon_L458_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.83 apply (zenon_L631_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.83 apply (zenon_L456_); trivial. % 30.68/30.83 exact (zenon_H18e zenon_H40). % 30.68/30.83 apply (zenon_L609_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L598_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.83 apply (zenon_L611_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.83 apply (zenon_L45_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.83 apply (zenon_L241_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.83 apply (zenon_L631_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.83 apply (zenon_L610_); trivial. % 30.68/30.83 apply (zenon_L101_); trivial. % 30.68/30.83 apply (zenon_L609_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_L18_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_L273_); trivial. % 30.68/30.83 apply (zenon_L25_); trivial. % 30.68/30.83 apply (zenon_L288_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L48_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.83 apply (zenon_L633_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.83 apply (zenon_L456_); trivial. % 30.68/30.83 exact (zenon_H18e zenon_H40). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L598_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.83 apply (zenon_L241_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.83 apply (zenon_L633_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.83 apply (zenon_L610_); trivial. % 30.68/30.83 apply (zenon_L101_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_L18_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_L273_); trivial. % 30.68/30.83 apply (zenon_L25_); trivial. % 30.68/30.83 apply (zenon_L288_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L48_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.83 apply (zenon_L49_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.83 apply (zenon_L207_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.83 apply (zenon_L626_); trivial. % 30.68/30.83 apply (zenon_L638_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.83 apply (zenon_L456_); trivial. % 30.68/30.83 exact (zenon_H18e zenon_H40). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L598_); trivial. % 30.68/30.83 apply (zenon_L267_); trivial. % 30.68/30.83 apply (zenon_L621_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_L601_); trivial. % 30.68/30.83 apply (zenon_L27_); trivial. % 30.68/30.83 apply (zenon_L140_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L48_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L642_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L584_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.83 apply (zenon_L16_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.83 apply (zenon_L42_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.83 apply (zenon_L645_); trivial. % 30.68/30.83 apply (zenon_L393_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L646_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L580_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L385_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.83 apply (zenon_L647_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.83 apply (zenon_L42_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.83 apply (zenon_L645_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.83 apply (zenon_L585_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.83 apply (zenon_L485_); trivial. % 30.68/30.83 apply (zenon_L137_); trivial. % 30.68/30.83 apply (zenon_L393_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_L157_); trivial. % 30.68/30.83 apply (zenon_L50_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L646_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L580_); trivial. % 30.68/30.83 apply (zenon_L648_); trivial. % 30.68/30.83 apply (zenon_L649_); trivial. % 30.68/30.83 apply (zenon_L139_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.83 exact (zenon_H74 zenon_H73). % 30.68/30.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.83 apply (zenon_L48_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.83 apply (zenon_L650_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.83 apply (zenon_L4_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.83 apply (zenon_L598_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.83 apply (zenon_L252_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.83 apply (zenon_L600_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.83 apply (zenon_L651_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.83 apply (zenon_L42_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.83 apply (zenon_L645_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.83 apply (zenon_L585_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.83 apply (zenon_L600_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.83 apply (zenon_L652_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.83 apply (zenon_L608_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.83 apply (zenon_L350_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.68/30.83 apply (zenon_L653_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.68/30.83 apply (zenon_L603_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.68/30.83 exact (zenon_Hd0 zenon_Hcc). % 30.68/30.83 apply (zenon_L193_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.83 apply (zenon_L490_); trivial. % 30.68/30.83 apply (zenon_L101_); trivial. % 30.68/30.83 apply (zenon_L654_); trivial. % 30.68/30.83 apply (zenon_L393_); trivial. % 30.68/30.83 apply (zenon_L461_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.83 apply (zenon_L601_); trivial. % 30.68/30.83 apply (zenon_L139_); trivial. % 30.68/30.83 apply (zenon_L140_); trivial. % 30.68/30.83 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.83 exact (zenon_H84 zenon_H88). % 30.68/30.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L641_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 apply (zenon_L146_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L498_); trivial. % 30.68/30.84 apply (zenon_L137_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L580_); trivial. % 30.68/30.84 apply (zenon_L647_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L120_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 apply (zenon_L146_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L500_); trivial. % 30.68/30.84 apply (zenon_L137_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L18_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 apply (zenon_L146_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L501_); trivial. % 30.68/30.84 apply (zenon_L137_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L157_); trivial. % 30.68/30.84 apply (zenon_L461_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L580_); trivial. % 30.68/30.84 apply (zenon_L648_); trivial. % 30.68/30.84 apply (zenon_L649_); trivial. % 30.68/30.84 apply (zenon_L139_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_L651_); trivial. % 30.68/30.84 apply (zenon_L140_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L655_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L656_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L349_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L657_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 apply (zenon_L146_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L231_); trivial. % 30.68/30.84 apply (zenon_L658_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L660_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L157_); trivial. % 30.68/30.84 apply (zenon_L461_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L580_); trivial. % 30.68/30.84 apply (zenon_L661_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L656_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L42_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L657_); trivial. % 30.68/30.84 apply (zenon_L662_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L49_); trivial. % 30.68/30.84 apply (zenon_L648_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L656_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L42_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L663_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L120_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 apply (zenon_L146_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L664_); trivial. % 30.68/30.84 apply (zenon_L658_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L151_); trivial. % 30.68/30.84 apply (zenon_L267_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L580_); trivial. % 30.68/30.84 apply (zenon_L472_); trivial. % 30.68/30.84 apply (zenon_L139_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L655_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L599_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L580_); trivial. % 30.68/30.84 apply (zenon_L661_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L599_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L49_); trivial. % 30.68/30.84 apply (zenon_L648_); trivial. % 30.68/30.84 apply (zenon_L665_); trivial. % 30.68/30.84 apply (zenon_L139_); trivial. % 30.68/30.84 apply (zenon_L140_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L642_); trivial. % 30.68/30.84 apply (zenon_L288_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L666_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L580_); trivial. % 30.68/30.84 apply (zenon_L288_); trivial. % 30.68/30.84 apply (zenon_L139_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L42_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.84 apply (zenon_L641_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.84 apply (zenon_L458_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.84 apply (zenon_L667_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.84 apply (zenon_L456_); trivial. % 30.68/30.84 exact (zenon_H18e zenon_H40). % 30.68/30.84 apply (zenon_L609_); trivial. % 30.68/30.84 apply (zenon_L669_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L598_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L382_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.84 apply (zenon_L641_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.84 apply (zenon_L45_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L241_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_L667_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_L490_); trivial. % 30.68/30.84 apply (zenon_L101_); trivial. % 30.68/30.84 apply (zenon_L654_); trivial. % 30.68/30.84 apply (zenon_L669_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L18_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L273_); trivial. % 30.68/30.84 apply (zenon_L25_); trivial. % 30.68/30.84 apply (zenon_L288_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.84 apply (zenon_L673_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.84 apply (zenon_L458_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.84 apply (zenon_L674_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.84 apply (zenon_L456_); trivial. % 30.68/30.84 exact (zenon_H18e zenon_H40). % 30.68/30.84 apply (zenon_L609_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L151_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.84 apply (zenon_L641_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.84 exact (zenon_H13b zenon_Hfd). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.84 apply (zenon_L282_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L18_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_L671_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_L490_); trivial. % 30.68/30.84 apply (zenon_L101_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.84 apply (zenon_L458_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L241_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_L674_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_L490_); trivial. % 30.68/30.84 apply (zenon_L101_); trivial. % 30.68/30.84 apply (zenon_L609_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L18_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L273_); trivial. % 30.68/30.84 apply (zenon_L461_); trivial. % 30.68/30.84 apply (zenon_L288_); trivial. % 30.68/30.84 apply (zenon_L681_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_L682_); trivial. % 30.68/30.84 apply (zenon_L27_); trivial. % 30.68/30.84 apply (zenon_L140_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L552_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L252_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L584_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L252_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L684_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L686_); trivial. % 30.68/30.84 apply (zenon_L50_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L554_); trivial. % 30.68/30.84 apply (zenon_L687_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L707_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L709_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L707_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L684_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L157_); trivial. % 30.68/30.84 apply (zenon_L568_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L554_); trivial. % 30.68/30.84 apply (zenon_L714_); trivial. % 30.68/30.84 apply (zenon_L139_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L552_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L252_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L584_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L252_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L18_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L717_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L42_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.84 apply (zenon_L686_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.84 apply (zenon_L683_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L696_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_L705_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_L685_); trivial. % 30.68/30.84 apply (zenon_L101_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L18_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_L718_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_L685_); trivial. % 30.68/30.84 apply (zenon_L101_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L696_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_L392_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_L685_); trivial. % 30.68/30.84 apply (zenon_L101_); trivial. % 30.68/30.84 apply (zenon_L568_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L554_); trivial. % 30.68/30.84 apply (zenon_L715_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_L716_); trivial. % 30.68/30.84 apply (zenon_L139_); trivial. % 30.68/30.84 apply (zenon_L140_); trivial. % 30.68/30.84 apply (zenon_L706_); trivial. % 30.68/30.84 apply (zenon_L579_); trivial. % 30.68/30.84 apply (zenon_L75_); trivial. % 30.68/30.84 apply (zenon_L723_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H399); [ zenon_intro zenon_H39e | zenon_intro zenon_H39d ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H39e). zenon_intro zenon_H10e. zenon_intro zenon_H39f. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H39f). zenon_intro zenon_H74. zenon_intro zenon_H3a0. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3a0). zenon_intro zenon_H73. zenon_intro zenon_H304. % 30.68/30.84 exact (zenon_H304 zenon_H10e). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H39d); [ zenon_intro zenon_H3a2 | zenon_intro zenon_H3a1 ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3a2). zenon_intro zenon_H10e. zenon_intro zenon_H3a3. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3a3). zenon_intro zenon_H74. zenon_intro zenon_H3a4. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3a4). zenon_intro zenon_Hfd. zenon_intro zenon_H28c. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L725_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L726_); trivial. % 30.68/30.84 apply (zenon_L727_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_L242_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L120_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 exact (zenon_H18f zenon_Hd2). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 exact (zenon_H28c zenon_H19a). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L729_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_L158_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.84 apply (zenon_L730_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.84 apply (zenon_L203_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.84 apply (zenon_L731_); trivial. % 30.68/30.84 apply (zenon_L732_); trivial. % 30.68/30.84 apply (zenon_L733_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_L95_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L192_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L154_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 exact (zenon_H18f zenon_Hd2). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 exact (zenon_H28c zenon_H19a). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L729_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_L158_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.68/30.84 apply (zenon_L730_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.68/30.84 apply (zenon_L203_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.68/30.84 apply (zenon_L731_); trivial. % 30.68/30.84 apply (zenon_L781_); trivial. % 30.68/30.84 apply (zenon_L758_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L639_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 exact (zenon_H18f zenon_Hd2). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 exact (zenon_H28c zenon_H19a). % 30.68/30.84 apply (zenon_L730_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_L267_); trivial. % 30.68/30.84 apply (zenon_L386_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L154_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L49_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L740_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L782_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L742_); trivial. % 30.68/30.84 apply (zenon_L783_); trivial. % 30.68/30.84 apply (zenon_L786_); trivial. % 30.68/30.84 apply (zenon_L787_); trivial. % 30.68/30.84 apply (zenon_L122_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_L242_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_L768_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_L95_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L192_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L154_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L49_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L745_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_L267_); trivial. % 30.68/30.84 apply (zenon_L790_); trivial. % 30.68/30.84 apply (zenon_L787_); trivial. % 30.68/30.84 apply (zenon_L122_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.68/30.84 apply (zenon_L791_); trivial. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H85 | zenon_intro zenon_H185 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_L242_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L808_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_L810_); trivial. % 30.68/30.84 apply (zenon_L811_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_L813_); trivial. % 30.68/30.84 apply (zenon_L814_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_L242_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L815_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_L816_); trivial. % 30.68/30.84 apply (zenon_L811_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_L813_); trivial. % 30.68/30.84 apply (zenon_L814_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_L95_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L192_); trivial. % 30.68/30.84 apply (zenon_L817_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H3a1); [ zenon_intro zenon_H3a6 | zenon_intro zenon_H3a5 ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3a6). zenon_intro zenon_H10e. zenon_intro zenon_H3a7. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3a7). zenon_intro zenon_H74. zenon_intro zenon_H3a8. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3a8). zenon_intro zenon_Hcc. zenon_intro zenon_Hd0. % 30.68/30.84 exact (zenon_Hd0 zenon_Hcc). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H3a5); [ zenon_intro zenon_H3aa | zenon_intro zenon_H3a9 ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3aa). zenon_intro zenon_H10e. zenon_intro zenon_H3ab. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3ab). zenon_intro zenon_H74. zenon_intro zenon_H3ac. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3ac). zenon_intro zenon_Hf4. zenon_intro zenon_H2a9. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_L818_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L192_); trivial. % 30.68/30.84 apply (zenon_L819_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_L242_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L822_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L120_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 exact (zenon_H18f zenon_Hd2). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L831_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L729_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_L846_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_L752_); trivial. % 30.68/30.84 apply (zenon_L733_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L192_); trivial. % 30.68/30.84 apply (zenon_L819_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L822_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L639_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 exact (zenon_H18f zenon_Hd2). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L831_); trivial. % 30.68/30.84 apply (zenon_L730_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_L851_); trivial. % 30.68/30.84 apply (zenon_L386_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L192_); trivial. % 30.68/30.84 apply (zenon_L819_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_L852_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L833_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L855_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L785_); trivial. % 30.68/30.84 apply (zenon_L288_); trivial. % 30.68/30.84 apply (zenon_L27_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_L242_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L120_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 exact (zenon_H18f zenon_Hd2). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.68/30.84 apply (zenon_L826_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.68/30.84 apply (zenon_L95_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.68/30.84 apply (zenon_L159_); trivial. % 30.68/30.84 apply (zenon_L857_); trivial. % 30.68/30.84 apply (zenon_L858_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L746_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_L863_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L192_); trivial. % 30.68/30.84 apply (zenon_L819_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L822_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L746_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_L851_); trivial. % 30.68/30.84 apply (zenon_L386_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_L852_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L833_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L765_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L746_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L765_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L861_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L866_); trivial. % 30.68/30.84 apply (zenon_L25_); trivial. % 30.68/30.84 apply (zenon_L27_); trivial. % 30.68/30.84 apply (zenon_L820_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_L242_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_L868_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L45_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L822_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L879_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L879_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L891_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L273_); trivial. % 30.68/30.84 apply (zenon_L892_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L893_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L850_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L894_); trivial. % 30.68/30.84 apply (zenon_L895_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L822_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L891_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L273_); trivial. % 30.68/30.84 apply (zenon_L892_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L598_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L850_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L894_); trivial. % 30.68/30.84 apply (zenon_L895_); trivial. % 30.68/30.84 apply (zenon_L386_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L822_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L879_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L883_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L273_); trivial. % 30.68/30.84 apply (zenon_L354_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_L896_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_L852_); trivial. % 30.68/30.84 apply (zenon_L885_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_L868_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L45_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L822_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L899_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L763_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L784_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.68/30.84 apply (zenon_L901_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.68/30.84 apply (zenon_L766_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.68/30.84 apply (zenon_L63_); trivial. % 30.68/30.84 apply (zenon_L84_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_L898_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L822_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L148_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L746_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_L903_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_L905_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_L910_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_L868_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_L901_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 exact (zenon_H84 zenon_H88). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L45_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L749_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L906_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L764_); trivial. % 30.68/30.84 apply (zenon_L908_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L765_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L746_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L893_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L911_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L894_); trivial. % 30.68/30.84 apply (zenon_L25_); trivial. % 30.68/30.84 apply (zenon_L288_); trivial. % 30.68/30.84 apply (zenon_L27_); trivial. % 30.68/30.84 apply (zenon_L820_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L912_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L148_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L738_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L273_); trivial. % 30.68/30.84 apply (zenon_L914_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L148_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L148_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L915_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L42_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L764_); trivial. % 30.68/30.84 apply (zenon_L916_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L157_); trivial. % 30.68/30.84 apply (zenon_L921_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L148_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L928_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L738_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L273_); trivial. % 30.68/30.84 apply (zenon_L921_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L192_); trivial. % 30.68/30.84 apply (zenon_L819_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L915_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L769_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L764_); trivial. % 30.68/30.84 apply (zenon_L916_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L935_); trivial. % 30.68/30.84 apply (zenon_L39_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L931_); trivial. % 30.68/30.84 apply (zenon_L386_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 exact (zenon_H18f zenon_Hd2). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L826_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L729_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_L937_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_L752_); trivial. % 30.68/30.84 apply (zenon_L733_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L734_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L734_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L738_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L273_); trivial. % 30.68/30.84 apply (zenon_L947_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L950_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L950_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L915_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L157_); trivial. % 30.68/30.84 apply (zenon_L921_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 exact (zenon_H18f zenon_Hd2). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L924_); trivial. % 30.68/30.84 apply (zenon_L951_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L928_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L738_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L273_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 exact (zenon_H18f zenon_Hd2). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L917_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.68/30.84 apply (zenon_L34_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.84 apply (zenon_L918_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.84 apply (zenon_L207_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.84 apply (zenon_L939_); trivial. % 30.68/30.84 apply (zenon_L919_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.68/30.84 apply (zenon_L752_); trivial. % 30.68/30.84 apply (zenon_L859_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L192_); trivial. % 30.68/30.84 apply (zenon_L819_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L915_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L935_); trivial. % 30.68/30.84 apply (zenon_L39_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L931_); trivial. % 30.68/30.84 apply (zenon_L386_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_L956_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L946_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L957_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L855_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L789_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_L27_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L912_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L148_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L746_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L958_); trivial. % 30.68/30.84 apply (zenon_L959_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_L967_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L971_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L769_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L764_); trivial. % 30.68/30.84 apply (zenon_L908_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L931_); trivial. % 30.68/30.84 apply (zenon_L386_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L734_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 apply (zenon_L734_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L18_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 exact (zenon_H18f zenon_Hd2). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L969_); trivial. % 30.68/30.84 apply (zenon_L729_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L866_); trivial. % 30.68/30.84 apply (zenon_L862_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_L967_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 apply (zenon_L538_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L4_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_L87_); trivial. % 30.68/30.84 apply (zenon_L971_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L740_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L42_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L764_); trivial. % 30.68/30.84 apply (zenon_L908_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L49_); trivial. % 30.68/30.84 apply (zenon_L847_); trivial. % 30.68/30.84 apply (zenon_L972_); trivial. % 30.68/30.84 apply (zenon_L820_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 apply (zenon_L979_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_L868_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_L984_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L940_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L45_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_L990_); trivial. % 30.68/30.84 apply (zenon_L993_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.68/30.84 apply (zenon_L994_); trivial. % 30.68/30.84 apply (zenon_L997_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H3a9); [ zenon_intro zenon_H3ae | zenon_intro zenon_H3ad ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3ae). zenon_intro zenon_H185. zenon_intro zenon_H3af. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3af). zenon_intro zenon_H85. zenon_intro zenon_H3b0. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3b0). zenon_intro zenon_H89. zenon_intro zenon_H30a. % 30.68/30.84 exact (zenon_H30a zenon_H185). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H3ad); [ zenon_intro zenon_H3b2 | zenon_intro zenon_H3b1 ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3b2). zenon_intro zenon_H185. zenon_intro zenon_H3b3. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3b3). zenon_intro zenon_H85. zenon_intro zenon_H3b4. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H3b4). zenon_intro zenon_H37. zenon_intro zenon_H2cc. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H64 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 exact (zenon_H1b3 zenon_H64). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 apply (zenon_L998_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 apply (zenon_L998_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L1013_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L1027_); trivial. % 30.68/30.84 apply (zenon_L1028_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L1033_); trivial. % 30.68/30.84 apply (zenon_L817_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L1035_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_L1045_); trivial. % 30.68/30.84 apply (zenon_L1046_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_L1047_); trivial. % 30.68/30.84 apply (zenon_L6_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 apply (zenon_L998_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 apply (zenon_L998_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L1013_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L49_); trivial. % 30.68/30.84 apply (zenon_L1028_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_L1033_); trivial. % 30.68/30.84 apply (zenon_L817_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L1035_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L1023_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_L1045_); trivial. % 30.68/30.84 apply (zenon_L1046_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_L1047_); trivial. % 30.68/30.84 apply (zenon_L117_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 apply (zenon_L1024_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_L1048_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 apply (zenon_L47_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L937_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L1032_); trivial. % 30.68/30.84 apply (zenon_L288_); trivial. % 30.68/30.84 apply (zenon_L817_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L1035_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L1025_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 apply (zenon_L1024_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_L1048_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 apply (zenon_L47_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L1002_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L1000_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L157_); trivial. % 30.68/30.84 apply (zenon_L1042_); trivial. % 30.68/30.84 apply (zenon_L848_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L1032_); trivial. % 30.68/30.84 apply (zenon_L288_); trivial. % 30.68/30.84 apply (zenon_L817_); trivial. % 30.68/30.84 apply (zenon_L27_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_L1047_); trivial. % 30.68/30.84 apply (zenon_L6_); trivial. % 30.68/30.84 apply (zenon_L1050_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.68/30.84 apply (zenon_L1051_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.68/30.84 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H29b); [ zenon_intro zenon_H74 | zenon_intro zenon_H10e ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H13b | zenon_intro zenon_H19a ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 apply (zenon_L912_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L912_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L1002_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L1052_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L273_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L1071_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L364_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.84 apply (zenon_L454_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.84 exact (zenon_H13b zenon_Hfd). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.84 apply (zenon_L282_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.68/30.84 apply (zenon_L444_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.68/30.84 apply (zenon_L618_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.68/30.84 apply (zenon_L350_); trivial. % 30.68/30.84 apply (zenon_L186_); trivial. % 30.68/30.84 apply (zenon_L886_); trivial. % 30.68/30.84 apply (zenon_L848_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L1002_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L18_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L1115_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L364_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.68/30.84 apply (zenon_L1116_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.68/30.84 exact (zenon_H13b zenon_Hfd). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.68/30.84 apply (zenon_L603_); trivial. % 30.68/30.84 apply (zenon_L257_); trivial. % 30.68/30.84 apply (zenon_L886_); trivial. % 30.68/30.84 apply (zenon_L50_); trivial. % 30.68/30.84 apply (zenon_L848_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L1002_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L1071_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L364_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L173_); trivial. % 30.68/30.84 apply (zenon_L886_); trivial. % 30.68/30.84 apply (zenon_L848_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L1002_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L1052_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 apply (zenon_L125_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L263_); trivial. % 30.68/30.84 exact (zenon_H2cc zenon_H182). % 30.68/30.84 apply (zenon_L39_); trivial. % 30.68/30.84 apply (zenon_L848_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L1065_); trivial. % 30.68/30.84 apply (zenon_L386_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_L1047_); trivial. % 30.68/30.84 apply (zenon_L117_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.68/30.84 apply (zenon_L1115_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L937_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L49_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L1002_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L1052_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_L16_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 apply (zenon_L125_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L1095_); trivial. % 30.68/30.84 exact (zenon_H2cc zenon_H182). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L364_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.84 apply (zenon_L1118_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.84 apply (zenon_L125_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.84 apply (zenon_L1121_); trivial. % 30.68/30.84 apply (zenon_L612_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 apply (zenon_L125_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L1078_); trivial. % 30.68/30.84 exact (zenon_H2cc zenon_H182). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.68/30.84 apply (zenon_L59_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.84 apply (zenon_L1118_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.84 apply (zenon_L125_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.84 apply (zenon_L608_); trivial. % 30.68/30.84 apply (zenon_L612_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 apply (zenon_L125_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L1103_); trivial. % 30.68/30.84 exact (zenon_H2cc zenon_H182). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.68/30.84 apply (zenon_L1118_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.68/30.84 apply (zenon_L125_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.68/30.84 apply (zenon_L1122_); trivial. % 30.68/30.84 apply (zenon_L718_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.68/30.84 apply (zenon_L125_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.68/30.84 apply (zenon_L1083_); trivial. % 30.68/30.84 exact (zenon_H2cc zenon_H182). % 30.68/30.84 apply (zenon_L886_); trivial. % 30.68/30.84 apply (zenon_L50_); trivial. % 30.68/30.84 apply (zenon_L848_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.68/30.84 apply (zenon_L1089_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L1002_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L1052_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.68/30.84 apply (zenon_L1071_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.68/30.84 apply (zenon_L364_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.68/30.84 apply (zenon_L1117_); trivial. % 30.68/30.84 apply (zenon_L886_); trivial. % 30.68/30.84 apply (zenon_L1096_); trivial. % 30.68/30.84 apply (zenon_L848_); trivial. % 30.68/30.84 apply (zenon_L817_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.68/30.84 apply (zenon_L1047_); trivial. % 30.68/30.84 apply (zenon_L117_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L937_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L1123_); trivial. % 30.68/30.84 apply (zenon_L288_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.68/30.84 exact (zenon_H74 zenon_H73). % 30.68/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.68/30.84 apply (zenon_L48_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.68/30.84 apply (zenon_L1123_); trivial. % 30.68/30.84 apply (zenon_L288_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.68/30.84 apply (zenon_L1002_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.68/30.84 exact (zenon_H85 zenon_H89). % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.68/30.84 apply (zenon_L1052_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.68/30.84 apply (zenon_L157_); trivial. % 30.68/30.84 apply (zenon_L25_); trivial. % 30.68/30.84 apply (zenon_L848_); trivial. % 30.68/30.84 apply (zenon_L27_); trivial. % 30.68/30.84 apply (zenon_L1104_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.68/30.84 apply (zenon_L1128_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.68/30.84 apply (zenon_L1128_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.68/30.84 apply (zenon_L1124_); trivial. % 30.68/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.68/30.84 apply (zenon_L1129_); trivial. % 30.80/30.84 apply (zenon_L1106_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_L1047_); trivial. % 30.80/30.84 apply (zenon_L117_); trivial. % 30.80/30.84 apply (zenon_L1104_); trivial. % 30.80/30.84 apply (zenon_L1114_); trivial. % 30.80/30.84 apply (zenon_L1091_); trivial. % 30.80/30.84 apply (zenon_L1130_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3b1); [ zenon_intro zenon_H3b6 | zenon_intro zenon_H3b5 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3b6). zenon_intro zenon_H185. zenon_intro zenon_H3b7. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3b7). zenon_intro zenon_H85. zenon_intro zenon_H3b8. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3b8). zenon_intro zenon_H1b9. zenon_intro zenon_H2e6. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H64 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H19f | zenon_intro zenon_H68 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.80/30.84 exact (zenon_H1b3 zenon_H64). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 apply (zenon_L1169_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_L1171_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_L1165_); trivial. % 30.80/30.84 apply (zenon_L117_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 apply (zenon_L1169_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_L1171_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.84 apply (zenon_L797_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.84 apply (zenon_L1154_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.84 apply (zenon_L1164_); trivial. % 30.80/30.84 apply (zenon_L1046_); trivial. % 30.80/30.84 apply (zenon_L117_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 apply (zenon_L1024_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L1024_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L1148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L1167_); trivial. % 30.80/30.84 apply (zenon_L1172_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L47_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L1174_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L1158_); trivial. % 30.80/30.84 apply (zenon_L288_); trivial. % 30.80/30.84 apply (zenon_L1141_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.84 apply (zenon_L1035_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.84 apply (zenon_L1150_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.84 apply (zenon_L1163_); trivial. % 30.80/30.84 apply (zenon_L27_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_L1166_); trivial. % 30.80/30.84 apply (zenon_L117_); trivial. % 30.80/30.84 apply (zenon_L1170_); trivial. % 30.80/30.84 apply (zenon_L1050_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 exact (zenon_H84 zenon_H88). % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.84 exact (zenon_H84 zenon_H88). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L1178_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.84 apply (zenon_L16_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.84 apply (zenon_L1182_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.84 apply (zenon_L347_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.84 apply (zenon_L175_); trivial. % 30.80/30.84 apply (zenon_L1088_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.84 apply (zenon_L784_); trivial. % 30.80/30.84 apply (zenon_L886_); trivial. % 30.80/30.84 apply (zenon_L1153_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L1186_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_L1149_); trivial. % 30.80/30.84 apply (zenon_L1188_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L160_); trivial. % 30.80/30.84 apply (zenon_L848_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.84 apply (zenon_L1192_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.84 apply (zenon_L769_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.84 apply (zenon_L1197_); trivial. % 30.80/30.84 apply (zenon_L886_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_L1149_); trivial. % 30.80/30.84 apply (zenon_L39_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L160_); trivial. % 30.80/30.84 apply (zenon_L848_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.84 exact (zenon_H84 zenon_H88). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 apply (zenon_L1178_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L1178_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_L273_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.84 apply (zenon_L1205_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.84 apply (zenon_L142_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.84 apply (zenon_L782_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.84 apply (zenon_L49_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.84 apply (zenon_L347_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.84 apply (zenon_L1208_); trivial. % 30.80/30.84 apply (zenon_L1088_); trivial. % 30.80/30.84 apply (zenon_L829_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.84 apply (zenon_L1179_); trivial. % 30.80/30.84 apply (zenon_L913_); trivial. % 30.80/30.84 apply (zenon_L1172_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L834_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_L273_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.84 apply (zenon_L1204_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.84 apply (zenon_L142_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.84 apply (zenon_L748_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.84 apply (zenon_L51_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.84 apply (zenon_L347_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.84 apply (zenon_L1208_); trivial. % 30.80/30.84 apply (zenon_L1088_); trivial. % 30.80/30.84 apply (zenon_L829_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.84 apply (zenon_L1210_); trivial. % 30.80/30.84 apply (zenon_L886_); trivial. % 30.80/30.84 apply (zenon_L1153_); trivial. % 30.80/30.84 apply (zenon_L817_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.84 apply (zenon_L1202_); trivial. % 30.80/30.84 apply (zenon_L1203_); trivial. % 30.80/30.84 apply (zenon_L117_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.80/30.84 apply (zenon_L1205_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.84 exact (zenon_H84 zenon_H88). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.84 apply (zenon_L1182_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 apply (zenon_L244_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_L1211_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L47_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.84 apply (zenon_L120_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.84 exact (zenon_H18f zenon_Hd2). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.84 apply (zenon_L1211_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.84 apply (zenon_L154_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.84 apply (zenon_L1212_); trivial. % 30.80/30.84 apply (zenon_L1184_); trivial. % 30.80/30.84 apply (zenon_L730_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L160_); trivial. % 30.80/30.84 apply (zenon_L848_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L49_); trivial. % 30.80/30.84 apply (zenon_L1213_); trivial. % 30.80/30.84 apply (zenon_L817_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.84 apply (zenon_L1192_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.84 apply (zenon_L1176_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.84 apply (zenon_L1197_); trivial. % 30.80/30.84 apply (zenon_L886_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_L1149_); trivial. % 30.80/30.84 apply (zenon_L39_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L160_); trivial. % 30.80/30.84 apply (zenon_L848_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_L1195_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.84 apply (zenon_L1192_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.84 apply (zenon_L769_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.84 apply (zenon_L4_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.84 apply (zenon_L59_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.84 apply (zenon_L1181_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.84 exact (zenon_H18f zenon_Hd2). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.84 apply (zenon_L1196_); trivial. % 30.80/30.84 apply (zenon_L730_); trivial. % 30.80/30.84 apply (zenon_L1185_); trivial. % 30.80/30.84 apply (zenon_L886_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_L1149_); trivial. % 30.80/30.84 apply (zenon_L39_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L160_); trivial. % 30.80/30.84 apply (zenon_L848_); trivial. % 30.80/30.84 apply (zenon_L817_); trivial. % 30.80/30.84 apply (zenon_L1216_); trivial. % 30.80/30.84 apply (zenon_L1189_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 exact (zenon_H84 zenon_H88). % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_L868_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.84 exact (zenon_H84 zenon_H88). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.84 apply (zenon_L45_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 apply (zenon_L244_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.84 apply (zenon_L1227_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.84 apply (zenon_L763_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.84 apply (zenon_L1179_); trivial. % 30.80/30.84 apply (zenon_L886_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.80/30.84 apply (zenon_L1229_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.80/30.84 apply (zenon_L1226_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.80/30.84 apply (zenon_L544_); trivial. % 30.80/30.84 exact (zenon_H2e6 zenon_Hf5). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L160_); trivial. % 30.80/30.84 apply (zenon_L848_); trivial. % 30.80/30.84 apply (zenon_L817_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_L1195_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_L1231_); trivial. % 30.80/30.84 apply (zenon_L817_); trivial. % 30.80/30.84 apply (zenon_L117_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 exact (zenon_H84 zenon_H88). % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_L868_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.84 exact (zenon_H84 zenon_H88). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.84 apply (zenon_L16_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.84 apply (zenon_L1227_); trivial. % 30.80/30.84 apply (zenon_L1232_); trivial. % 30.80/30.84 apply (zenon_L117_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.80/30.84 apply (zenon_L49_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.80/30.84 apply (zenon_L1240_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.80/30.84 apply (zenon_L544_); trivial. % 30.80/30.84 exact (zenon_H2e6 zenon_Hf5). % 30.80/30.84 apply (zenon_L1220_); trivial. % 30.80/30.84 apply (zenon_L1189_); trivial. % 30.80/30.84 apply (zenon_L1193_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.84 apply (zenon_L1241_); trivial. % 30.80/30.84 apply (zenon_L1242_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3b5); [ zenon_intro zenon_H3ba | zenon_intro zenon_H3b9 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3ba). zenon_intro zenon_H185. zenon_intro zenon_H3bb. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3bb). zenon_intro zenon_H85. zenon_intro zenon_H3bc. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_Hbc. zenon_intro zenon_Hb9. % 30.80/30.84 exact (zenon_Hb9 zenon_Hbc). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H3be | zenon_intro zenon_H3bd ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3be). zenon_intro zenon_H68. zenon_intro zenon_H3bf. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3bf). zenon_intro zenon_H19f. zenon_intro zenon_H37e. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_H64. zenon_intro zenon_H1b3. % 30.80/30.84 exact (zenon_H1b3 zenon_H64). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3bd); [ zenon_intro zenon_H3c1 | zenon_intro zenon_H3c0 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3c1). zenon_intro zenon_H68. zenon_intro zenon_H3c2. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3c2). zenon_intro zenon_H19f. zenon_intro zenon_H382. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H382). zenon_intro zenon_Hc3. zenon_intro zenon_H313. % 30.80/30.84 exact (zenon_H313 zenon_H68). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3c0); [ zenon_intro zenon_H3c4 | zenon_intro zenon_H3c3 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3c4). zenon_intro zenon_H68. zenon_intro zenon_H3c5. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3c5). zenon_intro zenon_H19f. zenon_intro zenon_H386. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H386). zenon_intro zenon_H142. zenon_intro zenon_H2ed. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.84 apply (zenon_L1243_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 exact (zenon_H2ed zenon_Hc9). % 30.80/30.84 apply (zenon_L1245_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.80/30.84 apply (zenon_L16_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.80/30.84 apply (zenon_L303_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 apply (zenon_L232_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_L1246_); trivial. % 30.80/30.84 apply (zenon_L25_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 exact (zenon_H2ed zenon_Hc9). % 30.80/30.84 apply (zenon_L288_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.84 apply (zenon_L1248_); trivial. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H85 | zenon_intro zenon_H185 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H103 | zenon_intro zenon_H182 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 exact (zenon_H2ed zenon_Hc9). % 30.80/30.84 apply (zenon_L1268_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 apply (zenon_L912_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 exact (zenon_H2ed zenon_Hc9). % 30.80/30.84 apply (zenon_L1276_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_L1278_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_L1280_); trivial. % 30.80/30.84 apply (zenon_L1282_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_L1284_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L47_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 exact (zenon_H2ed zenon_Hc9). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.84 apply (zenon_L1285_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.84 apply (zenon_L1249_); trivial. % 30.80/30.84 apply (zenon_L1286_); trivial. % 30.80/30.84 apply (zenon_L50_); trivial. % 30.80/30.84 apply (zenon_L106_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.80/30.84 apply (zenon_L16_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.80/30.84 apply (zenon_L303_); trivial. % 30.80/30.84 apply (zenon_L1291_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.84 apply (zenon_L208_); trivial. % 30.80/30.84 apply (zenon_L1302_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.84 apply (zenon_L95_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.84 apply (zenon_L1249_); trivial. % 30.80/30.84 apply (zenon_L1267_); trivial. % 30.80/30.84 apply (zenon_L110_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 exact (zenon_H2ed zenon_Hc9). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.84 apply (zenon_L1305_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.84 apply (zenon_L1249_); trivial. % 30.80/30.84 apply (zenon_L1267_); trivial. % 30.80/30.84 apply (zenon_L50_); trivial. % 30.80/30.84 apply (zenon_L1282_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.84 apply (zenon_L1306_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.84 apply (zenon_L1249_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.80/30.84 apply (zenon_L4_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.80/30.84 exact (zenon_H103 zenon_H37). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.80/30.84 apply (zenon_L1307_); trivial. % 30.80/30.84 apply (zenon_L753_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.84 apply (zenon_L93_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.84 apply (zenon_L1308_); trivial. % 30.80/30.84 apply (zenon_L330_); trivial. % 30.80/30.84 apply (zenon_L110_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.84 apply (zenon_L208_); trivial. % 30.80/30.84 apply (zenon_L1322_); trivial. % 30.80/30.84 apply (zenon_L1292_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H103 | zenon_intro zenon_H182 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.80/30.84 apply (zenon_L1302_); trivial. % 30.80/30.84 apply (zenon_L1322_); trivial. % 30.80/30.84 apply (zenon_L1292_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3c3); [ zenon_intro zenon_H3c7 | zenon_intro zenon_H3c6 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3c7). zenon_intro zenon_H68. zenon_intro zenon_H3c8. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H19f. zenon_intro zenon_H38a. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H38a). zenon_intro zenon_Hb1. zenon_intro zenon_H2fb. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.84 apply (zenon_L1323_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.84 apply (zenon_L1326_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.84 apply (zenon_L1329_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.84 apply (zenon_L1330_); trivial. % 30.80/30.84 apply (zenon_L869_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H29b); [ zenon_intro zenon_H74 | zenon_intro zenon_H10e ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H13b | zenon_intro zenon_H19a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L1324_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L1331_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_L1353_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L1324_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L4_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_L1359_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.80/30.84 apply (zenon_L16_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L49_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L1362_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L4_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 apply (zenon_L1362_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_L1358_); trivial. % 30.80/30.84 exact (zenon_H2fb zenon_H8a). % 30.80/30.84 apply (zenon_L772_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.84 apply (zenon_L1330_); trivial. % 30.80/30.84 apply (zenon_L869_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 apply (zenon_L912_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L1331_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.84 apply (zenon_L1364_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.84 exact (zenon_H19f zenon_Hc3). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.84 apply (zenon_L1366_); trivial. % 30.80/30.84 apply (zenon_L798_); trivial. % 30.80/30.84 exact (zenon_H2fb zenon_H8a). % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L552_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L1331_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L598_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.84 apply (zenon_L1369_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.84 exact (zenon_H19f zenon_Hc3). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.84 apply (zenon_L1366_); trivial. % 30.80/30.84 apply (zenon_L798_); trivial. % 30.80/30.84 exact (zenon_H2fb zenon_H8a). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L552_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L1371_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.84 apply (zenon_L16_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.84 exact (zenon_H19f zenon_Hc3). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.84 apply (zenon_L1413_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.84 exact (zenon_H19f zenon_Hc3). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.84 apply (zenon_L1370_); trivial. % 30.80/30.84 apply (zenon_L798_); trivial. % 30.80/30.84 apply (zenon_L84_); trivial. % 30.80/30.84 exact (zenon_H2fb zenon_H8a). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 apply (zenon_L912_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_L1415_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L552_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L1331_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L598_); trivial. % 30.80/30.84 apply (zenon_L1369_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L552_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L1371_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 apply (zenon_L148_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.84 apply (zenon_L16_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.84 exact (zenon_H19f zenon_Hc3). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.84 apply (zenon_L1413_); trivial. % 30.80/30.84 apply (zenon_L84_); trivial. % 30.80/30.84 exact (zenon_H2fb zenon_H8a). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.80/30.84 apply (zenon_L16_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L734_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L4_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 apply (zenon_L734_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.80/30.84 apply (zenon_L1364_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.80/30.84 apply (zenon_L45_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.80/30.84 apply (zenon_L797_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.80/30.84 apply (zenon_L1383_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.80/30.84 apply (zenon_L219_); trivial. % 30.80/30.84 apply (zenon_L1408_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.84 exact (zenon_H13b zenon_Hfd). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.84 apply (zenon_L212_); trivial. % 30.80/30.84 apply (zenon_L1355_); trivial. % 30.80/30.84 apply (zenon_L1381_); trivial. % 30.80/30.84 exact (zenon_H2fb zenon_H8a). % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_L1415_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L552_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.80/30.84 apply (zenon_L1331_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.80/30.84 apply (zenon_L1417_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.80/30.84 apply (zenon_L1333_); trivial. % 30.80/30.84 apply (zenon_L1389_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L4_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.80/30.84 apply (zenon_L4_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.80/30.84 apply (zenon_L1367_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.80/30.84 apply (zenon_L1333_); trivial. % 30.80/30.84 apply (zenon_L1418_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_L554_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L49_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.84 apply (zenon_L241_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.84 apply (zenon_L1417_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.84 apply (zenon_L1419_); trivial. % 30.80/30.84 apply (zenon_L1414_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L4_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.84 apply (zenon_L241_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.84 apply (zenon_L1367_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.84 apply (zenon_L1339_); trivial. % 30.80/30.84 apply (zenon_L1414_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.84 exact (zenon_H13b zenon_Hfd). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.84 apply (zenon_L555_); trivial. % 30.80/30.84 apply (zenon_L1355_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_L1421_); trivial. % 30.80/30.84 exact (zenon_H2fb zenon_H8a). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L552_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.80/30.84 apply (zenon_L1371_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.80/30.84 apply (zenon_L1424_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.80/30.84 apply (zenon_L1333_); trivial. % 30.80/30.84 apply (zenon_L1334_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L1331_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_L1425_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.84 apply (zenon_L554_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.84 exact (zenon_H74 zenon_H73). % 30.80/30.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.84 apply (zenon_L48_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.84 apply (zenon_L49_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.84 apply (zenon_L241_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.80/30.84 apply (zenon_L332_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.80/30.84 apply (zenon_L131_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.80/30.84 apply (zenon_L259_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.80/30.84 apply (zenon_L598_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.80/30.84 apply (zenon_L1422_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.80/30.84 apply (zenon_L171_); trivial. % 30.80/30.84 apply (zenon_L1398_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.80/30.84 apply (zenon_L147_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.80/30.84 apply (zenon_L219_); trivial. % 30.80/30.84 apply (zenon_L1423_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.84 apply (zenon_L1422_); trivial. % 30.80/30.84 apply (zenon_L1414_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.84 exact (zenon_H13b zenon_Hfd). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.84 apply (zenon_L575_); trivial. % 30.80/30.84 apply (zenon_L1355_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L1331_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1335_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.84 apply (zenon_L1425_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.84 exact (zenon_H13b zenon_Hfd). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.84 apply (zenon_L575_); trivial. % 30.80/30.84 apply (zenon_L1355_); trivial. % 30.80/30.84 apply (zenon_L772_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.84 apply (zenon_L1330_); trivial. % 30.80/30.84 apply (zenon_L869_); trivial. % 30.80/30.84 apply (zenon_L147_); trivial. % 30.80/30.84 apply (zenon_L1330_); trivial. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H85 | zenon_intro zenon_H185 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.84 exact (zenon_H85 zenon_H89). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.84 apply (zenon_L18_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.80/30.84 apply (zenon_L1426_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.80/30.84 apply (zenon_L1429_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.80/30.84 apply (zenon_L1149_); trivial. % 30.80/30.84 apply (zenon_L37_); trivial. % 30.80/30.84 exact (zenon_H2fb zenon_H8a). % 30.80/30.84 apply (zenon_L107_); trivial. % 30.80/30.84 apply (zenon_L869_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3c6); [ zenon_intro zenon_H3ca | zenon_intro zenon_H3c9 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_Hd2. zenon_intro zenon_H3cb. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3cb). zenon_intro zenon_H18f. zenon_intro zenon_H38e. % 30.80/30.84 exact (zenon_H18f zenon_Hd2). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3c9); [ zenon_intro zenon_H3cd | zenon_intro zenon_H3cc ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3cd). zenon_intro zenon_Hd2. zenon_intro zenon_H3ce. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3ce). zenon_intro zenon_H18f. zenon_intro zenon_H392. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_Hd2. zenon_intro zenon_H18f. % 30.80/30.84 exact (zenon_H18f zenon_Hd2). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3cc); [ zenon_intro zenon_H3d0 | zenon_intro zenon_H3cf ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3d0). zenon_intro zenon_Hd2. zenon_intro zenon_H3d1. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3d1). zenon_intro zenon_H18f. zenon_intro zenon_H396. % 30.80/30.84 exact (zenon_H18f zenon_Hd2). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3cf); [ zenon_intro zenon_H3d3 | zenon_intro zenon_H3d2 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3d3). zenon_intro zenon_Hd2. zenon_intro zenon_H3d4. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3d4). zenon_intro zenon_H18f. zenon_intro zenon_H39c. % 30.80/30.84 exact (zenon_H18f zenon_Hd2). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H3d2); [ zenon_intro zenon_H3d6 | zenon_intro zenon_H3d5 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3d6). zenon_intro zenon_H19a. zenon_intro zenon_H3d7. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3d7). zenon_intro zenon_H13b. zenon_intro zenon_H3a0. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H3a0). zenon_intro zenon_H73. zenon_intro zenon_H304. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H64 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H19f | zenon_intro zenon_H68 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H260 | zenon_intro zenon_Hc9 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.84 exact (zenon_H1b3 zenon_H64). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.84 apply (zenon_L998_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.84 apply (zenon_L1035_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.84 apply (zenon_L1435_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L232_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L4_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1430_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.84 apply (zenon_L94_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.84 exact (zenon_H13b zenon_Hfd). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.84 apply (zenon_L159_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.80/30.84 exact (zenon_H304 zenon_H10e). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.80/30.84 apply (zenon_L1438_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.80/30.84 exact (zenon_H260 zenon_H142). % 30.80/30.84 apply (zenon_L1439_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.84 exact (zenon_H13b zenon_Hfd). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.84 apply (zenon_L1440_); trivial. % 30.80/30.84 apply (zenon_L1443_); trivial. % 30.80/30.84 apply (zenon_L1444_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.84 apply (zenon_L136_); trivial. % 30.80/30.84 apply (zenon_L9_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.84 exact (zenon_H304 zenon_H10e). % 30.80/30.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.84 apply (zenon_L232_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.84 apply (zenon_L1445_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.84 apply (zenon_L1430_); trivial. % 30.80/30.84 apply (zenon_L848_); trivial. % 30.80/30.84 apply (zenon_L43_); trivial. % 30.80/30.84 apply (zenon_L1435_); trivial. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.80/30.84 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.84 apply (zenon_L1209_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.84 apply (zenon_L1475_); trivial. % 30.80/30.84 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 exact (zenon_H304 zenon_H10e). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1447_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L94_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L159_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L1479_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L1481_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L91_); trivial. % 30.80/30.85 apply (zenon_L1088_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L824_); trivial. % 30.80/30.85 apply (zenon_L1184_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L157_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L94_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L159_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L1482_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L1481_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L91_); trivial. % 30.80/30.85 apply (zenon_L737_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L824_); trivial. % 30.80/30.85 apply (zenon_L1184_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L94_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L159_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.80/30.85 exact (zenon_H304 zenon_H10e). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.80/30.85 apply (zenon_L1477_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.80/30.85 apply (zenon_L1484_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.80/30.85 apply (zenon_L43_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.80/30.85 apply (zenon_L88_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.80/30.85 apply (zenon_L828_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.80/30.85 apply (zenon_L235_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_L544_); trivial. % 30.80/30.85 apply (zenon_L304_); trivial. % 30.80/30.85 apply (zenon_L90_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L824_); trivial. % 30.80/30.85 apply (zenon_L1184_); trivial. % 30.80/30.85 apply (zenon_L39_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L117_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L1474_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 exact (zenon_H304 zenon_H10e). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L746_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1456_); trivial. % 30.80/30.85 apply (zenon_L848_); trivial. % 30.80/30.85 apply (zenon_L824_); trivial. % 30.80/30.85 apply (zenon_L130_); trivial. % 30.80/30.85 apply (zenon_L1475_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_L1485_); trivial. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H103 | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2eb); [ zenon_intro zenon_H1db | zenon_intro zenon_Hf5 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L1486_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 exact (zenon_H304 zenon_H10e). % 30.80/30.85 apply (zenon_L1517_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L1486_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 exact (zenon_H304 zenon_H10e). % 30.80/30.85 apply (zenon_L1533_); trivial. % 30.80/30.85 apply (zenon_L1432_); trivial. % 30.80/30.85 apply (zenon_L840_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3d5); [ zenon_intro zenon_H3d9 | zenon_intro zenon_H3d8 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3d9). zenon_intro zenon_H19a. zenon_intro zenon_H3da. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3da). zenon_intro zenon_H13b. zenon_intro zenon_H3a4. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3a4). zenon_intro zenon_Hfd. zenon_intro zenon_H28c. % 30.80/30.85 exact (zenon_H28c zenon_H19a). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H3dc | zenon_intro zenon_H3db ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3dc). zenon_intro zenon_H19a. zenon_intro zenon_H3dd. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H13b. zenon_intro zenon_H3a8. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3a8). zenon_intro zenon_Hcc. zenon_intro zenon_Hd0. % 30.80/30.85 exact (zenon_Hd0 zenon_Hcc). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3df | zenon_intro zenon_H3de ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3df). zenon_intro zenon_H19a. zenon_intro zenon_H3e0. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H13b. zenon_intro zenon_H3ac. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3ac). zenon_intro zenon_Hf4. zenon_intro zenon_H2a9. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H64 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H19f | zenon_intro zenon_H68 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 exact (zenon_H1b3 zenon_H64). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1488_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L1536_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L734_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L1445_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1006_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.80/30.85 apply (zenon_L1549_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.80/30.85 apply (zenon_L130_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.80/30.85 apply (zenon_L1550_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L1041_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.80/30.85 apply (zenon_L1445_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.80/30.85 apply (zenon_L937_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_L126_); trivial. % 30.80/30.85 apply (zenon_L80_); trivial. % 30.80/30.85 apply (zenon_L1548_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1551_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_L819_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1488_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L1536_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L1041_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.80/30.85 apply (zenon_L332_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.80/30.85 apply (zenon_L126_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.80/30.85 apply (zenon_L1554_); trivial. % 30.80/30.85 apply (zenon_L1555_); trivial. % 30.80/30.85 apply (zenon_L1548_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L4_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1006_); trivial. % 30.80/30.85 apply (zenon_L1549_); trivial. % 30.80/30.85 apply (zenon_L819_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L9_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L725_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L159_); trivial. % 30.80/30.85 apply (zenon_L525_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_L1556_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1557_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1557_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L1535_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1547_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L1558_); trivial. % 30.80/30.85 apply (zenon_L819_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L117_); trivial. % 30.80/30.85 apply (zenon_L1559_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H19f | zenon_intro zenon_H68 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L1560_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L1564_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L1445_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1006_); trivial. % 30.80/30.85 apply (zenon_L1549_); trivial. % 30.80/30.85 apply (zenon_L819_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L1564_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L1445_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1006_); trivial. % 30.80/30.85 apply (zenon_L1565_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_L1571_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L1572_); trivial. % 30.80/30.85 apply (zenon_L1559_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1573_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1656_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L1657_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1658_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1656_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L1655_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_L1664_); trivial. % 30.80/30.85 apply (zenon_L864_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1656_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L1655_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1665_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L59_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1666_); trivial. % 30.80/30.85 apply (zenon_L1663_); trivial. % 30.80/30.85 apply (zenon_L864_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L1671_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1672_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L59_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1667_); trivial. % 30.80/30.85 apply (zenon_L1654_); trivial. % 30.80/30.85 apply (zenon_L1478_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L929_); trivial. % 30.80/30.85 apply (zenon_L917_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1658_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_L819_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1703_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L1705_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L769_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L4_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L59_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1666_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L1702_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L842_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L235_); trivial. % 30.80/30.85 apply (zenon_L1651_); trivial. % 30.80/30.85 apply (zenon_L864_); trivial. % 30.80/30.85 apply (zenon_L39_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L538_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1703_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1645_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L769_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1666_); trivial. % 30.80/30.85 apply (zenon_L1704_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L769_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1636_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L59_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1666_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L1700_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L1659_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L350_); trivial. % 30.80/30.85 apply (zenon_L737_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.80/30.85 apply (zenon_L1677_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_L1743_); trivial. % 30.80/30.85 apply (zenon_L1735_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L513_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L235_); trivial. % 30.80/30.85 apply (zenon_L1651_); trivial. % 30.80/30.85 apply (zenon_L864_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L1673_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L769_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1642_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L59_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1667_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L1701_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L1481_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L1670_); trivial. % 30.80/30.85 apply (zenon_L737_); trivial. % 30.80/30.85 apply (zenon_L1478_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L929_); trivial. % 30.80/30.85 apply (zenon_L917_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1658_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L538_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L538_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L1673_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L769_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1642_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L59_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1481_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.80/30.85 apply (zenon_L1654_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.80/30.85 apply (zenon_L784_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.80/30.85 apply (zenon_L212_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.80/30.85 apply (zenon_L1744_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.80/30.85 apply (zenon_L1743_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.80/30.85 apply (zenon_L544_); trivial. % 30.80/30.85 apply (zenon_L1748_); trivial. % 30.80/30.85 apply (zenon_L56_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.80/30.85 exact (zenon_H56 zenon_H25). % 30.80/30.85 apply (zenon_L1476_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L1481_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L350_); trivial. % 30.80/30.85 apply (zenon_L737_); trivial. % 30.80/30.85 apply (zenon_L1478_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L1705_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L769_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_L1664_); trivial. % 30.80/30.85 apply (zenon_L864_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1747_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L1747_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L842_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L752_); trivial. % 30.80/30.85 apply (zenon_L1651_); trivial. % 30.80/30.85 apply (zenon_L39_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L538_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L1671_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L769_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1646_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L59_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1667_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.80/30.85 apply (zenon_L1654_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.80/30.85 apply (zenon_L49_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.80/30.85 apply (zenon_L212_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.80/30.85 apply (zenon_L1750_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.80/30.85 apply (zenon_L1743_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.80/30.85 apply (zenon_L544_); trivial. % 30.80/30.85 apply (zenon_L1748_); trivial. % 30.80/30.85 apply (zenon_L56_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.80/30.85 exact (zenon_H56 zenon_H25). % 30.80/30.85 apply (zenon_L1476_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L1481_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L350_); trivial. % 30.80/30.85 apply (zenon_L737_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L824_); trivial. % 30.80/30.85 apply (zenon_L1184_); trivial. % 30.80/30.85 apply (zenon_L1478_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L929_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1658_); trivial. % 30.80/30.85 apply (zenon_L386_); trivial. % 30.80/30.85 apply (zenon_L819_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1573_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L1751_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1756_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1460_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L1752_); trivial. % 30.80/30.85 apply (zenon_L39_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L1697_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1757_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L826_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1758_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L273_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1758_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L273_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L1765_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L142_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L1762_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L1716_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L939_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.80/30.85 apply (zenon_L25_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.80/30.85 apply (zenon_L1497_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.80/30.85 apply (zenon_L63_); trivial. % 30.80/30.85 apply (zenon_L690_); trivial. % 30.80/30.85 apply (zenon_L830_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_L784_); trivial. % 30.80/30.85 apply (zenon_L913_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1757_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L826_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1758_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L273_); trivial. % 30.80/30.85 apply (zenon_L1755_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_L1767_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1447_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1757_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1757_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L826_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1625_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L1481_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L842_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L235_); trivial. % 30.80/30.85 apply (zenon_L1769_); trivial. % 30.80/30.85 apply (zenon_L1654_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L192_); trivial. % 30.80/30.85 apply (zenon_L819_); trivial. % 30.80/30.85 apply (zenon_L1770_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1757_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1649_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L1761_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1754_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L142_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L1763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L1716_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L939_); trivial. % 30.80/30.85 apply (zenon_L1764_); trivial. % 30.80/30.85 apply (zenon_L830_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1757_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L826_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1649_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1754_); trivial. % 30.80/30.85 apply (zenon_L1654_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_L1767_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1447_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L925_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1771_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L955_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L538_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1772_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L930_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L740_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_L1606_); trivial. % 30.80/30.85 apply (zenon_L1459_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_L740_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L769_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_L1606_); trivial. % 30.80/30.85 apply (zenon_L1459_); trivial. % 30.80/30.85 apply (zenon_L853_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H64 | zenon_intro zenon_H247 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1447_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L1780_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1782_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L1742_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1783_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L117_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H69 | zenon_intro zenon_H248 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1447_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1707_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L1778_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L149_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1784_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L1778_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_L848_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1785_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L1778_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L1776_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L1786_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L1786_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1707_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L273_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1787_); trivial. % 30.80/30.85 apply (zenon_L848_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L1776_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L1788_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L1788_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1707_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L273_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1787_); trivial. % 30.80/30.85 apply (zenon_L848_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_L817_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1736_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1638_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L769_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1739_); trivial. % 30.80/30.85 apply (zenon_L1740_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L1789_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1792_); trivial. % 30.80/30.85 apply (zenon_L847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L117_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hdf | zenon_intro zenon_H8b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1447_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L1795_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L538_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L1482_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L1698_); trivial. % 30.80/30.85 apply (zenon_L1187_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L117_); trivial. % 30.80/30.85 apply (zenon_L853_); trivial. % 30.80/30.85 apply (zenon_L1735_); trivial. % 30.80/30.85 apply (zenon_L824_); trivial. % 30.80/30.85 apply (zenon_L130_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_L1697_); trivial. % 30.80/30.85 apply (zenon_L1710_); trivial. % 30.80/30.85 apply (zenon_L824_); trivial. % 30.80/30.85 apply (zenon_L130_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_L994_); trivial. % 30.80/30.85 apply (zenon_L997_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3de); [ zenon_intro zenon_H3e2 | zenon_intro zenon_H3e1 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3e2). zenon_intro zenon_H182. zenon_intro zenon_H3e3. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3e3). zenon_intro zenon_H103. zenon_intro zenon_H3b0. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3b0). zenon_intro zenon_H89. zenon_intro zenon_H30a. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_L1796_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.85 cut (((op (e1) (op (e1) (e3))) = (e3)) = ((op (e1) (e1)) = (e3))). % 30.80/30.85 intro zenon_D_pnotp. % 30.80/30.85 apply zenon_H103. % 30.80/30.85 rewrite <- zenon_D_pnotp. % 30.80/30.85 exact zenon_H4e. % 30.80/30.85 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 30.80/30.85 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 30.80/30.85 congruence. % 30.80/30.85 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 30.80/30.85 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (op (e1) (e3))) = (op (e1) (e1)))). % 30.80/30.85 intro zenon_D_pnotp. % 30.80/30.85 apply zenon_H27a. % 30.80/30.85 rewrite <- zenon_D_pnotp. % 30.80/30.85 exact zenon_Hc4. % 30.80/30.85 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 30.80/30.85 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 30.80/30.85 congruence. % 30.80/30.85 apply (zenon_L728_); trivial. % 30.80/30.85 apply zenon_Hc5. apply refl_equal. % 30.80/30.85 apply zenon_Hc5. apply refl_equal. % 30.80/30.85 apply zenon_H2f. apply refl_equal. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H29b); [ zenon_intro zenon_H74 | zenon_intro zenon_H10e ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H13b | zenon_intro zenon_H19a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_L148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L1797_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L1913_); trivial. % 30.80/30.85 exact (zenon_H30a zenon_H185). % 30.80/30.85 apply (zenon_L1907_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L1856_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L554_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1924_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L1944_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1930_); trivial. % 30.80/30.85 apply (zenon_L1849_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1921_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L1945_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1843_); trivial. % 30.80/30.85 apply (zenon_L1849_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L554_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1919_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L1946_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1843_); trivial. % 30.80/30.85 apply (zenon_L1949_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L1105_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L554_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1920_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L1953_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1936_); trivial. % 30.80/30.85 apply (zenon_L1950_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L552_); trivial. % 30.80/30.85 apply (zenon_L386_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L797_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L552_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1922_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L1970_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1843_); trivial. % 30.80/30.85 apply (zenon_L1849_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L554_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L552_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1922_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L1977_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1843_); trivial. % 30.80/30.85 apply (zenon_L1849_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1923_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L1945_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1843_); trivial. % 30.80/30.85 apply (zenon_L1849_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L554_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L1919_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L1978_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1843_); trivial. % 30.80/30.85 apply (zenon_L1949_); trivial. % 30.80/30.85 apply (zenon_L1966_); trivial. % 30.80/30.85 apply (zenon_L115_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L1924_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L1998_); trivial. % 30.80/30.85 exact (zenon_H30a zenon_H185). % 30.80/30.85 apply (zenon_L1907_); trivial. % 30.80/30.85 apply (zenon_L1999_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H13b | zenon_intro zenon_H19a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_L1913_); trivial. % 30.80/30.85 apply (zenon_L1907_); trivial. % 30.80/30.85 apply (zenon_L1998_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_L734_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L734_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1805_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L1832_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.80/30.85 apply (zenon_L4_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.80/30.85 exact (zenon_H103 zenon_H37). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_L145_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L2001_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L1848_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L224_); trivial. % 30.80/30.85 apply (zenon_L2002_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L1847_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L1848_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L1853_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L1848_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L224_); trivial. % 30.80/30.85 apply (zenon_L2002_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L1804_); trivial. % 30.80/30.85 apply (zenon_L386_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L192_); trivial. % 30.80/30.85 apply (zenon_L1831_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L115_); trivial. % 30.80/30.85 apply (zenon_L1830_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_L2011_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_L734_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L734_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L1805_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L2009_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L539_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L192_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L539_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 apply (zenon_L154_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L575_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.80/30.85 apply (zenon_L2007_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.80/30.85 apply (zenon_L218_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.80/30.85 apply (zenon_L2012_); trivial. % 30.80/30.85 apply (zenon_L934_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L552_); trivial. % 30.80/30.85 apply (zenon_L386_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L115_); trivial. % 30.80/30.85 apply (zenon_L2013_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3e1); [ zenon_intro zenon_H3e5 | zenon_intro zenon_H3e4 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3e5). zenon_intro zenon_H182. zenon_intro zenon_H3e6. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3e6). zenon_intro zenon_H103. zenon_intro zenon_H3b4. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3b4). zenon_intro zenon_H37. zenon_intro zenon_H2cc. % 30.80/30.85 exact (zenon_H2cc zenon_H182). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3e4); [ zenon_intro zenon_H3e8 | zenon_intro zenon_H3e7 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3e8). zenon_intro zenon_H182. zenon_intro zenon_H3e9. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3e9). zenon_intro zenon_H103. zenon_intro zenon_H3b8. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3b8). zenon_intro zenon_H1b9. zenon_intro zenon_H2e6. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H64 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H19f | zenon_intro zenon_H68 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H260 | zenon_intro zenon_Hc9 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 exact (zenon_H1b3 zenon_H64). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L998_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2014_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L734_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L4_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1157_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L734_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L2020_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_L795_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L1030_); trivial. % 30.80/30.85 apply (zenon_L1135_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L1149_); trivial. % 30.80/30.85 apply (zenon_L2017_); trivial. % 30.80/30.85 apply (zenon_L1141_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L1035_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L119_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L244_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2014_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L2022_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H136 ]. % 30.80/30.85 apply (zenon_L2023_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H55 | zenon_intro zenon_H137 ]. % 30.80/30.85 apply (zenon_L787_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hf5 ]. % 30.80/30.85 apply (zenon_L544_); trivial. % 30.80/30.85 exact (zenon_H2e6 zenon_Hf5). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L1030_); trivial. % 30.80/30.85 apply (zenon_L1135_); trivial. % 30.80/30.85 apply (zenon_L1141_); trivial. % 30.80/30.85 apply (zenon_L1444_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L2028_); trivial. % 30.80/30.85 apply (zenon_L115_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L2029_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L2030_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L2031_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L2016_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1157_); trivial. % 30.80/30.85 apply (zenon_L2035_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2014_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L192_); trivial. % 30.80/30.85 apply (zenon_L1141_); trivial. % 30.80/30.85 apply (zenon_L2036_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 exact (zenon_H1b3 zenon_H64). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L2040_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L726_); trivial. % 30.80/30.85 apply (zenon_L2036_); trivial. % 30.80/30.85 apply (zenon_L2030_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H19f | zenon_intro zenon_H68 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L2030_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L244_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2014_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L1564_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L2016_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1157_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_L1564_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L2045_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L1149_); trivial. % 30.80/30.85 apply (zenon_L2017_); trivial. % 30.80/30.85 apply (zenon_L1141_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L1564_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L2016_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L1157_); trivial. % 30.80/30.85 apply (zenon_L2035_); trivial. % 30.80/30.85 apply (zenon_L2017_); trivial. % 30.80/30.85 apply (zenon_L2030_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L729_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 exact (zenon_H103 zenon_H37). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L2049_); trivial. % 30.80/30.85 apply (zenon_L733_); trivial. % 30.80/30.85 apply (zenon_L2051_); trivial. % 30.80/30.85 apply (zenon_L872_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_L1241_); trivial. % 30.80/30.85 apply (zenon_L1242_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3e7); [ zenon_intro zenon_H3eb | zenon_intro zenon_H3ea ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3eb). zenon_intro zenon_H182. zenon_intro zenon_H3ec. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3ec). zenon_intro zenon_H103. zenon_intro zenon_H3bc. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_Hbc. zenon_intro zenon_Hb9. % 30.80/30.85 exact (zenon_Hb9 zenon_Hbc). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3ea); [ zenon_intro zenon_H3ee | zenon_intro zenon_H3ed ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3ee). zenon_intro zenon_Hc9. zenon_intro zenon_H3ef. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3ef). zenon_intro zenon_H260. zenon_intro zenon_H37e. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_H64. zenon_intro zenon_H1b3. % 30.80/30.85 exact (zenon_H1b3 zenon_H64). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3ed); [ zenon_intro zenon_H3f1 | zenon_intro zenon_H3f0 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3f1). zenon_intro zenon_Hc9. zenon_intro zenon_H3f2. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3f2). zenon_intro zenon_H260. zenon_intro zenon_H382. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H382). zenon_intro zenon_Hc3. zenon_intro zenon_H313. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_L2052_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L763_); trivial. % 30.80/30.85 apply (zenon_L769_); trivial. % 30.80/30.85 apply (zenon_L42_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H29b); [ zenon_intro zenon_H74 | zenon_intro zenon_H10e ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H13b | zenon_intro zenon_H19a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L2061_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.80/30.85 apply (zenon_L2055_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.80/30.85 apply (zenon_L218_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.80/30.85 apply (zenon_L256_); trivial. % 30.80/30.85 apply (zenon_L2060_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L2055_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 apply (zenon_L906_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L2071_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H126 ]. % 30.80/30.85 apply (zenon_L2061_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H127 ]. % 30.80/30.85 apply (zenon_L906_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H98 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L49_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L2072_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 exact (zenon_H260 zenon_H142). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.80/30.85 apply (zenon_L598_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.80/30.85 apply (zenon_L2073_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.80/30.85 apply (zenon_L1135_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.80/30.85 apply (zenon_L358_); trivial. % 30.80/30.85 exact (zenon_H231 zenon_Hf4). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_L628_); trivial. % 30.80/30.85 apply (zenon_L2066_); trivial. % 30.80/30.85 apply (zenon_L2074_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L1101_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_L2077_); trivial. % 30.80/30.85 apply (zenon_L2075_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L940_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L2055_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 apply (zenon_L906_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L2062_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H17b | zenon_intro zenon_H268 ]. % 30.80/30.85 apply (zenon_L2079_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H155 | zenon_intro zenon_H269 ]. % 30.80/30.85 apply (zenon_L1135_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 exact (zenon_H231 zenon_Hf4). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L42_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L2103_); trivial. % 30.80/30.85 apply (zenon_L2104_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2067_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L2068_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L2067_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 exact (zenon_H13b zenon_Hfd). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L49_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L347_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 exact (zenon_H260 zenon_H142). % 30.80/30.85 apply (zenon_L2109_); trivial. % 30.80/30.85 apply (zenon_L552_); trivial. % 30.80/30.85 apply (zenon_L2071_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H13b | zenon_intro zenon_H19a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.80/30.85 apply (zenon_L2111_); trivial. % 30.80/30.85 apply (zenon_L552_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.80/30.85 apply (zenon_L2113_); trivial. % 30.80/30.85 apply (zenon_L552_); trivial. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H85 | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2eb); [ zenon_intro zenon_H1db | zenon_intro zenon_Hf5 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 apply (zenon_L906_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L2114_); trivial. % 30.80/30.85 apply (zenon_L2140_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L42_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 apply (zenon_L906_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L2114_); trivial. % 30.80/30.85 apply (zenon_L2142_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_L2143_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L2146_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L940_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L2115_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L43_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2147_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L192_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 exact (zenon_H85 zenon_H89). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L2148_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L273_); trivial. % 30.80/30.85 apply (zenon_L39_); trivial. % 30.80/30.85 apply (zenon_L2104_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L2115_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 exact (zenon_H85 zenon_H89). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 apply (zenon_L906_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L2114_); trivial. % 30.80/30.85 apply (zenon_L2158_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 apply (zenon_L906_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L2114_); trivial. % 30.80/30.85 apply (zenon_L2159_); trivial. % 30.80/30.85 apply (zenon_L1309_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L42_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 apply (zenon_L906_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L2149_); trivial. % 30.80/30.85 apply (zenon_L2165_); trivial. % 30.80/30.85 apply (zenon_L2104_); trivial. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_L2104_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3f0); [ zenon_intro zenon_H3f4 | zenon_intro zenon_H3f3 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3f4). zenon_intro zenon_Hc9. zenon_intro zenon_H3f5. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3f5). zenon_intro zenon_H260. zenon_intro zenon_H386. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H386). zenon_intro zenon_H142. zenon_intro zenon_H2ed. % 30.80/30.85 exact (zenon_H2ed zenon_Hc9). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3f3); [ zenon_intro zenon_H3f7 | zenon_intro zenon_H3f6 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3f7). zenon_intro zenon_Hc9. zenon_intro zenon_H3f8. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3f8). zenon_intro zenon_H260. zenon_intro zenon_H38a. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H38a). zenon_intro zenon_Hb1. zenon_intro zenon_H2fb. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_L1323_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L2166_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L2167_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_L2173_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L2175_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 apply (zenon_L2173_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L18_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L320_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.80/30.85 apply (zenon_L2182_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.80/30.85 apply (zenon_L203_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_L2171_); trivial. % 30.80/30.85 apply (zenon_L1354_); trivial. % 30.80/30.85 apply (zenon_L2184_); trivial. % 30.80/30.85 apply (zenon_L2177_); trivial. % 30.80/30.85 apply (zenon_L798_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L2186_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L2187_); trivial. % 30.80/30.85 apply (zenon_L2201_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L2204_); trivial. % 30.80/30.85 apply (zenon_L2208_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L2210_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L746_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L2187_); trivial. % 30.80/30.85 apply (zenon_L2212_); trivial. % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H89 | zenon_intro zenon_H8e ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L142_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_L122_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L2175_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 apply (zenon_L58_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H76 | zenon_intro zenon_H1d6 ]. % 30.80/30.85 apply (zenon_L273_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H3d | zenon_intro zenon_H1d7 ]. % 30.80/30.85 apply (zenon_L2171_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1c5 ]. % 30.80/30.85 apply (zenon_L2183_); trivial. % 30.80/30.85 apply (zenon_L2213_); trivial. % 30.80/30.85 apply (zenon_L2177_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6e | zenon_intro zenon_H8f ]. % 30.80/30.85 apply (zenon_L770_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H76 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_L273_); trivial. % 30.80/30.85 exact (zenon_H2fb zenon_H8a). % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_L2166_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H13b | zenon_intro zenon_H19a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L2224_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L2055_); trivial. % 30.80/30.85 apply (zenon_L2231_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L2234_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L2296_); trivial. % 30.80/30.85 apply (zenon_L869_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L2217_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L2235_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L151_); trivial. % 30.80/30.85 apply (zenon_L2238_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_L2105_); trivial. % 30.80/30.85 apply (zenon_L2297_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L2217_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L4_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L151_); trivial. % 30.80/30.85 apply (zenon_L2238_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L2266_); trivial. % 30.80/30.85 apply (zenon_L869_); trivial. % 30.80/30.85 apply (zenon_L552_); trivial. % 30.80/30.85 apply (zenon_L2310_); trivial. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2eb); [ zenon_intro zenon_H1db | zenon_intro zenon_Hf5 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.80/30.85 apply (zenon_L2311_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.80/30.85 apply (zenon_L2312_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_L2313_); trivial. % 30.80/30.85 apply (zenon_L36_); trivial. % 30.80/30.85 apply (zenon_L107_); trivial. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3f6); [ zenon_intro zenon_H3fa | zenon_intro zenon_H3f9 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3fa). zenon_intro zenon_H55. zenon_intro zenon_H3fb. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3fb). zenon_intro zenon_H56. zenon_intro zenon_H38e. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H38e). zenon_intro zenon_H88. zenon_intro zenon_H317. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H64 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H260 | zenon_intro zenon_Hc9 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 exact (zenon_H1b3 zenon_H64). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 exact (zenon_H317 zenon_H1e). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L2315_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L734_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L2316_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L2317_); trivial. % 30.80/30.85 apply (zenon_L848_); trivial. % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_L2318_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_L2326_); trivial. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2eb); [ zenon_intro zenon_H1db | zenon_intro zenon_Hf5 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 exact (zenon_H317 zenon_H1e). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L2327_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L2328_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H6c | zenon_intro zenon_H209 ]. % 30.80/30.85 apply (zenon_L809_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H20a ]. % 30.80/30.85 apply (zenon_L212_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H25 | zenon_intro zenon_H1e5 ]. % 30.80/30.85 exact (zenon_H56 zenon_H25). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.80/30.85 apply (zenon_L797_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.80/30.85 apply (zenon_L2331_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.80/30.85 exact (zenon_H56 zenon_H25). % 30.80/30.85 apply (zenon_L1297_); trivial. % 30.80/30.85 apply (zenon_L2332_); trivial. % 30.80/30.85 apply (zenon_L2344_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 exact (zenon_H317 zenon_H1e). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H26 | zenon_intro zenon_H1a3 ]. % 30.80/30.85 apply (zenon_L797_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H19a | zenon_intro zenon_H1a4 ]. % 30.80/30.85 apply (zenon_L2149_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a0 ]. % 30.80/30.85 exact (zenon_H56 zenon_H25). % 30.80/30.85 apply (zenon_L1297_); trivial. % 30.80/30.85 apply (zenon_L2346_); trivial. % 30.80/30.85 apply (zenon_L1253_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3f9); [ zenon_intro zenon_H3fd | zenon_intro zenon_H3fc ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3fd). zenon_intro zenon_H55. zenon_intro zenon_H3fe. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3fe). zenon_intro zenon_H56. zenon_intro zenon_H392. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_Hd2. zenon_intro zenon_H18f. % 30.80/30.85 exact (zenon_H18f zenon_Hd2). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3fc); [ zenon_intro zenon_H400 | zenon_intro zenon_H3ff ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H400). zenon_intro zenon_H55. zenon_intro zenon_H401. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H401). zenon_intro zenon_H56. zenon_intro zenon_H396. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H396). zenon_intro zenon_H25. zenon_intro zenon_H46. % 30.80/30.85 exact (zenon_H46 zenon_H55). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H3ff); [ zenon_intro zenon_H403 | zenon_intro zenon_H402 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H403). zenon_intro zenon_H55. zenon_intro zenon_H404. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H404). zenon_intro zenon_H56. zenon_intro zenon_H39c. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H39c). zenon_intro zenon_H112. zenon_intro zenon_H18e. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H64 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H260 | zenon_intro zenon_Hc9 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 exact (zenon_H1b3 zenon_H64). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L2349_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L88_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L2359_); trivial. % 30.80/30.85 apply (zenon_L2314_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L2349_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L88_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L192_); trivial. % 30.80/30.85 apply (zenon_L2314_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L2360_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L88_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L2361_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_L2362_); trivial. % 30.80/30.85 apply (zenon_L817_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 exact (zenon_H1b3 zenon_H64). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L734_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L4_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_L2317_); trivial. % 30.80/30.85 apply (zenon_L2365_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L88_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L2366_); trivial. % 30.80/30.85 apply (zenon_L2314_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L1035_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_L2363_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L2367_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L88_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L2366_); trivial. % 30.80/30.85 apply (zenon_L2314_); trivial. % 30.80/30.85 apply (zenon_L139_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L2025_); trivial. % 30.80/30.85 apply (zenon_L2368_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L2369_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L88_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L192_); trivial. % 30.80/30.85 apply (zenon_L2314_); trivial. % 30.80/30.85 apply (zenon_L2370_); trivial. % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H260 | zenon_intro zenon_Hc9 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L88_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.85 apply (zenon_L1569_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.85 apply (zenon_L124_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H2c | zenon_intro zenon_H43 ]. % 30.80/30.85 apply (zenon_L124_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H37 | zenon_intro zenon_H44 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.80/30.85 apply (zenon_L2041_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.80/30.85 apply (zenon_L2374_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.80/30.85 apply (zenon_L2350_); trivial. % 30.80/30.85 exact (zenon_H122 zenon_Hb1). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3d | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_L126_); trivial. % 30.80/30.85 exact (zenon_H18e zenon_H40). % 30.80/30.85 apply (zenon_L2380_); trivial. % 30.80/30.85 apply (zenon_L2314_); trivial. % 30.80/30.85 apply (zenon_L2383_); trivial. % 30.80/30.85 apply (zenon_L282_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_L141_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_L2326_); trivial. % 30.80/30.85 apply (zenon_L723_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H402); [ zenon_intro zenon_H406 | zenon_intro zenon_H405 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H406). zenon_intro zenon_Hcc. zenon_intro zenon_H407. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H407). zenon_intro zenon_Hd0. zenon_intro zenon_H3a0. % 30.80/30.85 exact (zenon_Hd0 zenon_Hcc). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H405); [ zenon_intro zenon_H409 | zenon_intro zenon_H408 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H409). zenon_intro zenon_Hcc. zenon_intro zenon_H40a. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H40a). zenon_intro zenon_Hd0. zenon_intro zenon_H3a4. % 30.80/30.85 exact (zenon_Hd0 zenon_Hcc). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H408); [ zenon_intro zenon_H40c | zenon_intro zenon_H40b ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H40c). zenon_intro zenon_Hcc. zenon_intro zenon_H40d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H40d). zenon_intro zenon_Hd0. zenon_intro zenon_H3a8. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3a8). zenon_intro zenon_Hcc. zenon_intro zenon_Hd0. % 30.80/30.85 exact (zenon_Hd0 zenon_Hcc). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H40b); [ zenon_intro zenon_H40f | zenon_intro zenon_H40e ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H40f). zenon_intro zenon_Hcc. zenon_intro zenon_H410. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H410). zenon_intro zenon_Hd0. zenon_intro zenon_H3ac. % 30.80/30.85 exact (zenon_Hd0 zenon_Hcc). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H40e); [ zenon_intro zenon_H412 | zenon_intro zenon_H411 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H412). zenon_intro zenon_Hf5. zenon_intro zenon_H413. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H413). zenon_intro zenon_H1db. zenon_intro zenon_H3b0. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3b0). zenon_intro zenon_H89. zenon_intro zenon_H30a. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_L1796_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2408_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L2410_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L2407_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_L2418_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L2399_); trivial. % 30.80/30.85 apply (zenon_L90_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_L2418_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L2405_); trivial. % 30.80/30.85 apply (zenon_L90_); trivial. % 30.80/30.85 apply (zenon_L405_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2419_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L2424_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L2431_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L2424_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_L2418_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L2399_); trivial. % 30.80/30.85 apply (zenon_L90_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 exact (zenon_H18f zenon_Hd2). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L2422_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L2384_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L158_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L2414_); trivial. % 30.80/30.85 apply (zenon_L2432_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L2399_); trivial. % 30.80/30.85 apply (zenon_L90_); trivial. % 30.80/30.85 apply (zenon_L2423_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L2424_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_L2418_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L2405_); trivial. % 30.80/30.85 apply (zenon_L90_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 exact (zenon_H18f zenon_Hd2). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L2422_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L2384_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L2385_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L2414_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L2433_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L2432_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L2434_); trivial. % 30.80/30.85 apply (zenon_L294_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L2405_); trivial. % 30.80/30.85 apply (zenon_L90_); trivial. % 30.80/30.85 apply (zenon_L2423_); trivial. % 30.80/30.85 apply (zenon_L405_); trivial. % 30.80/30.85 apply (zenon_L2440_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2444_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L2410_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L2407_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L2445_); trivial. % 30.80/30.85 apply (zenon_L2442_); trivial. % 30.80/30.85 apply (zenon_L405_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2419_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L2446_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 apply (zenon_L2445_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 exact (zenon_H18f zenon_Hd2). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L2423_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 apply (zenon_L2442_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 exact (zenon_H18f zenon_Hd2). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L136_); trivial. % 30.80/30.85 apply (zenon_L2423_); trivial. % 30.80/30.85 apply (zenon_L405_); trivial. % 30.80/30.85 apply (zenon_L2440_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L232_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2453_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L2454_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L2407_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_L2459_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L18_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L158_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L2414_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L740_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L2457_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L2434_); trivial. % 30.80/30.85 apply (zenon_L294_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L2451_); trivial. % 30.80/30.85 apply (zenon_L90_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L2407_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_L742_); trivial. % 30.80/30.85 apply (zenon_L744_); trivial. % 30.80/30.85 apply (zenon_L405_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2419_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L2424_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H69 | zenon_intro zenon_H177 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1e | zenon_intro zenon_H297 ]. % 30.80/30.85 apply (zenon_L2431_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H298 ]. % 30.80/30.85 apply (zenon_L763_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H1ba | zenon_intro zenon_H95 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 apply (zenon_L2459_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 exact (zenon_H18f zenon_Hd2). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L2421_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 apply (zenon_L2458_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L824_); trivial. % 30.80/30.85 apply (zenon_L1184_); trivial. % 30.80/30.85 apply (zenon_L2423_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_Hdc | zenon_intro zenon_H179 ]. % 30.80/30.85 apply (zenon_L48_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_Hfd | zenon_intro zenon_H17a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L2384_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L2385_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L2414_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hdf | zenon_intro zenon_H201 ]. % 30.80/30.85 apply (zenon_L2433_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1ba | zenon_intro zenon_H202 ]. % 30.80/30.85 apply (zenon_L2457_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H142 | zenon_intro zenon_H1e1 ]. % 30.80/30.85 apply (zenon_L2434_); trivial. % 30.80/30.85 apply (zenon_L294_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H17a); [ zenon_intro zenon_Hed | zenon_intro zenon_H155 ]. % 30.80/30.85 apply (zenon_L2405_); trivial. % 30.80/30.85 apply (zenon_L90_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 exact (zenon_H18f zenon_Hd2). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L2384_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L2385_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L235_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H10e | zenon_intro zenon_H14c ]. % 30.80/30.85 apply (zenon_L2456_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14d ]. % 30.80/30.85 apply (zenon_L2409_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H142 | zenon_intro zenon_H9c ]. % 30.80/30.85 apply (zenon_L2434_); trivial. % 30.80/30.85 apply (zenon_L2395_); trivial. % 30.80/30.85 apply (zenon_L2460_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H178 ]. % 30.80/30.85 apply (zenon_L2407_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14f ]. % 30.80/30.85 apply (zenon_L742_); trivial. % 30.80/30.85 apply (zenon_L744_); trivial. % 30.80/30.85 apply (zenon_L405_); trivial. % 30.80/30.85 apply (zenon_L2440_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L2538_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L2539_); trivial. % 30.80/30.85 exact (zenon_H30a zenon_H185). % 30.80/30.85 apply (zenon_L2387_); trivial. % 30.80/30.85 apply (zenon_L1253_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_L868_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2558_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L2561_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 apply (zenon_L748_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L1253_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L2384_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L125_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L2563_); trivial. % 30.80/30.85 apply (zenon_L2565_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_L2552_); trivial. % 30.80/30.85 apply (zenon_L405_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2558_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L47_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_He9 | zenon_intro zenon_H104 ]. % 30.80/30.85 apply (zenon_L2561_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hfd | zenon_intro zenon_H105 ]. % 30.80/30.85 apply (zenon_L154_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H55 | zenon_intro zenon_H9d ]. % 30.80/30.85 apply (zenon_L1253_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H6e | zenon_intro zenon_H170 ]. % 30.80/30.85 apply (zenon_L2384_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H37 | zenon_intro zenon_H171 ]. % 30.80/30.85 apply (zenon_L839_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H15e | zenon_intro zenon_H16c ]. % 30.80/30.85 apply (zenon_L2563_); trivial. % 30.80/30.85 apply (zenon_L2565_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_L2552_); trivial. % 30.80/30.85 apply (zenon_L405_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L2537_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L2564_); trivial. % 30.80/30.85 exact (zenon_H30a zenon_H185). % 30.80/30.85 apply (zenon_L2387_); trivial. % 30.80/30.85 apply (zenon_L1253_); trivial. % 30.80/30.85 apply (zenon_L2538_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_L2566_); trivial. % 30.80/30.85 apply (zenon_L2013_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H411); [ zenon_intro zenon_H415 | zenon_intro zenon_H414 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H415). zenon_intro zenon_Hf5. zenon_intro zenon_H416. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H416). zenon_intro zenon_H1db. zenon_intro zenon_H3b4. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3b4). zenon_intro zenon_H37. zenon_intro zenon_H2cc. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H64 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H260 | zenon_intro zenon_Hc9 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 apply (zenon_L2573_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 apply (zenon_L125_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L2567_); trivial. % 30.80/30.85 exact (zenon_H2cc zenon_H182). % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H260 | zenon_intro zenon_Hc9 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L2574_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1a9 ]. % 30.80/30.85 apply (zenon_L2583_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1aa ]. % 30.80/30.85 apply (zenon_L125_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H19a | zenon_intro zenon_H182 ]. % 30.80/30.85 apply (zenon_L2567_); trivial. % 30.80/30.85 exact (zenon_H2cc zenon_H182). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L2585_); trivial. % 30.80/30.85 apply (zenon_L405_); trivial. % 30.80/30.85 apply (zenon_L2576_); trivial. % 30.80/30.85 apply (zenon_L627_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_L1051_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_L2566_); trivial. % 30.80/30.85 apply (zenon_L1130_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H414); [ zenon_intro zenon_H418 | zenon_intro zenon_H417 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H418). zenon_intro zenon_Hf5. zenon_intro zenon_H419. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H419). zenon_intro zenon_H1db. zenon_intro zenon_H3b8. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3b8). zenon_intro zenon_H1b9. zenon_intro zenon_H2e6. % 30.80/30.85 exact (zenon_H2e6 zenon_Hf5). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H417); [ zenon_intro zenon_H41b | zenon_intro zenon_H41a ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H41b). zenon_intro zenon_Hf5. zenon_intro zenon_H41c. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H41c). zenon_intro zenon_H1db. zenon_intro zenon_H3bc. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_Hbc. zenon_intro zenon_Hb9. % 30.80/30.85 exact (zenon_Hb9 zenon_Hbc). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H41a); [ zenon_intro zenon_H41e | zenon_intro zenon_H41d ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H41e). zenon_intro zenon_H8a. zenon_intro zenon_H41f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H41f). zenon_intro zenon_H122. zenon_intro zenon_H37e. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_H64. zenon_intro zenon_H1b3. % 30.80/30.85 exact (zenon_H1b3 zenon_H64). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H41d); [ zenon_intro zenon_H421 | zenon_intro zenon_H420 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H421). zenon_intro zenon_H8a. zenon_intro zenon_H422. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H422). zenon_intro zenon_H122. zenon_intro zenon_H382. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H382). zenon_intro zenon_Hc3. zenon_intro zenon_H313. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_L2052_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 exact (zenon_H84 zenon_H88). % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_L2586_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_L2587_); trivial. % 30.80/30.85 apply (zenon_L2588_); trivial. % 30.80/30.85 apply (zenon_L862_); trivial. % 30.80/30.85 apply (zenon_L906_); trivial. % 30.80/30.85 apply (zenon_L42_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H29b); [ zenon_intro zenon_H74 | zenon_intro zenon_H10e ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H13b | zenon_intro zenon_H19a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2595_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L2602_); trivial. % 30.80/30.85 apply (zenon_L2603_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_L2617_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.85 apply (zenon_L797_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.85 exact (zenon_H313 zenon_H68). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L2619_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L2620_); trivial. % 30.80/30.85 apply (zenon_L2603_); trivial. % 30.80/30.85 apply (zenon_L39_); trivial. % 30.80/30.85 apply (zenon_L2589_); trivial. % 30.80/30.85 apply (zenon_L461_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H73 | zenon_intro zenon_H226 ]. % 30.80/30.85 exact (zenon_H74 zenon_H73). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_He9 | zenon_intro zenon_H227 ]. % 30.80/30.85 apply (zenon_L568_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_Hda | zenon_intro zenon_H17b ]. % 30.80/30.85 apply (zenon_L554_); trivial. % 30.80/30.85 apply (zenon_L2603_); trivial. % 30.80/30.85 apply (zenon_L461_); trivial. % 30.80/30.85 apply (zenon_L2641_); trivial. % 30.80/30.85 apply (zenon_L2643_); trivial. % 30.80/30.85 apply (zenon_L2656_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H420); [ zenon_intro zenon_H424 | zenon_intro zenon_H423 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H424). zenon_intro zenon_H8a. zenon_intro zenon_H425. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H425). zenon_intro zenon_H122. zenon_intro zenon_H386. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H386). zenon_intro zenon_H142. zenon_intro zenon_H2ed. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_L1243_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H84 | zenon_intro zenon_H1e ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H18f | zenon_intro zenon_Hd2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2b4); [ zenon_intro zenon_H185 | zenon_intro zenon_H2b5 ]. % 30.80/30.85 apply (zenon_L2702_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H14f | zenon_intro zenon_H2b6 ]. % 30.80/30.85 apply (zenon_L913_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H1e1 | zenon_intro zenon_Hb1 ]. % 30.80/30.85 apply (zenon_L296_); trivial. % 30.80/30.85 exact (zenon_H122 zenon_Hb1). % 30.80/30.85 apply (zenon_L862_); trivial. % 30.80/30.85 apply (zenon_L2686_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.85 apply (zenon_L1209_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.85 apply (zenon_L2703_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.85 exact (zenon_H2ed zenon_Hc9). % 30.80/30.85 apply (zenon_L50_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 apply (zenon_L2675_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L2676_); trivial. % 30.80/30.85 apply (zenon_L1217_); trivial. % 30.80/30.85 apply (zenon_L862_); trivial. % 30.80/30.85 apply (zenon_L2675_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_L1248_); trivial. % 30.80/30.85 apply (zenon_L2656_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H423); [ zenon_intro zenon_H427 | zenon_intro zenon_H426 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H427). zenon_intro zenon_H8a. zenon_intro zenon_H428. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H428). zenon_intro zenon_H122. zenon_intro zenon_H38a. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H38a). zenon_intro zenon_Hb1. zenon_intro zenon_H2fb. % 30.80/30.85 exact (zenon_H2fb zenon_H8a). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H426); [ zenon_intro zenon_H42a | zenon_intro zenon_H429 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H42a). zenon_intro zenon_H40. zenon_intro zenon_H42b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H42b). zenon_intro zenon_H1ab. zenon_intro zenon_H38e. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H38e). zenon_intro zenon_H88. zenon_intro zenon_H317. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H64 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 exact (zenon_H1b3 zenon_H64). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 exact (zenon_H317 zenon_H1e). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L2704_); trivial. % 30.80/30.85 apply (zenon_L2705_); trivial. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.85 apply (zenon_L2318_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1af. zenon_intro zenon_H299. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hcc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 exact (zenon_H317 zenon_H1e). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L2713_); trivial. % 30.80/30.85 apply (zenon_L2714_); trivial. % 30.80/30.85 apply (zenon_L1806_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H231 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.85 apply (zenon_L912_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.85 exact (zenon_H317 zenon_H1e). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.85 apply (zenon_L2716_); trivial. % 30.80/30.85 apply (zenon_L2714_); trivial. % 30.80/30.85 apply (zenon_L1806_); trivial. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.80/30.85 apply (zenon_L2717_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.80/30.85 apply (zenon_L2718_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.80/30.85 apply (zenon_L2719_); trivial. % 30.80/30.85 apply (zenon_L1806_); trivial. % 30.80/30.85 apply (zenon_L753_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H429); [ zenon_intro zenon_H42d | zenon_intro zenon_H42c ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H42d). zenon_intro zenon_H40. zenon_intro zenon_H42e. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H42e). zenon_intro zenon_H1ab. zenon_intro zenon_H392. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_Hd2. zenon_intro zenon_H18f. % 30.80/30.85 exact (zenon_H18f zenon_Hd2). % 30.80/30.85 apply (zenon_or_s _ _ zenon_H42c); [ zenon_intro zenon_H430 | zenon_intro zenon_H42f ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H430). zenon_intro zenon_H40. zenon_intro zenon_H431. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H431). zenon_intro zenon_H1ab. zenon_intro zenon_H396. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H396). zenon_intro zenon_H25. zenon_intro zenon_H46. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.80/30.85 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.85 apply (zenon_L2739_); trivial. % 30.80/30.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.85 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.86 apply (zenon_L1035_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.86 apply (zenon_L2740_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.86 apply (zenon_L17_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H73 | zenon_intro zenon_He5 ]. % 30.80/30.86 apply (zenon_L2720_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hdc | zenon_intro zenon_He6 ]. % 30.80/30.86 apply (zenon_L2723_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hc9 | zenon_intro zenon_He2 ]. % 30.80/30.86 apply (zenon_L2744_); trivial. % 30.80/30.86 apply (zenon_L386_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.86 apply (zenon_L3_); trivial. % 30.80/30.86 apply (zenon_L8_); trivial. % 30.80/30.86 apply (zenon_L862_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.86 apply (zenon_L10_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.86 apply (zenon_L13_); trivial. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Ha3. zenon_intro zenon_H273. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H9b. zenon_intro zenon_H274. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_Hb3. zenon_intro zenon_H275. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbc ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H1fd); [ zenon_intro zenon_H117 | zenon_intro zenon_H1fe ]. % 30.80/30.86 apply (zenon_L2717_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H15e | zenon_intro zenon_H1ff ]. % 30.80/30.86 apply (zenon_L2718_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H1b9 | zenon_intro zenon_Hb6 ]. % 30.80/30.86 apply (zenon_L1138_); trivial. % 30.80/30.86 apply (zenon_L1806_); trivial. % 30.80/30.86 apply (zenon_L753_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H42f); [ zenon_intro zenon_H433 | zenon_intro zenon_H432 ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H433). zenon_intro zenon_H40. zenon_intro zenon_H434. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H434). zenon_intro zenon_H1ab. zenon_intro zenon_H39c. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H39c). zenon_intro zenon_H112. zenon_intro zenon_H18e. % 30.80/30.86 exact (zenon_H18e zenon_H40). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H432); [ zenon_intro zenon_H436 | zenon_intro zenon_H435 ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H436). zenon_intro zenon_Hb6. zenon_intro zenon_H437. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H437). zenon_intro zenon_H231. zenon_intro zenon_H3a0. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H3a0). zenon_intro zenon_H73. zenon_intro zenon_H304. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.80/30.86 apply (zenon_L52_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.80/30.86 apply (zenon_L1441_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.80/30.86 apply (zenon_L204_); trivial. % 30.80/30.86 exact (zenon_H231 zenon_Hf4). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H1ab | zenon_intro zenon_H40 ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.86 apply (zenon_L1209_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.86 apply (zenon_L2748_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.86 exact (zenon_H304 zenon_H10e). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H11c ]. % 30.80/30.86 apply (zenon_L869_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H112 | zenon_intro zenon_H11d ]. % 30.80/30.86 exact (zenon_H1ab zenon_H112). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hbc ]. % 30.80/30.86 exact (zenon_H231 zenon_Hf4). % 30.80/30.86 apply (zenon_L1303_); trivial. % 30.80/30.86 apply (zenon_L1806_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.86 apply (zenon_L1485_); trivial. % 30.80/30.86 apply (zenon_L2749_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H435); [ zenon_intro zenon_H439 | zenon_intro zenon_H438 ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H439). zenon_intro zenon_Hb6. zenon_intro zenon_H43a. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H43a). zenon_intro zenon_H231. zenon_intro zenon_H3a4. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H3a4). zenon_intro zenon_Hfd. zenon_intro zenon_H28c. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H2ec | zenon_intro zenon_H397 ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2d6. zenon_intro zenon_H2ee. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H188. zenon_intro zenon_H2ef. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H198. zenon_intro zenon_H2f0. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H36. zenon_intro zenon_H2f1. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H64 ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H64 | zenon_intro zenon_H302 ]. % 30.80/30.86 exact (zenon_H1b3 zenon_H64). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H1e | zenon_intro zenon_H303 ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.80/30.86 apply (zenon_L2750_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.80/30.86 apply (zenon_L1134_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.80/30.86 apply (zenon_L304_); trivial. % 30.80/30.86 exact (zenon_H122 zenon_Hb1). % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H88 | zenon_intro zenon_H93 ]. % 30.80/30.86 apply (zenon_L1035_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H68 | zenon_intro zenon_H94 ]. % 30.80/30.86 apply (zenon_L119_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 30.80/30.86 apply (zenon_L2751_); trivial. % 30.80/30.86 apply (zenon_L2752_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.86 apply (zenon_L2024_); trivial. % 30.80/30.86 apply (zenon_L2754_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H10e | zenon_intro zenon_H185 ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.80/30.86 apply (zenon_L727_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.80/30.86 apply (zenon_L60_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.80/30.86 apply (zenon_L204_); trivial. % 30.80/30.86 exact (zenon_H231 zenon_Hf4). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H89 | zenon_intro zenon_H175 ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.80/30.86 apply (zenon_L2755_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.80/30.86 apply (zenon_L60_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.80/30.86 apply (zenon_L204_); trivial. % 30.80/30.86 exact (zenon_H231 zenon_Hf4). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H2c | zenon_intro zenon_H176 ]. % 30.80/30.86 apply (zenon_L2753_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H117 | zenon_intro zenon_H16b ]. % 30.80/30.86 apply (zenon_L151_); trivial. % 30.80/30.86 apply (zenon_L2756_); trivial. % 30.80/30.86 apply (zenon_L461_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H122 | zenon_intro zenon_H8a ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H88 | zenon_intro zenon_Hc1 ]. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H8b | zenon_intro zenon_Hbe ]. % 30.80/30.86 apply (zenon_L2041_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H95 | zenon_intro zenon_Hbf ]. % 30.80/30.86 apply (zenon_L1134_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb1 ]. % 30.80/30.86 apply (zenon_L304_); trivial. % 30.80/30.86 exact (zenon_H122 zenon_Hb1). % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H1f | zenon_intro zenon_Hc2 ]. % 30.80/30.86 apply (zenon_L2759_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H26 | zenon_intro zenon_H33 ]. % 30.80/30.86 apply (zenon_L2024_); trivial. % 30.80/30.86 apply (zenon_L2754_); trivial. % 30.80/30.86 apply (zenon_L461_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H397); [ zenon_intro zenon_H45 | zenon_intro zenon_H398 ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_He2 | zenon_intro zenon_Hfa ]. % 30.80/30.86 apply (zenon_L2760_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfb ]. % 30.80/30.86 apply (zenon_L60_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Heb | zenon_intro zenon_Hf4 ]. % 30.80/30.86 apply (zenon_L204_); trivial. % 30.80/30.86 exact (zenon_H231 zenon_Hf4). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H398); [ zenon_intro zenon_H5a | zenon_intro zenon_H270 ]. % 30.80/30.86 apply (zenon_L791_); trivial. % 30.80/30.86 apply (zenon_L2749_); trivial. % 30.80/30.86 apply (zenon_or_s _ _ zenon_H438); [ zenon_intro zenon_H43c | zenon_intro zenon_H43b ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H43c). zenon_intro zenon_Hb6. zenon_intro zenon_H43d. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H43d). zenon_intro zenon_H231. zenon_intro zenon_H3a8. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H3a8). zenon_intro zenon_Hcc. zenon_intro zenon_Hd0. % 30.80/30.86 exact (zenon_Hd0 zenon_Hcc). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H43b); [ zenon_intro zenon_H43f | zenon_intro zenon_H43e ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H43f). zenon_intro zenon_Hb6. zenon_intro zenon_H440. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H440). zenon_intro zenon_H231. zenon_intro zenon_H3ac. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H3ac). zenon_intro zenon_Hf4. zenon_intro zenon_H2a9. % 30.80/30.86 exact (zenon_H2a9 zenon_Hb6). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H43e); [ zenon_intro zenon_H442 | zenon_intro zenon_H441 ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H442). zenon_intro zenon_Hbc. zenon_intro zenon_H443. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H443). zenon_intro zenon_Hb9. zenon_intro zenon_H3b0. % 30.80/30.86 exact (zenon_Hb9 zenon_Hbc). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H441); [ zenon_intro zenon_H445 | zenon_intro zenon_H444 ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H445). zenon_intro zenon_Hbc. zenon_intro zenon_H446. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H446). zenon_intro zenon_Hb9. zenon_intro zenon_H3b4. % 30.80/30.86 exact (zenon_Hb9 zenon_Hbc). % 30.80/30.86 apply (zenon_or_s _ _ zenon_H444); [ zenon_intro zenon_H448 | zenon_intro zenon_H447 ]. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H448). zenon_intro zenon_Hbc. zenon_intro zenon_H449. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H449). zenon_intro zenon_Hb9. zenon_intro zenon_H3b8. % 30.80/30.86 exact (zenon_Hb9 zenon_Hbc). % 30.80/30.86 apply (zenon_and_s _ _ zenon_H447). zenon_intro zenon_Hbc. zenon_intro zenon_H44a. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H44a). zenon_intro zenon_Hb9. zenon_intro zenon_H3bc. % 30.80/30.86 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_Hbc. zenon_intro zenon_Hb9. % 30.80/30.86 exact (zenon_Hb9 zenon_Hbc). % 30.80/30.86 Qed. % 30.80/30.86 % SZS output end Proof % 30.80/30.86 (* END-PROOF *) % 30.80/30.86 nodes searched: 316985 % 30.80/30.86 max branch formulas: 361 % 30.80/30.86 proof nodes created: 30438 % 30.80/30.86 formulas created: 151766 % 30.80/30.86 %------------------------------------------------------------------------------